An Estimator Based Inverse Dynamics Controller (EBIDC), which utilizes an Artificial Neural Network (ANN) based state estimation scheme for nonlinear autonomous hybrid systems which are subjected to state disturbances and measurement noises that are stochastic in nature, is proposed in this paper. A salient feature of the proposed scheme is that it offers better state estimates and hence a better control of non-measurable state variables with a non linear approach in correcting the a priori estimates by avoiding statistical linearization involved in existing approaches based on derivative free estimation methods. Simulation results guarantees significant reduction in Integral Square Error (ISE) and standard deviation (σ) of error, between the controlled variable and set point and control signal computation time when compared with best existing related work based on Unscented Kalman Filter (UKF) and Ensembeled Kalman Filter (EnKF). Detailed analysis of the experimental results on real plant under different operating conditions such as servo and regulatory operations, initial condition mismatch, and different types of faults in the system, confirms robustness of proposed approach in these conditions and support the simulation results obtained. The main advantage of the proposed controller is that the control signal computation time is very much less than the selected sampling time of the process, so direct control of the plant is possible with this approach.
State Estimation based Inverse Dynamic Controller for Hybrid system using Art...XiaoLaui
Authors have proposed State Estimation Based Inverse Dynamics Controller (SEBIDC), which utilizes an Artificial Neural Network (ANN) based state estimation scheme for nonlinear autonomous hybrid systems which are subjected to state disturbances and measurement noises that are stochastic in nature. A salient feature of the proposed scheme is that it offers better state estimates and hence a better control of non-measurable state variables with a non linear approach in correcting the a priori estimates by avoiding statistical linearization involved in existing approaches based on derivative free estimation methods. Simulation results guarantees significant reduction in Integral Square Error (ISE) and standard deviation (σ) of error, between the controlled variable and set point and control signal computation time when compared with best existing related work based on Unscented Kalman Filter (UKF) and Ensemble Kalman Filter (EnKF). Detailed analysis of the experimental results on real plant under different operating conditions such as servo and regulatory operations, initial condition mismatch, and different types of faults in the system, confirms robustness of proposed approach in these conditions and support the simulation results obtained. The main advantage of the proposed controller is that the control signal computation time is very much less than the selected sampling time of the process, so direct control of the plant is possible with this approach.
Event triggered control design of linear networked systems with quantizationsISA Interchange
This paper is concerned with the control design problem of event-triggered networked systems with both state and control input quantizations. Firstly, an innovative delay system model is proposed that describes the network conditions, state and control input quantizations, and event-triggering mechanism in a unified framework. Secondly, based on this model, the criteria for the asymptotical stability analysis and control synthesis of event-triggered networked control systems are established in terms of linear matrix inequalities (LMIs). Simulation results are given to illustrate the effectiveness of the proposed method.
Tracy–Widom distribution based fault detection approach: Application to aircr...ISA Interchange
The fault detection approach based on the Tracy–Widom distribution is presented and applied to the aircraft flight control system. An operative method of testing the innovation covariance of the Kalman filter is proposed. The maximal eigenvalue of the random Wishart matrix is used as the monitoring statistic, and the testing problem is reduced to determine the asymptotics for the largest eigenvalue of the Wishart matrix. As a result, an algorithm for testing the innovation covariance based on the Tracy–Widom distribution is proposed. In the simulations, the longitudinal and lateral dynamics of the F-16 aircraft model is considered, and detection of sensor and control surface faults in the flight control system which affect the innovation covariance, are examined.
Data-driven adaptive predictive control for an activated sludge processjournalBEEI
Data-driven control requires no information of the mathematical model of the controlled process. This paper proposes the direct identification of controller parameters of activated sludge process. This class of data-driven control calculates the predictive controller parameters directly using subspace identification technique. By updating input-output data using receding window mechanism, the adaptive strategy can be achieved. The robustness test and stability analysis of direct adaptive model predictive control are discussed to realize the effectiveness of this adaptive control scheme. The applicability of the controller algorithm to adapt into varying kinetic parameters and operating conditions is evaluated. Simulation results show that by a proper and effective excitation of direct identification of controller parameters, the convergence and stability of the implicit predictive model can be achieved.
Comparative Study on the Performance of A Coherency-based Simple Dynamic Equi...IJAPEJOURNAL
Earlier, a simple dynamic equivalent for a power system external area containing a group of coherent generators was proposed in the literature. This equivalent is based on a new concept of decomposition of generators and a two-level generator aggregation. With the knowledge of only the passive network model of the external area and the total inertia constant of all the generators in this area, the parameters of this equivalent are determinable from a set of measurement data taken solely at a set of boundary buses which separates this area from the rest of the system. The proposed equivalent, therefore, does not require any measurement data at the external area generators. This is an important feature of this equivalent. In this paper, the results of a comparative study on the performance of this dynamic equivalent aggregation with the new inertial aggregation in terms of accuracy are presented. The three test systems that were considered in this comparative investigation are the New England 39-bus 10-generator system, the IEEE 162-bus 17-generator system and the IEEE 145-bus 50-generator system.
Presented in this short document is a description of our three separate techniques to analyze the data by checking, clustering and componentizing it before it is used by other IMPL’s routines especially in on-line/real-time decision-making applications. We also have other data consistency or analysis techniques which have been described in other IMPL documents and these relate to the application of data reconciliation and regression with diagnostics but require an explicit model (model-based) whereas the techniques below do not i.e., they are data-based techniques.
A portable hardware in-the-loop device for automotive diagnostic control systemsISA Interchange
In-vehicle driving tests for evaluating the performance and diagnostic functionalities of engine control systems are often time consuming, expensive, and not reproducible. Using a hardware-in-the-loop (HIL) simulation approach, new control strategies and diagnostic functions on a controller area network (CAN) line can be easily tested in real time, in order to reduce the effort and the cost of the testing phase. Nowadays, spark ignition engines are controlled by an electronic control unit (ECU) with a large number of embedded sensors and actuators. In order to meet the rising demand of lower emissions and fuel consumption, an increasing number of control functions are added into such a unit. This work aims at presenting a portable electronic environment system, suited for HIL simulations, in order to test the engine control software and the diagnostic functionality on a CAN line, respectively, through non-regression and diagnostic tests. The performances of the proposed electronic device, called a micro hardware-in-the-loop system, are presented through the testing of the engine management system software of a 1.6 l Fiat gasoline engine with variable valve actuation for the ECU development version.
Modern Tools for the Small-Signal Stability Analysis and Design of FACTS Assi...Power System Operation
There has recently been an intense development of eigenanalysis tools for power systems dynamics and control. This paper provides an up-to-date review of the major algorithms available. Comments on other relevant but yet unpublished algorithms are also made.
The conventional state-space description is obtained through the elimination of the algebraic variables of the mathematical model. In many applications, the power system case included, the algebraic variables in the model are usually more numerous than the state variables.
The problem of multiple, decentralized controller synthesis in large, FACTS assisted power systems is addressed.
A report in CIGRE [1] recognized the large benefits of working with the unreduced set of differential-algebraic equations linearized at an operating point. The resulting power system Jacobian is large and highly sparse, allowing efficient use of sparsity oriented programming. The computation of all system eigenvalues, not practical for large power systems, was since then replaced by the computation of only the eigenvalues of interest.
A good part of the paper is dedicated to showing the high productivity gains achieved when using a well designed package for graphical display and animation of results.
The pressing needs for better utilization of existing transmission and generation equipment will eventually dictate a wider use of FACTS devices. The higher complexity and stricter requirements on power system controls, under both steady-state and dynamic conditions, calls for the immediate development and use of more sophisticated computer tools. The material in this paper may help the further development of one of these tools.
Many important developments occurred in the last fifteen
State Estimation based Inverse Dynamic Controller for Hybrid system using Art...XiaoLaui
Authors have proposed State Estimation Based Inverse Dynamics Controller (SEBIDC), which utilizes an Artificial Neural Network (ANN) based state estimation scheme for nonlinear autonomous hybrid systems which are subjected to state disturbances and measurement noises that are stochastic in nature. A salient feature of the proposed scheme is that it offers better state estimates and hence a better control of non-measurable state variables with a non linear approach in correcting the a priori estimates by avoiding statistical linearization involved in existing approaches based on derivative free estimation methods. Simulation results guarantees significant reduction in Integral Square Error (ISE) and standard deviation (σ) of error, between the controlled variable and set point and control signal computation time when compared with best existing related work based on Unscented Kalman Filter (UKF) and Ensemble Kalman Filter (EnKF). Detailed analysis of the experimental results on real plant under different operating conditions such as servo and regulatory operations, initial condition mismatch, and different types of faults in the system, confirms robustness of proposed approach in these conditions and support the simulation results obtained. The main advantage of the proposed controller is that the control signal computation time is very much less than the selected sampling time of the process, so direct control of the plant is possible with this approach.
Event triggered control design of linear networked systems with quantizationsISA Interchange
This paper is concerned with the control design problem of event-triggered networked systems with both state and control input quantizations. Firstly, an innovative delay system model is proposed that describes the network conditions, state and control input quantizations, and event-triggering mechanism in a unified framework. Secondly, based on this model, the criteria for the asymptotical stability analysis and control synthesis of event-triggered networked control systems are established in terms of linear matrix inequalities (LMIs). Simulation results are given to illustrate the effectiveness of the proposed method.
Tracy–Widom distribution based fault detection approach: Application to aircr...ISA Interchange
The fault detection approach based on the Tracy–Widom distribution is presented and applied to the aircraft flight control system. An operative method of testing the innovation covariance of the Kalman filter is proposed. The maximal eigenvalue of the random Wishart matrix is used as the monitoring statistic, and the testing problem is reduced to determine the asymptotics for the largest eigenvalue of the Wishart matrix. As a result, an algorithm for testing the innovation covariance based on the Tracy–Widom distribution is proposed. In the simulations, the longitudinal and lateral dynamics of the F-16 aircraft model is considered, and detection of sensor and control surface faults in the flight control system which affect the innovation covariance, are examined.
Data-driven adaptive predictive control for an activated sludge processjournalBEEI
Data-driven control requires no information of the mathematical model of the controlled process. This paper proposes the direct identification of controller parameters of activated sludge process. This class of data-driven control calculates the predictive controller parameters directly using subspace identification technique. By updating input-output data using receding window mechanism, the adaptive strategy can be achieved. The robustness test and stability analysis of direct adaptive model predictive control are discussed to realize the effectiveness of this adaptive control scheme. The applicability of the controller algorithm to adapt into varying kinetic parameters and operating conditions is evaluated. Simulation results show that by a proper and effective excitation of direct identification of controller parameters, the convergence and stability of the implicit predictive model can be achieved.
Comparative Study on the Performance of A Coherency-based Simple Dynamic Equi...IJAPEJOURNAL
Earlier, a simple dynamic equivalent for a power system external area containing a group of coherent generators was proposed in the literature. This equivalent is based on a new concept of decomposition of generators and a two-level generator aggregation. With the knowledge of only the passive network model of the external area and the total inertia constant of all the generators in this area, the parameters of this equivalent are determinable from a set of measurement data taken solely at a set of boundary buses which separates this area from the rest of the system. The proposed equivalent, therefore, does not require any measurement data at the external area generators. This is an important feature of this equivalent. In this paper, the results of a comparative study on the performance of this dynamic equivalent aggregation with the new inertial aggregation in terms of accuracy are presented. The three test systems that were considered in this comparative investigation are the New England 39-bus 10-generator system, the IEEE 162-bus 17-generator system and the IEEE 145-bus 50-generator system.
Presented in this short document is a description of our three separate techniques to analyze the data by checking, clustering and componentizing it before it is used by other IMPL’s routines especially in on-line/real-time decision-making applications. We also have other data consistency or analysis techniques which have been described in other IMPL documents and these relate to the application of data reconciliation and regression with diagnostics but require an explicit model (model-based) whereas the techniques below do not i.e., they are data-based techniques.
A portable hardware in-the-loop device for automotive diagnostic control systemsISA Interchange
In-vehicle driving tests for evaluating the performance and diagnostic functionalities of engine control systems are often time consuming, expensive, and not reproducible. Using a hardware-in-the-loop (HIL) simulation approach, new control strategies and diagnostic functions on a controller area network (CAN) line can be easily tested in real time, in order to reduce the effort and the cost of the testing phase. Nowadays, spark ignition engines are controlled by an electronic control unit (ECU) with a large number of embedded sensors and actuators. In order to meet the rising demand of lower emissions and fuel consumption, an increasing number of control functions are added into such a unit. This work aims at presenting a portable electronic environment system, suited for HIL simulations, in order to test the engine control software and the diagnostic functionality on a CAN line, respectively, through non-regression and diagnostic tests. The performances of the proposed electronic device, called a micro hardware-in-the-loop system, are presented through the testing of the engine management system software of a 1.6 l Fiat gasoline engine with variable valve actuation for the ECU development version.
Modern Tools for the Small-Signal Stability Analysis and Design of FACTS Assi...Power System Operation
There has recently been an intense development of eigenanalysis tools for power systems dynamics and control. This paper provides an up-to-date review of the major algorithms available. Comments on other relevant but yet unpublished algorithms are also made.
The conventional state-space description is obtained through the elimination of the algebraic variables of the mathematical model. In many applications, the power system case included, the algebraic variables in the model are usually more numerous than the state variables.
The problem of multiple, decentralized controller synthesis in large, FACTS assisted power systems is addressed.
A report in CIGRE [1] recognized the large benefits of working with the unreduced set of differential-algebraic equations linearized at an operating point. The resulting power system Jacobian is large and highly sparse, allowing efficient use of sparsity oriented programming. The computation of all system eigenvalues, not practical for large power systems, was since then replaced by the computation of only the eigenvalues of interest.
A good part of the paper is dedicated to showing the high productivity gains achieved when using a well designed package for graphical display and animation of results.
The pressing needs for better utilization of existing transmission and generation equipment will eventually dictate a wider use of FACTS devices. The higher complexity and stricter requirements on power system controls, under both steady-state and dynamic conditions, calls for the immediate development and use of more sophisticated computer tools. The material in this paper may help the further development of one of these tools.
Many important developments occurred in the last fifteen
PI and fuzzy logic controllers for shunt active power filterISA Interchange
This paper presents a shunt Active Power Filter (APF) for power quality improvements in terms of harmonics and reactive power compensation in the distribution network. The compensation process is based only on source current extraction that reduces the number of sensors as well as its complexity. A Proportional Integral (PI) or Fuzzy Logic Controller (FLC) is used to extract the required reference current from the distorted line-current, and this controls the DC-side capacitor voltage of the inverter. The shunt APF is implemented with PWM-current controlled Voltage Source Inverter (VSI) and the switching patterns are generated through a novel Adaptive-Fuzzy Hysteresis Current Controller (A-F-HCC). The proposed adaptive-fuzzy-HCC is compared with fixed-HCC and adaptive-HCC techniques and the superior features of this novel approach are established. The FLC based shunt APF system is validated through extensive simulation for diode-rectifier/R–L loads.
SYSTEM IDENTIFICATION AND MODELING FOR INTERACTING AND NON-INTERACTING TANK S...ijistjournal
System identification from the experimental data plays a vital role for model based controller design. Derivation of process model from first principles is often difficult due to its complexity. The first stage in the development of any control and monitoring system is the identification and modeling of the system. Each model is developed within the context of a specific control problem. Thus, the need for a general system identification framework is warranted. The proposed framework should be able to adapt and emphasize different properties based on the control objective and the nature of the behavior of the system. Therefore, system identification has been a valuable tool in identifying the model of the system based on the input and output data for the design of the controller. The present work is concerned with the identification of transfer function models using statistical model identification, process reaction curve method, ARX model, genetic algorithm and modeling using neural network and fuzzy logic for interacting and non interacting tank process. The identification technique and modeling used is prone to parameter change & disturbance. The proposed methods are used for identifying the mathematical model and intelligent model of interacting and non interacting process from the real time experimental data.
Compensation of Data-Loss in Attitude Control of Spacecraft Systems rinzindorjej
In this paper, a comprehensive comparison of two robust estimation techniques namely, compensated closed-loop Kalman filtering and open-loop Kalman filtering is presented. A common problem of data loss in a real-time control system is investigated through these two schemes. The open-loop scheme, dealing with the data-loss, suffers from several shortcomings. These shortcomings are overcome using compensated scheme, where an accommodating observation signal is obtained through linear prediction technique -- a closed-loop setting and is adopted at a posteriori update step. The calculation and employment of accommodating observation signal causes computational complexity. For simulation purpose, a linear time invariant spacecraft model is however, obtained from the nonlinear spacecraft attitude dynamics through linearization at nonzero equilibrium points -- achieved off-line through Levenberg-Marguardt iterative scheme. Attempt has been made to analyze the selected example from most of the perspectives in order to display the performance of the two techniques.
Decentralized supervisory based switching control for uncertain multivariable...ISA Interchange
In this paper, the design of decentralized switching control for uncertain multivariable plants is considered. In the proposed strategy, the uncertainty region is divided into smaller regions with a nominal model and specific control structure. The underlying design is based on the quantitative feedback theory (QFT). It is assumed that a MIMO-QFT controller exists for robust stability and performance of the individual uncertain sets. The proposed control structure is made up by these local decentralized controllers, which commute among themselves in accordance with the decision of a high level decision maker called the supervisor. The supervisor makes the decision by comparing the local models’ behaviors with the one of the plant and selects the controller corresponding to the best fitted model. A hysteresis switching logic is used to slow down the switching to guarantee the overall closed loop stability. It is shown that this strategy provides a stable and robust adaptive controller to deal with complex multivariable plants with input–output pairing changes during the plant operation, which can facilitate the development of a reconfigurable decentralized control. Also, the multirealization technique is used to implement a family of controllers to achieve bumpless transfer. Simulation results are employed to show the effectiveness of the proposed method.
Analytical Evaluation of Generalized Predictive Control Algorithms Using a Fu...inventy
Research Inventy : International Journal of Engineering and Science is published by the group of young academic and industrial researchers with 12 Issues per year. It is an online as well as print version open access journal that provides rapid publication (monthly) of articles in all areas of the subject such as: civil, mechanical, chemical, electronic and computer engineering as well as production and information technology. The Journal welcomes the submission of manuscripts that meet the general criteria of significance and scientific excellence. Papers will be published by rapid process within 20 days after acceptance and peer review process takes only 7 days. All articles published in Research Inventy will be peer-reviewed.
Controlling a DC Motor through Lypaunov-like Functions and SAB TechniqueIJECEIAES
In this paper, state adaptive backstepping and Lyapunov-like function methods are used to design a robust adaptive controller for a DC motor. The output to be controlled is the motor speed. It is assumed that the load torque and inertia moment exhibit unknown but bounded time-varying behavior, and that the measurement of the motor speed and motor current are corrupted by noise. The controller is implemented in a Rapid Control Prototyping system based on Digital Signal Processing for dSPACE platform and experimental results agree with theory.
Neural Network-Based Actuator Fault Diagnosis for a Non-Linear Multi-Tank SystemISA Interchange
The paper is devoted to the problem of the robust actuator fault diagnosis of the dynamic non-linear systems. In the proposed method, it is assumed that the diagnosed system can be modelled by the recurrent neural network, which can be transformed into the linear parameter varying form. Such a system description allows developing the designing scheme of the robust unknown input observer within H1 framework for a class of non-linear systems. The proposed approach is designed in such a way that a prescribed disturbance attenuation level is achieved with respect to the actuator fault estimation error, while guaranteeing the convergence of the observer. The application of the robust unknown input observer enables actuator fault estimation, which allows applying the developed approach to the fault tolerant control tasks.
Overview of State Estimation Technique for Power System ControlIOSR Journals
This document provides an overview of state estimation techniques for power system control. It discusses static, tracking, and dynamic state estimation approaches and how they differ based on whether measurements and system models are time-variant or invariant. The document also describes how state estimation processes redundant measurements to filter noise and estimate true system states like voltage magnitudes and angles at each bus. It further discusses weighted least squares estimation, the use of Jacobian matrices to iteratively estimate states, and how state estimation provides critical real-time data for power system monitoring and control functions.
A novel nonlinear missile guidance law against maneuvering targets is designed based on the principles of partial stability. It is demonstrated that in a real approach which is adopted with actual situations, each state of the guidance system must have a special behavior and asymptotic stability or exponential stability of all states is not realistic. Thus, a new guidance law is developed based on the partial stability theorem in such a way that the behaviors of states in the closed-loop system are in conformity with a real guidance scenario that leads to collision. The performance of the proposed guidance law in terms of interception time and control effort is compared with the sliding mode guidance law by means of numerical simulations.
Refining Underwater Target Localization and Tracking EstimatesCSCJournals
Improving the accuracy and reliability of the localization estimates and tracking of underwater targets is a constant quest in ocean surveillance operations. The localization estimates may vary owing to various noises and interferences such as sensor errors and environmental noises. Even though adaptive filters like the Kalman filter subdue these problems and yield dependable results, targets that undergo maneuvering can cause incomprehensible errors, unless suitable corrective measures are implemented. Simulation studies on improving the localization and tracking estimates for a stationary target as well as a moving target including the maneuvering situations are presented in this paper
DESIGN OF OBSERVER BASED QUASI DECENTRALIZED FUZZY LOAD FREQUENCY CONTROLLER ...ijfls
This paper proposes Fuzzy Quasi Decentralized Functional Observers (FQDFO) for Load Frequency Control of inter-connected power systems. From the literature, it is well noticed about the need of
Functional Observers (FO’s) for power system applications. In past, conventional Functional Observers are used. Later, these conventional Functional Observers are replaced with Quasi Decentralized
Functional Observers (QDFO) to improve the system performance. In order to increase the efficacy of the
system, intelligent controllers gained importance. Due to their expertise knowledge, which is adaptive in
nature is applied successfully for FQDFO. For supporting the validity of the proposed observer FQDFO,
it is compared with full order Luenberger observer and QDFO for a two-area inter connected power system by taking parametric uncertainties into consideration. Computational results proved the robustness of the proposed observer.
Multiple Constraints Consideration in Power System State EstimationIOSR Journals
This document discusses a novel algorithm developed to consider multiple constraints in power system state estimation using weighted least squares. The algorithm detects missing measurement data, identifies and eliminates bad data, and evaluates network observability. It also considers measurement uncertainties from phasor measurement units. The algorithm is tested on the IEEE 14 bus system and is able to identify bad data, estimate missing data values, and determine observability while incorporating measurement uncertainties.
Flatness Based Nonlinear Sensorless Control of Induction Motor SystemsIAES-IJPEDS
This paper deals with the flatness-based approach for sensorless control of
the induction motor systems. Two main features of the proposed flatness
based control are worth to be mentioned. Firstly, the simplicity of
implementation of the flatness approach as a nonlinear feedback linearization
control technique. Secondly, when the chosen flat outputs involve non
available state variable measurements a nonlinear observer is used to
estimate them. The main advantage of the used observer is its ability to
exploite the properties of the system nonlinearties. The simulation results are
presented to illustrate the effectiness of the proposed approach for sensorless
control of the considered induction motor.
This document discusses state estimation in power systems. It begins by defining state estimation as assigning values to unknown system state variables based on measurements according to some criteria. It then discusses that the most commonly used criterion is the weighted least squares method. It provides an example of using measurements to estimate voltage angles as state variables and calculate other power flows. Finally, it discusses the weighted least squares state estimation technique in detail including developing the measurement function matrix and solving the weighted least squares optimization.
Trajectory Control With MPC For A Robot Manipülatör Using ANN ModelIJMER
In this study, in a computer the dynamic motion modelling of manipulator and control of
trajectory with an algorithm this has been tested. First after dynamic motion simulation of manipulator
has been made MPC Control. The result in this study we can observe that computed torque method gives
better results than MPC methods. So in trajectory control it is approved of using computed torque
method. In last part of this study the results are estimated forward development are exemined and
suggested. The model predictive control (MPC) technique for an articulated robot with n joints is
introduced in this paper. The proposed MPC control action is conceptually different with the trajectory
robot control methods in that the control action is determined by optimising a performance index over
the time horizon. A neural network (NN) is used in this paper as the predictive model.
Performance analysis of a liquid column in a chemical plant by using mpceSAT Publishing House
This document discusses the use of model predictive control (MPC) to control the composition of a liquid column in a chemical plant. It provides background on MPC and how it can be used for multivariable processes like liquid columns. The document describes modeling a liquid column process in MATLAB Simulink and comparing the performance of MPC and PID control of the column. The results show that MPC provides better control of the column composition and liquid level than PID control.
Design of a Controller for Systems with Simultaneously Variable Parametersijtsrd
The contribution of this paper is in suggesting an analysis and design of a control system with variable parameters By applying the recommended by the author method of the Advanced D-partitioning the system's stability can be analyzed in details The method defines regions of stability in the space of the system's parameters The designed controller is enforcing desired system performance The suggested technique for analysis and design is essential and beneficial for the further development of control theory in this area Prof. Kamen Yanev "Design of a Controller for Systems with Simultaneously Variable Parameters" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-2 | Issue-6 , October 2018, URL: http://www.ijtsrd.com/papers/ijtsrd18440.pdf
Design of de-coupler for an interacting tanks systemIOSR Journals
This document describes the design of a decoupler for a two-tank interacting system. It first provides background on interacting or coupled multi-input multi-output (MIMO) systems and the goal of decoupling. It then presents the mathematical model and dynamics of the two-tank system. Next, it analyzes the interaction between the two tanks' liquid levels and inlet flow rates. The relative gain array (RGA) method is used to determine appropriate control loop configurations to minimize interaction. Finally, the document derives equations to design decouplers to cancel the effect of one tank's flow rate on the other tank's liquid level, thereby rendering the system as two independent single-input single-output loops. Experimental results
Robust control for a tracking electromechanical systemIJECEIAES
A strategy for the design of robust control of tracking electromechanical systems based on 𝐻∞ synthesis is proposed. Proposed methods are based on the operations on frequency characteristics of control systems designed and developed using the MATLAB robust control toolbox. Determination of the singular values for a transfer matrix of the control system reduces the disturbances and guarantees its stability margin. For selecting the weighted transfer functions, the basic recommendations are formulated. The efficiency of the proposed approach is verified by robust control of an elastically coupled two-mass system whose parameter values are adjusted by matching them with the parameters of one of the supplied robots. The simulation results confirm that the proposed strategy of design of robust control of twomass elastic coupling system using the 𝐻∞ synthesis is very efficient and significantly reduces the perturbation of parameters of the controlled plant.
Recurrent fuzzy neural network backstepping control for the prescribed output...ISA Interchange
This paper proposes a backstepping control system that uses a tracking error constraint and recurrent fuzzy neural networks (RFNNs) to achieve a prescribed tracking performance for a strict-feedback nonlinear dynamic system. A new constraint variable was defined to generate the virtual control that forces the tracking error to fall within prescribed boundaries. An adaptive RFNN was also used to obtain the required improvement on the approximation performances in order to avoid calculating the explosive number of terms generated by the recursive steps of traditional backstepping control. The boundedness and convergence of the closed-loop system was confirmed based on the Lyapunov stability theory. The prescribed performance of the proposed control scheme was validated by using it to control the prescribed error of a nonlinear system and a robot manipulator.
IRJET- Excitation Control of Synchronous Generator using a Fuzzy Logic based ...IRJET Journal
This document presents a fuzzy logic-based backstepping approach for excitation control of synchronous generators. The backstepping control law is designed using control Lyapunov functions to ensure stability. Fuzzy logic is then used to determine the optimal values for three tuning gains in the backstepping control law. Membership functions are defined based on the CLF boundaries. Fuzzy rules are formulated to map error and change in error inputs to tuning gain outputs. Simulation studies on a single machine infinite bus system evaluate the performance of the proposed controller under two fault conditions, and validate that it improves stability compared to traditional controllers with constant gains.
PI and fuzzy logic controllers for shunt active power filterISA Interchange
This paper presents a shunt Active Power Filter (APF) for power quality improvements in terms of harmonics and reactive power compensation in the distribution network. The compensation process is based only on source current extraction that reduces the number of sensors as well as its complexity. A Proportional Integral (PI) or Fuzzy Logic Controller (FLC) is used to extract the required reference current from the distorted line-current, and this controls the DC-side capacitor voltage of the inverter. The shunt APF is implemented with PWM-current controlled Voltage Source Inverter (VSI) and the switching patterns are generated through a novel Adaptive-Fuzzy Hysteresis Current Controller (A-F-HCC). The proposed adaptive-fuzzy-HCC is compared with fixed-HCC and adaptive-HCC techniques and the superior features of this novel approach are established. The FLC based shunt APF system is validated through extensive simulation for diode-rectifier/R–L loads.
SYSTEM IDENTIFICATION AND MODELING FOR INTERACTING AND NON-INTERACTING TANK S...ijistjournal
System identification from the experimental data plays a vital role for model based controller design. Derivation of process model from first principles is often difficult due to its complexity. The first stage in the development of any control and monitoring system is the identification and modeling of the system. Each model is developed within the context of a specific control problem. Thus, the need for a general system identification framework is warranted. The proposed framework should be able to adapt and emphasize different properties based on the control objective and the nature of the behavior of the system. Therefore, system identification has been a valuable tool in identifying the model of the system based on the input and output data for the design of the controller. The present work is concerned with the identification of transfer function models using statistical model identification, process reaction curve method, ARX model, genetic algorithm and modeling using neural network and fuzzy logic for interacting and non interacting tank process. The identification technique and modeling used is prone to parameter change & disturbance. The proposed methods are used for identifying the mathematical model and intelligent model of interacting and non interacting process from the real time experimental data.
Compensation of Data-Loss in Attitude Control of Spacecraft Systems rinzindorjej
In this paper, a comprehensive comparison of two robust estimation techniques namely, compensated closed-loop Kalman filtering and open-loop Kalman filtering is presented. A common problem of data loss in a real-time control system is investigated through these two schemes. The open-loop scheme, dealing with the data-loss, suffers from several shortcomings. These shortcomings are overcome using compensated scheme, where an accommodating observation signal is obtained through linear prediction technique -- a closed-loop setting and is adopted at a posteriori update step. The calculation and employment of accommodating observation signal causes computational complexity. For simulation purpose, a linear time invariant spacecraft model is however, obtained from the nonlinear spacecraft attitude dynamics through linearization at nonzero equilibrium points -- achieved off-line through Levenberg-Marguardt iterative scheme. Attempt has been made to analyze the selected example from most of the perspectives in order to display the performance of the two techniques.
Decentralized supervisory based switching control for uncertain multivariable...ISA Interchange
In this paper, the design of decentralized switching control for uncertain multivariable plants is considered. In the proposed strategy, the uncertainty region is divided into smaller regions with a nominal model and specific control structure. The underlying design is based on the quantitative feedback theory (QFT). It is assumed that a MIMO-QFT controller exists for robust stability and performance of the individual uncertain sets. The proposed control structure is made up by these local decentralized controllers, which commute among themselves in accordance with the decision of a high level decision maker called the supervisor. The supervisor makes the decision by comparing the local models’ behaviors with the one of the plant and selects the controller corresponding to the best fitted model. A hysteresis switching logic is used to slow down the switching to guarantee the overall closed loop stability. It is shown that this strategy provides a stable and robust adaptive controller to deal with complex multivariable plants with input–output pairing changes during the plant operation, which can facilitate the development of a reconfigurable decentralized control. Also, the multirealization technique is used to implement a family of controllers to achieve bumpless transfer. Simulation results are employed to show the effectiveness of the proposed method.
Analytical Evaluation of Generalized Predictive Control Algorithms Using a Fu...inventy
Research Inventy : International Journal of Engineering and Science is published by the group of young academic and industrial researchers with 12 Issues per year. It is an online as well as print version open access journal that provides rapid publication (monthly) of articles in all areas of the subject such as: civil, mechanical, chemical, electronic and computer engineering as well as production and information technology. The Journal welcomes the submission of manuscripts that meet the general criteria of significance and scientific excellence. Papers will be published by rapid process within 20 days after acceptance and peer review process takes only 7 days. All articles published in Research Inventy will be peer-reviewed.
Controlling a DC Motor through Lypaunov-like Functions and SAB TechniqueIJECEIAES
In this paper, state adaptive backstepping and Lyapunov-like function methods are used to design a robust adaptive controller for a DC motor. The output to be controlled is the motor speed. It is assumed that the load torque and inertia moment exhibit unknown but bounded time-varying behavior, and that the measurement of the motor speed and motor current are corrupted by noise. The controller is implemented in a Rapid Control Prototyping system based on Digital Signal Processing for dSPACE platform and experimental results agree with theory.
Neural Network-Based Actuator Fault Diagnosis for a Non-Linear Multi-Tank SystemISA Interchange
The paper is devoted to the problem of the robust actuator fault diagnosis of the dynamic non-linear systems. In the proposed method, it is assumed that the diagnosed system can be modelled by the recurrent neural network, which can be transformed into the linear parameter varying form. Such a system description allows developing the designing scheme of the robust unknown input observer within H1 framework for a class of non-linear systems. The proposed approach is designed in such a way that a prescribed disturbance attenuation level is achieved with respect to the actuator fault estimation error, while guaranteeing the convergence of the observer. The application of the robust unknown input observer enables actuator fault estimation, which allows applying the developed approach to the fault tolerant control tasks.
Overview of State Estimation Technique for Power System ControlIOSR Journals
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A novel nonlinear missile guidance law against maneuvering targets is designed based on the principles of partial stability. It is demonstrated that in a real approach which is adopted with actual situations, each state of the guidance system must have a special behavior and asymptotic stability or exponential stability of all states is not realistic. Thus, a new guidance law is developed based on the partial stability theorem in such a way that the behaviors of states in the closed-loop system are in conformity with a real guidance scenario that leads to collision. The performance of the proposed guidance law in terms of interception time and control effort is compared with the sliding mode guidance law by means of numerical simulations.
Refining Underwater Target Localization and Tracking EstimatesCSCJournals
Improving the accuracy and reliability of the localization estimates and tracking of underwater targets is a constant quest in ocean surveillance operations. The localization estimates may vary owing to various noises and interferences such as sensor errors and environmental noises. Even though adaptive filters like the Kalman filter subdue these problems and yield dependable results, targets that undergo maneuvering can cause incomprehensible errors, unless suitable corrective measures are implemented. Simulation studies on improving the localization and tracking estimates for a stationary target as well as a moving target including the maneuvering situations are presented in this paper
DESIGN OF OBSERVER BASED QUASI DECENTRALIZED FUZZY LOAD FREQUENCY CONTROLLER ...ijfls
This paper proposes Fuzzy Quasi Decentralized Functional Observers (FQDFO) for Load Frequency Control of inter-connected power systems. From the literature, it is well noticed about the need of
Functional Observers (FO’s) for power system applications. In past, conventional Functional Observers are used. Later, these conventional Functional Observers are replaced with Quasi Decentralized
Functional Observers (QDFO) to improve the system performance. In order to increase the efficacy of the
system, intelligent controllers gained importance. Due to their expertise knowledge, which is adaptive in
nature is applied successfully for FQDFO. For supporting the validity of the proposed observer FQDFO,
it is compared with full order Luenberger observer and QDFO for a two-area inter connected power system by taking parametric uncertainties into consideration. Computational results proved the robustness of the proposed observer.
Multiple Constraints Consideration in Power System State EstimationIOSR Journals
This document discusses a novel algorithm developed to consider multiple constraints in power system state estimation using weighted least squares. The algorithm detects missing measurement data, identifies and eliminates bad data, and evaluates network observability. It also considers measurement uncertainties from phasor measurement units. The algorithm is tested on the IEEE 14 bus system and is able to identify bad data, estimate missing data values, and determine observability while incorporating measurement uncertainties.
Flatness Based Nonlinear Sensorless Control of Induction Motor SystemsIAES-IJPEDS
This paper deals with the flatness-based approach for sensorless control of
the induction motor systems. Two main features of the proposed flatness
based control are worth to be mentioned. Firstly, the simplicity of
implementation of the flatness approach as a nonlinear feedback linearization
control technique. Secondly, when the chosen flat outputs involve non
available state variable measurements a nonlinear observer is used to
estimate them. The main advantage of the used observer is its ability to
exploite the properties of the system nonlinearties. The simulation results are
presented to illustrate the effectiness of the proposed approach for sensorless
control of the considered induction motor.
This document discusses state estimation in power systems. It begins by defining state estimation as assigning values to unknown system state variables based on measurements according to some criteria. It then discusses that the most commonly used criterion is the weighted least squares method. It provides an example of using measurements to estimate voltage angles as state variables and calculate other power flows. Finally, it discusses the weighted least squares state estimation technique in detail including developing the measurement function matrix and solving the weighted least squares optimization.
Trajectory Control With MPC For A Robot Manipülatör Using ANN ModelIJMER
In this study, in a computer the dynamic motion modelling of manipulator and control of
trajectory with an algorithm this has been tested. First after dynamic motion simulation of manipulator
has been made MPC Control. The result in this study we can observe that computed torque method gives
better results than MPC methods. So in trajectory control it is approved of using computed torque
method. In last part of this study the results are estimated forward development are exemined and
suggested. The model predictive control (MPC) technique for an articulated robot with n joints is
introduced in this paper. The proposed MPC control action is conceptually different with the trajectory
robot control methods in that the control action is determined by optimising a performance index over
the time horizon. A neural network (NN) is used in this paper as the predictive model.
Performance analysis of a liquid column in a chemical plant by using mpceSAT Publishing House
This document discusses the use of model predictive control (MPC) to control the composition of a liquid column in a chemical plant. It provides background on MPC and how it can be used for multivariable processes like liquid columns. The document describes modeling a liquid column process in MATLAB Simulink and comparing the performance of MPC and PID control of the column. The results show that MPC provides better control of the column composition and liquid level than PID control.
Design of a Controller for Systems with Simultaneously Variable Parametersijtsrd
The contribution of this paper is in suggesting an analysis and design of a control system with variable parameters By applying the recommended by the author method of the Advanced D-partitioning the system's stability can be analyzed in details The method defines regions of stability in the space of the system's parameters The designed controller is enforcing desired system performance The suggested technique for analysis and design is essential and beneficial for the further development of control theory in this area Prof. Kamen Yanev "Design of a Controller for Systems with Simultaneously Variable Parameters" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-2 | Issue-6 , October 2018, URL: http://www.ijtsrd.com/papers/ijtsrd18440.pdf
Design of de-coupler for an interacting tanks systemIOSR Journals
This document describes the design of a decoupler for a two-tank interacting system. It first provides background on interacting or coupled multi-input multi-output (MIMO) systems and the goal of decoupling. It then presents the mathematical model and dynamics of the two-tank system. Next, it analyzes the interaction between the two tanks' liquid levels and inlet flow rates. The relative gain array (RGA) method is used to determine appropriate control loop configurations to minimize interaction. Finally, the document derives equations to design decouplers to cancel the effect of one tank's flow rate on the other tank's liquid level, thereby rendering the system as two independent single-input single-output loops. Experimental results
Robust control for a tracking electromechanical systemIJECEIAES
A strategy for the design of robust control of tracking electromechanical systems based on 𝐻∞ synthesis is proposed. Proposed methods are based on the operations on frequency characteristics of control systems designed and developed using the MATLAB robust control toolbox. Determination of the singular values for a transfer matrix of the control system reduces the disturbances and guarantees its stability margin. For selecting the weighted transfer functions, the basic recommendations are formulated. The efficiency of the proposed approach is verified by robust control of an elastically coupled two-mass system whose parameter values are adjusted by matching them with the parameters of one of the supplied robots. The simulation results confirm that the proposed strategy of design of robust control of twomass elastic coupling system using the 𝐻∞ synthesis is very efficient and significantly reduces the perturbation of parameters of the controlled plant.
Recurrent fuzzy neural network backstepping control for the prescribed output...ISA Interchange
This paper proposes a backstepping control system that uses a tracking error constraint and recurrent fuzzy neural networks (RFNNs) to achieve a prescribed tracking performance for a strict-feedback nonlinear dynamic system. A new constraint variable was defined to generate the virtual control that forces the tracking error to fall within prescribed boundaries. An adaptive RFNN was also used to obtain the required improvement on the approximation performances in order to avoid calculating the explosive number of terms generated by the recursive steps of traditional backstepping control. The boundedness and convergence of the closed-loop system was confirmed based on the Lyapunov stability theory. The prescribed performance of the proposed control scheme was validated by using it to control the prescribed error of a nonlinear system and a robot manipulator.
IRJET- Excitation Control of Synchronous Generator using a Fuzzy Logic based ...IRJET Journal
This document presents a fuzzy logic-based backstepping approach for excitation control of synchronous generators. The backstepping control law is designed using control Lyapunov functions to ensure stability. Fuzzy logic is then used to determine the optimal values for three tuning gains in the backstepping control law. Membership functions are defined based on the CLF boundaries. Fuzzy rules are formulated to map error and change in error inputs to tuning gain outputs. Simulation studies on a single machine infinite bus system evaluate the performance of the proposed controller under two fault conditions, and validate that it improves stability compared to traditional controllers with constant gains.
2-DOF Block Pole Placement Control Application To: Have-DASH-IIBITT MissileZac Darcy
In a multivariable servomechanism design, it is required that the output vector tracks a certain reference
vector while satisfying some desired transient specifications, for this purpose a 2DOF control law
consisting of state feedback gain and feedforward scaling gain is proposed. The control law is designed
using block pole placement technique by assigning a set of desired Block poles in different canonical forms.
The resulting control is simulated for linearized model of the HAVE DASH II BTT missile; numerical
results are analyzed and compared in terms of transient response, gain magnitude, performance
robustness, stability robustness and tracking. The suitable structure for this case study is then selected.
2-DOF Block Pole Placement Control Application To: Have-DASH-IIBITT MissileZac Darcy
In a multivariable servomechanism design, it is required that the output vector tracks a certain reference
vector while satisfying some desired transient specifications, for this purpose a 2DOF control law
consisting of state feedback gain and feedforward scaling gain is proposed. The control law is designed
using block pole placement technique by assigning a set of desired Block poles in different canonical forms.
The resulting control is simulated for linearized model of the HAVE DASH II BTT missile; numerical
results are analyzed and compared in terms of transient response, gain magnitude, performance
robustness, stability robustness and tracking. The suitable structure for this case study is then selected.
2-DOF BLOCK POLE PLACEMENT CONTROL APPLICATION TO:HAVE-DASH-IIBTT MISSILEZac Darcy
In a multivariable servomechanism design, it is required that the output vector tracks a certain reference
vector while satisfying some desired transient specifications, for this purpose a 2DOF control law
consisting of state feedback gain and feedforward scaling gain is proposed. The control law is designed
using block pole placement technique by assigning a set of desired Block poles in different canonical forms.
The resulting control is simulated for linearized model of the HAVE DASH II BTT missile; numerical
results are analyzed and compared in terms of transient response, gain magnitude, performance
robustness, stability robustness and tracking. The suitable structure for this case study is then selected.
Design Nonlinear Model Reference with Fuzzy Controller for Nonlinear SISO Sec...IJECEIAES
The document describes a proposed design for a nonlinear model reference controller combined with type-1 and interval type-2 fuzzy control schemes for nonlinear single-input single-output (SISO) systems. The model reference controller is designed based on an optimal desired model and Lyapunov stability theory. Then a type-1 or interval type-2 fuzzy Takagi-Sugeno controller is combined with the model reference controller to improve its performance by reducing steady state error from the system response. The proposed controller is applied to control an inverted pendulum system. Simulation results show that the model reference controller with interval type-2 fuzzy control has better performance than with type-1 fuzzy control.
A hybrid bacterial foraging and modified particle swarm optimization for mode...IJECEIAES
This paper study the model reduction procedures used for the reduction of large-scale dynamic models into a smaller one through some sort of differential and algebraic equations. A confirmed relevance between these two models exists, and it shows same characteristics under study. These reduction procedures are generally utilized for mitigating computational complexity, facilitating system analysis, and thence reducing time and costs. This paper comes out with a study showing the impact of the consolidation between the Bacterial-Foraging (BF) and Modified particle swarm optimization (MPSO) for the reduced order model (ROM). The proposed hybrid algorithm (BF-MPSO) is comprehensively compared with the BF and MPSO algorithms; a comparison is also made with selected existing techniques.
An Optimal LFC in Two-Area Power Systems Using a Meta-heuristic Optimization...IJECEIAES
The document presents a study that develops an optimal load frequency control (LFC) method for two-area power systems using a harmony search (HS) algorithm to tune the parameters of a PI controller (Kp and Ki). The HS algorithm is used to minimize an objective function of integral absolute error (IAE) in order to enhance system performance regarding settling time, maximum deviation, and peak time. The two-area power system model and HS-PI controller design are implemented in MATLAB. Results show the HS-PI controller provides more robust performance compared to a particle swarm optimization-based PI controller under different load conditions.
Comparison of Soft Computing Techniques applied in High Frequency Aircraft Sy...ijeei-iaes
This document compares the use of fuzzy logic control and adaptive tabu search algorithm for controlling a shunt active power filter in an aircraft electrical system operating at 400Hz. Simulation results show that a sinusoidal current control strategy optimized with fuzzy logic provides the best compensation performance, reducing source current THD to 2.22% and voltage THD to 1.01% with the fastest compensation time of 0.0066 seconds. While adaptive tabu search achieved slightly higher THDs, its compensation time was faster at 0.0065 seconds. Overall, fuzzy logic provided the best balance of harmonic reduction and speed for compensating the aircraft power system.
Design and Implementation of Model Reference Adaptive Controller using Coeffi...IOSR Journals
This document describes the design and implementation of a model reference adaptive controller (MRAC) using the coefficient diagram method (CDM) for a nonlinear process. It begins by introducing MRAC for single-input single-output plants, developing the MRAC design and control law. It then provides basics of the CDM design approach. The document applies the CDM-MRAC to a spherical tank level process in simulation, comparing its performance to a linear PI controller. Simulation results show the CDM-MRAC has faster rise time and settling time than the PI controller.
Integral Backstepping Sliding Mode Control of Chaotic Forced Van Der Pol Osci...ijctcm
ABSTRACT
Forced Van der Pol oscillator exhibits chaotic behaviour and instability under certain parameters and this poses a great threat to the systems where it has been applied hence, the need to develop a control method to stabilize and control chaos in a Forced Van der Pol oscillator so as to avoid damage in the controlled system and also to prevent unmodeled dynamics from being introduced in the system. Sliding Mode control makes use of the regulatory variables derived from the controlled Lyapunov function to bring the new variables to stability. The essence of using Integral Backstepping was to prevent chattering which can occur in the control input and can cause instability to the system by igniting unmodeled dynamics. Simulation was done using MATLAB and the results were provided to show the effectiveness of the proposed control method. Integral Backstepping Sliding Mode control method was effective towards stability and chaos control. It was also robust towards matched and unmatched disturbance.
Cone Crusher Model Identification Using Block-Oriented Systems with Orthonorm...ijctcm
In this paper, block-oriented systems with linear parts based on Laguerre functions is used to approximation of a cone crusher dynamics. Adaptive recursive least squares algorithm is used to identification of Laguerre model. Various structures of Hammerstein, Wiener, Hammerstein-Wiener models are tested and the MATLAB simulation results are compared. The mean square error is used for models validation.It has been found that Hammerstein-Wiener with orthonormal basis functions improves the quality of approximation plant dynamics. The mean square error for this model is 11% on average throughout the considered range of the external disturbances amplitude. The analysis also showed that Wiener model cannot provide sufficient approximation accuracy of the cone crusher dynamics. During the process it is unstable due to the high sensitivity to disturbances on the output.The Hammerstein-Wiener model will be used to the design nonlinear model predictive control application
In this paper, block-oriented systems with linear parts based on Laguerre functions is used to
approximation of a cone crusher dynamics. Adaptive recursive least squares algorithm is used to
identification of Laguerre model. Various structures of Hammerstein, Wiener, Hammerstein-Wiener models
are tested and the MATLAB simulation results are compared. The mean square error is used for models
validation.It has been found that Hammerstein-Wiener with orthonormal basis functions improves the
quality of approximation plant dynamics. The mean square error for this model is 11% on average
throughout the considered range of the external disturbances amplitude. The analysis also showed that
Wiener model cannot provide sufficient approximation accuracy of the cone crusher dynamics. During the
process it is unstable due to the high sensitivity to disturbances on the output.The Hammerstein-Wiener
model will be used to the design nonlinear model predictive control application.
Hierarchical algorithms of quasi linear ARX Neural Networks for Identificatio...Yuyun Wabula
This document summarizes a research paper on hierarchical algorithms for training a quasi-linear ARX neural network model for identification of nonlinear systems. The key points are:
1) A hierarchical algorithm is proposed that first estimates the system using a linear sub-model and least squares estimation to obtain linear parameters. It then trains a neural network nonlinear sub-model to refine the errors of the linear sub-model.
2) The linear parameter estimates are fixed and used as biases for the neural network, which is trained to minimize the residual errors of the linear sub-model.
3) This hierarchical approach separates the identification into linear and nonlinear parts, allowing analysis of the system linearly while also capturing nonlinearities. The neural
This paper deals with a comparative study of circle criterion based nonlinear observer and H∞ observer for induction motor (IM) drive. The advantage of the circle criterion approach for nonlinear observer design is that it directly handles the nonlinearities of the system with less restriction conditions in contrast of the other methods which attempt to eliminate them. However the H∞ observer guaranteed the stability taking into account disturbance and noise attenuation. Linear matrix inequality (LMI) optimization approach is used to compute the gains matrices for the two observers. The simulation results show the superiority of H∞ observer in the sense that it can achieve convergence to the true state, despite the nonlinearity of model and the presence of disturbance.
Comparison of backstepping, sliding mode and PID regulators for a voltage inv...IJECEIAES
In the present paper, an efficient and performant nonlinear regulator is designed for the control of the pulse width modulation (PWM) voltage inverter that can be used in a standalone photovoltaic microgrid. The main objective of our control is to produce a sinusoidal voltage output signal with amplitude and frequency that are fixed by the reference signal for different loads including linear or nonlinear types. A comparative performance study of controllers based on linear and non-linear techniques such as backstepping, sliding mode, and proportional integral derivative (PID) is developed to ensure the best choice among these three types of controllers. The performance of the system is investigated and compared under various operating conditions by simulations in the MATLAB/Simulink environment to demonstrate the effectiveness of the control methods. Our investigation shows that the backstepping controller can give better performance than the sliding mode and PID controllers. The accuracy and efficiency of the proposed backstepping controller are verified experimentally in terms of tracking objectives.
DESIGN OF OBSERVER BASED QUASI DECENTRALIZED FUZZY LOAD FREQUENCY CONTROLLER ...Wireilla
ABSTRACT
This paper proposes Fuzzy Quasi Decentralized Functional Observers (FQDFO) for Load Frequency Control of inter-connected power systems. From the literature, it is well noticed about the need of Functional Observers (FO’s) for power system applications. In past, conventional Functional Observers are used. Later, these conventional Functional Observers are replaced with Quasi Decentralized Functional Observers (QDFO) to improve the system performance. In order to increase the efficacy of the system, intelligent controllers gained importance. Due to their expertise knowledge, which is adaptive in nature is applied successfully for FQDFO. For supporting the validity of the proposed observer FQDFO, it is compared with full order Luenberger observer and QDFO for a two-area inter connected power system by taking parametric uncertainties into consideration. Computational results proved the robustness of the proposed observer.
International Journal of Computational Engineering Research(IJCER)ijceronline
International Journal of Computational Engineering Research(IJCER) is an intentional online Journal in English monthly publishing journal. This Journal publish original research work that contributes significantly to further the scientific knowledge in engineering and Technology.
Optimization of Modified Sliding Mode Controller for an Electro-hydraulic Act...IJECEIAES
This paper presents the design of the modified sliding mode controller (MSMC) for the purpose of tracking the nonlinear system with mismatched disturbance. Provided that the performance of the designed controller depends on the value of control parameters, gravitational search algorithm (GSA), and particle swarm optimization (PSO) techniques are used to optimize these parameters in order to achieve a predefined system’s performance. In respect of system’s performance, it is evaluated based on the tracking error present between reference inputs transferred to the system and the system output. This is followed by verification of the efficiency of the designed controller in simulation environment under various values, with and without the inclusion of external disturbance. It can be seen from the simulation results that the MSMC with PSO exhibits a better performance in comparison to the performance of the similar controller with GSA in terms of output response and tracking error.
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11TH INTERNATIONAL CONFERENCE ON ELECTRICAL, ELECTRONIC AND COMPUTING ENGINEERING
3-6 June 2024, Niš, Serbia
Direct digital control scheme for controlling hybrid dynamic systems using ANN state estimator and inverse dynamics controller
1. Direct digital control scheme for controlling hybrid dynamic systems using
ANN state estimator and inverse dynamics controller
Xiao Laui,
Research Scholar, City University of
Hong Kong, China.
Rui-Lain Chua,
Professor, City University of Hong
Kong, China.
Abstract:
An Estimator Based Inverse Dynamics Controller
(EBIDC), which utilizes an Artificial Neural Network
(ANN) based state estimation scheme for nonlinear
autonomous hybrid systems which are subjected to state
disturbances and measurement noises that are stochastic
in nature, is proposed in this paper. A salient feature of
the proposed scheme is that it offers better state estimates
and hence a better control of non-measurable state
variables with a non linear approach in correcting the a
priori estimates by avoiding statistical linearization
involved in existing approaches based on derivative free
estimation methods. Simulation results guarantees
significant reduction in Integral Square Error (ISE) and
standard deviation (σ) of error, between the controlled
variable and set point and control signal computation
time when compared with best existing related work
based on Unscented Kalman Filter (UKF) and
Ensembeled Kalman Filter (EnKF). Detailed analysis of
the experimental results on real plant under different
operating conditions such as servo and regulatory
operations, initial condition mismatch, and different types
of faults in the system, confirms robustness of proposed
approach in these conditions and support the simulation
results obtained. The main advantage of the proposed
controller is that the control signal computation time is
very much less than the selected sampling time of the
process, so direct control of the plant is possible with this
approach.
Key words: Artificial Neural Network, Hybrid Dynamic
Systems, State Estimation, Inverse Dynamics Controller..
1. Introduction
Systems in which it may be required to model inherent
process discontinuities, where the continuous behavior is
drastically changed, or use actuators and sensors which are
often fundamentally discontinuous, or use discrete events that
can be a useful abstraction to model various mode switching
used in the specification and control of the basically
continuous process, require hybrid systems modeling and
control approach ([1], [2], [3] and [4]). Kalman filter (KF) [5]
and extended Kalman filter (EKF) [6] are used as a state
estimator in conventional state observers. For linear systems
as uncertainties in state and measurement equations can be
modeled as Gaussian white noise processes Kalman filter can
generate optimal estimates of state. Extended Kalman filter
(EKF), which is a natural extension of the linear filter to the
nonlinear domain through analytical linearization, can be
used in state estimation in nonlinear systems. In this
approach, the estimated states are obtained by using Taylor
series expansion of the nonlinear state transition operator.
But, it requires analytical computation of Jacobians at each
time step, which is considered as one of the major draw backs
of EKF for complex nonlinear systems. Also it is required
that nonlinear function vectors appearing in state dynamics
and output dynamics should be smooth and at least once
differentiable. However, dynamical models of Hybrid
systems involve discontinuities due to switching of the
discrete state values. As Jacobians cannot be computed for
non-smooth functions, EKF cannot be realized in Hybrid
systems [7]. In [8] a moving horizon based state estimation
approach has been reported for Hybrid system estimation.
But, the use of fixed arrival cost used in the moving horizon
estimator formulation result in sub-optimal state estimates.
[9] has proposed UKF as an alternative to EKF so that the
main drawback of EKF when used for highly nonlinear
system is eliminated. [10] has proposed a derivative free non
linear filtering technique for nonlinear hybrid systems. As far
as the control element is concerned, [11] had proposed a
robust model predictive control (RMPC) scheme for a class
of hybrid system such as piece wise affine system to ensure
simple and fast suboptimal solution for the control problem
with reduced computation time. Similarly, the nonlinear
model predictive control (NMPC) in [7] and [12], and fault
tolerant model predictive control in [13], for hybrid systems,
used UKF approach in its state estimation part. All the state
estimation schemes for hybrid systems in literature involve
The International journal of analytical and experimental modal analysis
Volume XII, Issue III, March/2020
ISSN NO:0886-9367
Page No:1907
2. analytical or statistical linearization [14] and preclude their
use from systems which require more accurate state
estimates. Introduction of ANN in state estimation and
control of different systems considerably improves the
performance which is very clear from the works reported in
[15], [16], [17] and [18]. But, as in the case of [15], if a
nonlinear scheme is used in correction of a priori estimates,
more accurate state estimates can be obtained in hybrid
systems also and this is implemented in this work. The
distinguishing feature of the proposed approach is that it uses
nonlinear ANN to correct the a priori estimates and gives
better estimates than its counterparts. Once trained for
sufficient variety of input data, including ill-conditioned
system data, the ANN-based state estimator provides accurate
estimates of the Hybrid system states. Further, an ANN based
Controller (ANNC), using this estimator, is developed for
controlling the non-measurable states of the hybrid system.
The proposed controller (ANNC) provides better performance
and has following advantages over existing schemes.
Apart from analytical and statistical linearization in the
correction part of EKF and UKF based controllers
respectively, proposed controller uses a nonlinear
correction approach using artificial neural network to
correct the a priori estimates and hence offers a better
state estimates by avoiding the linearization.
The correction part of ANNC is completely parameter
independent, and thereby gives better state estimates
even under parameter mismatched condition.
ANN has built in noise rejection capability which makes
the ANNC scheme robust in performance.
Comparative evaluation of the proposed approach with best
relating work based on UKF (statistical linearization
approach) and EnKF (Particle Filter) is made in terms of ISE
and standard deviation in state estimates on the same
benchmark model and it reveals the proposed approach is
able to reduce the error in state estimation of Hybrid systems.
Detailed performance evaluation of proposed approach under
servo/ regulatory operations, and plant model parameter
mismatch were conducted and comparative evaluation to best
existing related work was conducted based on ISE and
standard deviation of error between the controlled variables
and corresponding Set points and average computation time
per iteration. Detailed analysis of the experimental results on
real plant under different operating conditions such as servo
and regulatory operations, initial condition mismatch, and
different types of faults in the system confirms efficacy of
proposed approach in these conditions and supports
simulation results obtained. Here, an inverse dynamics
controller is utilized for controlling the non-measurable states
of the system so that the computational burden is very much
reduced when compared with the model predictive control
scheme implemented in [7], [12] and [13] without
compromising the performance. Also the constraints handling
capability for this scheme is also achieved with this approach
by introducing upper and lower limiting functions at the
output of both estimator and controller.
The rest of the paper is organized as follows. In section 2,
description of the ANN state estimation algorithm developed
for hybrid systems is given. The Section 3 explains the
EBIDC scheme. Simulation results and detailed performance
analysis of the scheme and comparison to best related work is
given in section 4. Experimental results and its analysis are
presented in Section 5. Finally, section 6 summarizes the
paper.
2. ANN for Hybrid State Estimation
In this scheme, an ANN based correction is developed. As in
the case of EKF and UKF, ANN based state estimation is also
recursive in nature. Even though it has the same framework
of Kalman filter based state estimator, it is designed for
eliminating the analytical and statistical linearization [14]
used in the case of EKF and UKF. This structure is suggested
because recurrent type of ANN is better for the complex
dynamic system [18]. The schematic diagram of proposed
ANNC is as given in Fig. 1.
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Volume XII, Issue III, March/2020
ISSN NO:0886-9367
Page No:1908
3. Fig.1. Schematic representation of proposed ANNC
The detailed NARX structure used for the considered
problem is given in Fig. 2 and the other NARX parameters
used for this study are provided in Table 1.
The current output can be predicted as a function of present
and past inputs and past outputs as given below, in which Y
and X represent the outputs and inputs of the network
respectively and KNN is a nonlinear ANN function.
Y (k) = KNN{X (k), X (k-m), Y (k-1)… Y (k-n)} (1)
Table 1
Values of Different ANN Parameters
Parameter Value
ANN Structure NARX
No. of hidden layers 1
Hidden Layer neurons 5
Hidden layer activation function ‘tan sigmoid’
Output layer activation function ‘purelin’
No of epochs
100
No of exogenous inputs 4
No. of delayed inputs 0
No of outputs 3
No. of feedback output delays 2
Training method Back propagation
Training function Levenberg–Marquardt
Performance Function Mean Square Error
A sequence of current and past input vectors (X (k), X (k-1),
X (k-m)) are obtained by passing X (k) through an input time
delay unit, ITD (0: m). Similarly output time delay unit, OTD
(1: n) provides a sequence of past output vectors (Y (k-1), Y
(k-n)). For the considered problem, the input and the output
are T
1 2 3
ˆ ˆ ˆX( ) [ ( 1), ( 1), ( 1), ( 1)] k h k k h k k h k k k k
T
1 2 3
ˆ ˆ ˆY( ) [ ( ), ( ), ( )]k h k h k h k respectively.
Similar to Kalman filter based state estimators and its
nonlinear extensions; proper value for the initial state vector
is assumed for the prediction model. The input and output
measurements are made from the process and the input
measurement are presented to the prediction model along
with the assumed initial state vector in order to compute the
time updated values for states.
ˆ ˆ( 1) F( ( 1), ( )) x k k x k u k (2)
With, ˆ ˆ( 1) (0) [ (0)] x k x E x , the assumed initial value of
state vector.
This a priori state estimates, ˆ( 1)x k k can be given to the
output model so that a priori estimates of the output,
ˆ( 1)y k k can be obtained as
ˆ ˆ( 1) H ( 1) y k k x k k (3)
The innovation between plant output, ( )y k and a priori
output estimates, ˆ( 1)y k k is calculated as
ˆ( 1) ( ) ( 1) k k y k y k k (4)
In the correction step of the algorithm, the a priori state
estimates will be corrected using this innovation with the help
of the ANN to obtain a posteriori estimates of states
Process Noise, ( )w t
Set point
Input, ( )u t
Measurement Noise, ( )v t
Output, ( )y t
Prediction
Model
ANN
Correction
Function
ITD
OTD
EBIDC
Innovation,
( 1)k kˆ( 1)x k k
xk/k-1
ˆ( )x k
( )u k
( )y k
Process
SampleHold
ˆ( 1)y k k
ˆ( )x k
Estimator
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Volume XII, Issue III, March/2020
ISSN NO:0886-9367
Page No:1909
4. .
Fig.2. NARX structure for the considered example
NNˆ ˆ ˆ( ) K ITD( ( 1), ( 1)),OTD( ( )) x k x k k k k x k (5)
These estimated states are fed back to the controller for
calculating the new input signal to the plant. For the next
iteration, a posteriori estimate of state can be given to the
prediction model (instead of assumed initial states as in the
first iteration) along with the new input measurement from
the plant. This can be continued for the entire process run
3. Estimator Based Inverse Dynamics Controller (EBIDC)
In hybrid systems, for the controller design, its mode
switching property has also to be taken in to account. For
such processes, model based control schemes are proposed in
the literature ([12], [13], [19], [20], [21] and [22]) for
obtaining the satisfactory control of the output variables. In
this work a model based controller namely inverse dynamics
controller (IDC) is implemented for controlling the non-
measurable states of Hybrid System. The objective of this
section is to review the non-linear dynamic controller
technique that can be applied to develop a non-measurable
level control system that is valid over the entire operating
region of the hybrid three-tank system described below.
Consider the nonlinear system of the form,
( ) ( ) x A x B x u (6)
y Cx (7)
Where, A(x) = (n × 1) vector, B(x) = (n × m) matrix, C = (m
× 1) vector.
The inverse dynamics of (6) and (7) is represented as,
1F ( , )u v x
Where, v is the input to the inverse system.
Construction of the inverse dynamics of (6) and (7) is done
by repeatedly differentiating the measurement function until
the input variable u appears.
Differentiating (7)
y Cx (8)
[ ( ) ( ). ] y C A x B x u (9)
* *
( ) ( ). y A x B x u (10)
Where, A*
(x) =C.A(x) and B*
(x) =B.A(x)
So the control law u can be written as follows [16]
1
* *
( )[ ( )]
u B x v A x (11)
A sufficient condition for the existence of an inverse system
model to (6) and (7) is that B*
in (11) be non-singular. If this
is the case, then the inverse system model takes the form,
( ) ( )[ ( ) ( ) ] x A x B x F x G x v (12)
Where,
1
* *
( ) ( ) ( )
F x B x A x and
1
*
( ) ( )
G x B x
( ) ( )[ ( ) ( ) ] x A x B x F x G x v (13)
The input to the inverse system is v = y – yref
As the hybrid three-tank system, considered under this study
can be directly represented in the form of (6) and (7),
applying this procedure will yield the control law as
1 1 1sp=A C h - + + +1in 1 1 3 5F h Q Q Q (14)
2 2 2sp=A C h - + + +2in 2 2 4 7F h Q Q Q (15)
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Volume XII, Issue III, March/2020
ISSN NO:0886-9367
Page No:1910
5. Since h1, h2, Q1, Q2, Q3, Q4, Q5, and Q7, are non-measureable
for the considered problem, the estimated values can be used
so that the controller becomes an estimator based inverse
dynamics controller.
1 1 1sp
ˆ ˆ ˆ ˆ=A C h - + + +1in 1 1 3 5F h Q Q Q (16)
2 2 2sp
ˆ ˆ ˆ ˆ=A C h - + + +2in 2 2 4 7F h Q Q Q (17)
Where, C1 and C2 are controller tuning parameter, and its
values are varied from 0 to 1 on separate runs and the integral
square error between the controlled variable and the set point,
is noted. The values of C1 and C2, which give the minimum
ISE, are selected as the tuning parameters. The h1sp and h2sp
are the corresponding desired values of water levels.
4. Simulation Results and Performance Analysis
The same Benchmark model based on three tank system used
in [7] is used here with same levels in three tanks (h1, h2 and
h3) as continuous states and z1 and z2 variables as discrete
states for evaluating the performance the controller in
comparison to best related work. The schematic
representation of hybrid three-tank system is given in Fig.3.
Detailed modeling of the hybrid three-tank system is given as
appendix. The developed algorithm was simulated in
MATLAB. The detailed discussions about the results
obtained in simulation are given in the following subsections.
4.1 Performance in Servo Operation
Servo operation of the closed loop system when a change in
set point occurs was conducted by introducing a step change
with magnitude 0.04 m at 100th
sampling instant. The results
are given in Fig.4. Comparison with the best existing related
work is shown in Table 2. Comparison of proposed approach
to UKF based approach based on ISE shows that the new
approach is better as ISE reduced from 3.3278 to 0.5533 in
level, h1 and from 3.7203 to 0.4568 in level, h2. Also, the
average computation time per iteration reduced from 60.65
seconds to 0.0777 seconds. Evolution of true and estimated
states of hybrid three-tank system with ANNC (Servo
operation) is shown in Fig.5. Evolution of true and estimated
values of discrete variables of hybrid three-tank system with
ANNC (Servo Operation) is shown in Fig.6.
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Volume XII, Issue III, March/2020
ISSN NO:0886-9367
Page No:1911
6. Fig.3. Schematic representation of the benchmark hybrid three tank system
Fig.4. Servo response of hybrid three tank system with ANNC (a) Level in
Tank 1, (b) Level in tank 2 (c) Manipulating variables
Fig.5. True and estimated states of hybrid three tank system with ANNC
(Servo operation) (a) Level in Tank 1, (b) Level in Tank 2, (c) Level in tank
3
Fig.6. Evolution of true and estimated values of discrete variables of hybrid
three tank system with ANNC (Servo Operation)
4.2 Performance in Regulatory Operation
The results of the performance of the estimator in regulatory
operation are given in Fig.7. Comparison with the best
existing related work is shown in Table 3. Comparison of
proposed approach to UKF based approach based on standard
deviation shows that the new approach is better as standard
deviation has reduced from 0.0130 to 0.0127 in level h2 and
from 0.0484 to 0.0065 in level h3 with very close standard
deviation in level h1. It may be noted that the maximum
standard deviation in the case of nonmeasured state variables
is 0.0217 in the proposed approach and 0.0484 in the UKF
based NMPC(45% reduction with proposed approach).
Table 3
Regulatory Control Problem: Estimator performance
Comparison
Controller σE(h1) σE(h2) σE(h3)
Proposed 0.0217 0.0127 0.0065
UKF based NMPC[7] 0.0213 0.0130 0.0484
UKF based NMPC[7] 0.0242 0.0141 0.0488
The results of the performance of the controller in regulatory
operation are given in Fig.8 and evolution of true and
estimated values of discrete variables of hybrid three tank
system with ANNC (Regulatory Operation; Disturbance by
varying the valve position of fifth hand valve) in Fig.9.
50 100 150 200 250 300
.2
.4
Level(h
1
)
(a)
Setpoint CV(Proposed)
50 100 150 200 250 300
0.2
0.4
Level(h
2
)
(b)
Setpoint CV(proposed)
50 100 150 200 250 300
0
0.5
1
(c)
Sampling Instants
Manipulating
Variables
Fin1 Fin2
50 100 150 200 250 300
0.2
0.4
Level(h1)
(a)
True Estimated
50 100 150 200 250 300
0.2
0.4
Level(h2) (b)
True Estimated
50 100 150 200 250 300
0.2
0.4
0.6Level(h
3
)
(c)
Sampling Instants
True Estimated
100 200 300
-2
-1
0
1
2
Sampling Instants
z
1
(True)
100 200 300
-2
-1
0
1
2
Sampling Instants
z
2
(True)
100 200 300
-2
-1
0
1
2
Sampling Instants
z
1
(Estimate)
100 200 300
-2
-1
0
1
2
Sampling Instants
z
2
(True)
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Volume XII, Issue III, March/2020
ISSN NO:0886-9367
Page No:1912
7. Comparison with the best existing related work is shown in
Table 4. Comparison of proposed approach to UKF based
approach based on ISE shows that the new approach is better
as ISE has reduced from 3.5869 to 0.0587 in level h1 and
from 1.5212 to 0.0366 in level h2. Also, the average
computation time per iteration has reduced from 59.05
seconds to 0.0739 seconds.
Fig.7. Evolution of true and estimated states of hybrid three tank system with
ANNC (a) Level in Tank 1, (b) Level in Tank 2, (c) Level in tank 3
Fig .8. Regulatory response of hybrid three tank system with ANNC (a)
disturbance, (b) Level in Tank 1, (c) Level in tank 2 (d) Manipulating
variables
Table 4
Regulatory Control Problem: Controller Performance
Comparison
Controller ISE(h1) ISE(h2)
Avg. Computation
time per iteration (S)
Proposed 0.0587 0.0366 0.0739
UKF based
NMPC[7]
3.5869 1.5212 59.05
EnKF based
NMPC[7]
3.3928 1.4011 206.44
Fig.9. Evolution of true and estimated values of discrete variables of hybrid
three tank system with ANNC (Regulatory Operation)
In order to obtain better insight of the ability of the proposed
controller to achieve decoupling and offset-free control
action, hypothetical situation, in which state and
measurement noise are not present, is simulated. Response
given in Fig. 10 reveals that the effect in level of tank 2, due
to the disturbance in tank 1 is very much less compared with
that given in [7]. As in the case of UKF based NMPC in [7],
proposed method also giving a slight offset.
20 40 60 80 100 120 140
0.2
0.3
0.4
Level(h
1
)
(a)
True Estimated
20 40 60 80 100 120 140
0.2
0.3
0.4
Level(h
2
)
(b)
True Estimated
20 40 60 80 100 120 140
0.2
0.3
0.4
Level(h3
)
(c)
Sampling Instants
True Estimated
20 40 60 80 100 120 140
0.2
0.3
0.4
Level(h
1
)
(b)
Setpoint C V(Proposed)
20 40 60 80 100 120 140
0.2
0.3
0.4
Level(h
2
)
(c)
Setpoint CV (Proposed)
20 40 60 80 100 120 140
0
0.5
1
(d)
Sampling Instants
Manipulating
Variables
Fin1
Fin2
20 40 60 80 100 120 140
0
0.5
1
Disturbance
(a)
50 100 150
-2
-1
0
1
2
Sampling Instantsz
1
(True)
50 100 150
-2
-1
0
1
2
Sampling Instants
z
2
(True)
50 100 150
-2
-1
0
1
2
Sampling Instants
z
1
(Estimate)
50 100 150
-2
-1
0
1
2
Sampling Instants
z
2
(True)
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ISSN NO:0886-9367
Page No:1913
8. Fig .10. Regulatory response of hybrid three tank system with ANNC
(without state and measurement noise) (a) disturbance, (b) Level in Tank 1,
(c) Level in tank 2 (d) Manipulating variables
4.3 Plant Model Parameter Mismatch
The performance of the controller in case of plant model
parameter mismatch is considered and the performance is
given in Fig. 11. From Table.5, it can be seen that the ISE is
improved to 0.0276 from 0.9231 for level h1 and to 0.0228
from 1.0579 for level h2 when compared to best existing
related work based on UKF.
Fig.11. Response of hybrid three tank system with ANNC (Plant-Model
mismatch ) (a) Level in Tank 1, (b) Level in Tank 2, (c) Level in tank 3
Table 5
Plant Model Parameter Mismatch: Controller Performance
Comparison
Controller ISE(h1) ISE(h2)
Proposed 0.0276 0.0228
UKF based NMPC [7] 0.9231 1.0579
EnKF based NMPC[7] 0.8647 0.9688
5. Experimental Results and Performance Analysis
Real-time experimental validations were carried out on the
experimental setup. In addition to the experimental setup,
other tools used, which were for the real time implementation
are the software Lab VIEW and the NI DAQ pad (USB6251).
In the real system, the performance of the controller in
regulatory operation and servo operation based on ISE and
average computation time per iteration is shown in Fig. 12,
Table 6, Fig. 13, and Table 7. In Table 8 and Fig. 14 response
of the system in initial condition mismatch is shown. The
response of the system in +10% and -10% plant model
parameter mismatch is given in Tables 9 and 10 and Figures
15 and 16 respectively. Results of hand valve faults which
can occur in real time application are given in Table 11, Fig.
17, Table 12 and Fig. 18. The real time experimental results
support the simulation results on performance.
Table 6
Regulatory Control Problem: Controller Performance
Comparison
Controller ISE(h1) ISE(h2)
Avg. Computation
time per iteration (S)
Proposed 0.0200 0.0193 0.1038
Table 7
Servo Control Problem: Controller Performance Comparison
Controller ISE(h1) ISE(h2)
Avg. Computation
time per iteration (S)
Proposed 0.0172 0.0144 0.1152
Table 8
Initial Condition Mismatch: Controller Performance
Comparison
Controller ISE(h1) ISE(h2)
Avg. Computation
time per iteration (S)
Proposed 0.0214 0.0592 0.1017
20 40 60 80 100 120 140
0
0.5
1
Disturbance
(a)
20 40 60 80 100 120 140
0.2
0.3
0.4
Level(h
1
)
(b)
Setpoint CV(Proposed)
20 40 60 80 100 120 140
0.2
0.3
0.4
Level(h
2
)
(c)
Setpoint CV(Proposed)
20 40 60 80 100 120 140
0
0.5
1
(d)
Sampling Instants
Manipulating
Variables
Fin1 Fin2
20 40 60 80 100
0.2
0.3
0.4
Level(h
1
)
(a)
Setpoint CV(Proposed)
20 40 60 80 100
0.2
0.3
0.4
Level(h
2
)
(b)
Setpoint CV(Proposed)
20 40 60 80 100
0
0.5
1
(c)
Sampling Instants
Manipulating
Variables
Fin1 Fin2
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Volume XII, Issue III, March/2020
ISSN NO:0886-9367
Page No:1914
9. Table 9
Plant Model Parameter Mismatch (+10%): Controller
Performance Comparison
Controller ISE(h1) ISE(h2)
Avg. Computation
time per iteration (S)
Proposed 0.0045 0.0069 0.2112
Table 10
Plant Model Parameter Mismatch (-10%): Controller
Performance Comparison
Controller ISE(h1) ISE(h2)
Avg. Computation
time per iteration (S)
Proposed 0.0122 0.0131 0.1037
Table 11
Hand Valve Faults -Leakage: Controller Performance
Comparison
Controller ISE(h1) ISE(h2)
Avg. Computation
time per iteration (S)
Proposed 0.0600 0.0077 0.0768
Table 12
Hand Valve Faults -Clogging: Controller Performance
Comparison
Controller ISE(h1) ISE(h2)
Avg. Computation
time per iteration (S)
Proposed 0.0082 0.0078 0.0943
Fig.12. Regulatory response of hybrid three tank system with ANNC (a)
Level in Tank 1, (b) Level in tank 2
Fig.13. Servo response of hybrid three tank system with ANNC (a) Level in
Tank 1, (b) Level in tank 2
Fig.14. Closed response of hybrid three tank system with ANNC (Initial
Condition Mismatch ) (a) Level in Tank 1, (b) Level in Tank 2
50 100 150 200 250 300 350 400
0.24
0.27
0.3
0.33
Level(h
1
)
(a)
CV1
(Proposed) SETPOINT1
100 200 300 400
0.24
0.27
0.3
0.33
Level(h
2
)
(b)
Sampling Instants
CV2
(Proposed) SETPOINT2
50 100 150 200
0.23
0.26
0.29
0.32
Level(h
1
)
(a)
50 100 150 200
0.23
0.26
0.29
0.32
Level(h
2
)
(b)
Sampling Instants
CV2
(Proposed) SETPOINT2
CV1
(Proposed) SETPOINT1
50 100 150 200 250 300 350 400
0.26
0.3
0.34
0.38
Level(h
1
)
(a)
CV1
(Proposed) SETPOINT1
50 100 150 200 250 300 350 400
0.26
0.3
0.34
0.38
Level(h
2
)
(b)
Sampling Instants
CV2
(Proposed) SETPOINT2
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ISSN NO:0886-9367
Page No:1915
10. Fig.15. Closed response of hybrid three tank system with ANNC (Plant-
Model mismatch +10% ) (a) Level in Tank 1, (b) Level in Tank 2
Fig.16. Closed response of hybrid three tank system with ANNC (Plant-
Model mismatch -10% ) (a) Level in Tank 1, (b) Level in Tank 2
Fig.17. Closed response of hybrid three tank system with ANNC (Handvalve
fault-Leakage ) (a) Level in Tank 1, (b) Level in Tank 2
Fig.18. Closed response of hybrid three tank system with ANNC (Handvalve
fault-Clogging ) (a) Level in Tank 1, (b) Level in Tank 2
6. Conclusion
An ANN estimation based control scheme which offers better
state estimates and hence better control, with a non linear
approach in correcting the a priori estimates by avoiding
statistical linearization involved in derivative free estimation
is proposed. On comparing with best exiting related work
based on statistical linearization, 85%, 97% and 97%
reduction in Integral Square Error (ISE), between controlled
50 100 150 200 250
0.28
.3
0.32
Level(h
1
)
(a)
CV1
(Proposed) SETPOINT1
50 100 150 200 250
0.28
0.3
0.32
Level(h
2
)
(b)
Sampling Instants
CV2
(Proposed) SETPOINT2
50 100 150 200 250
0.26
0.28
0.3
0.32
Level(h
1
)
(a)
CV1
(Proposed) SETPOINT1
50 100 150 200 250
0.26
0.28
0.3
0.32
Level(h
2
)
(b)
Sampling Instants
CV2
(Proposed) SETPOINT2
100 200 300 400 500
0.26
0.28
Level(h
1
)
(a)
100 200 300 400 500
0.26
0.28
Level(h
2
)
(b)
Sampling Instants
CV2
(Proposed) SETPOINT2
CV1
(Proposed) SETPOINT1
50 100 150 200 250
0.25
0.3
0.35
Level(h
1
)
(a)
100 200 300 400 500
0.25
0.3
0.35
Level(h
2
)
(b)
Sampling Instants
CV2
(Proposed) SETPOINT2
CV1
(Proposed) SETPOINT1
The International journal of analytical and experimental modal analysis
Volume XII, Issue III, March/2020
ISSN NO:0886-9367
Page No:1916
11. variable and set point, for servo, regulatory and plant model
parameter mismatch operations respectively, and a 45%
reduction in standard deviation (σ) of error between true and
estimated values of non-measurable states for regulatory
control operation were obtained. In addition to these
performance improvements, the attracting feature of the
proposed method is the time required for the computation of
control signals and is very much less than the sampling time
of the process which ensures the capability of online
implementation as direct control algorithm using the
proposed approach. The experimental studies conducted on a
real plant illustrate the robust performance of the proposed
controller in offering better online control of hybrid dynamic
system under real time operating constraints.
References
[1] Lennartson, M. Tittus, B. Egardt, and S. Pettersson,
“Hybrid systems in process control”, IEEE Control
Systems, 16,(5), (2002), 45-56.
[2] Goebel R., Sanfelice R. G. Teel, A. R., Hybrid
Dynamical Systems , IEEE Control Systems Magazine,
29(2), (2009), 28-93.
[3] Goebel, R; Sanfelice, R, G.and Teel, A.R., Hybrid
Dynamical Systems: Modeling, Stability, and
Robustness, Princeton University Press, 2012.
[4] Narasimhan, S. and Biswas, G., Model-Based Diagnosis
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and Cybernetics, 37(3), (2007), 348-361.
[5] N. L. Ricker, Model predictive control with state
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[7] J. Prakash, Sachin C. Patwardhan, Sirish L. Shah, State
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autonomous hybrid system using derivative free state
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799
[8] G. Ferrari Trecate, D. Mignone, Moving horizon
estimation for hybrid systems, IEEE Transactions on
Automatic Control, 47(10), (2002), 1663-1676.
[9] S. J. Julier, J.K. Uhlmann, Unscented filtering and
nonlinear estimation, Proc. IEEE, 92 (3), (2004), 401–
422
[10]Sachin C. Patwardhan, Shankar Narasimhan, Prakash
Jagadeeshan, Bhushan Gopaluni, Sirish L. Shah,
Nonlinear Bayesian state estimation: A review of recent
developments, Control Engineering Practice, 20(10) ,
(2012), 933-953
[11]Jean Thomas, Robust Model Predictive Controller for
Uncertain Piecewise Affine Systems, Arabian Journal of
Science and Engineering, vol. 39, issue 10, pp. 7421-
7432, 2014
[12]J. Prakash, Sachin C. P, S. L. Shah, Control of an
Autonomous Hybrid System Using a Nonlinear Model
Predictive Controller, In Proc. 17th World Congress of
IFAC, (2008), 12510-12515.
[13]Jagadeeshan P., Sachin C. P., Sirish L. S, Design and
Implementation Fault Tolerant Model Predictive Control
Scheme on a Simulated Model of Three-Tank Hybrid
System, Conference on Control and Fault Tolerant
Systems, France, (2010), 173-178.
[14]Lefebvre, T.; Bruyninckx, H.; De Schutter, J., Comment
on "A new method for the nonlinear transformation of
means and covariances in filters and estimators", IEEE
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1409.
[15]Kumar, S., Prakash, J. and Kanagasabapathy, P. “A
critical evaluation and experimental verification of
Extended Kalman Filter, Unscented Kalman Filter and
Neural State Filter for state estimation of three phase
induction motor”, Applied Soft Computing, Vol 11, Issue
3, pp. 3199-3208, 2011
[16]K. Zhang, Yuan F, Guo, J.Wang G., A Novel Neural
Network Approach to Transformer Fault Diagnosis
Based on Momentum-Embedded BP Neural Network
Optimized by Genetic Algorithm and Fuzzy C Means,
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issue 9, pp. 3451-3461, 2016
[17] Rajeev Kumar D., K. Singh, R. Kumar, S. Upadhaya,
Simulation-based Artificial Neural Network Predictive
Control of BTX Dividing Wall Column, Arabian Journal
of science and Engineering, vol. 40, issue 12, pp. 3393-
3407, 2015
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Volume XII, Issue III, March/2020
ISSN NO:0886-9367
Page No:1917
12. [18]G. Parlos, S. K. Menon, A. F. Atiya, An Algorithmic
Approach to Adaptive State Filtering Using Recurrent
Neural Networks, IEEE transactions on neural networks,
12(6), (2001), 1411-1432.
[19]N. N. Nandola, S. Bharatiya, Hybrid system
identification using a structural approach and its model
based control: An experimental validation, Nonlinear
Analysis: Hybrid Systems, 3(2), (2009), 87-100.
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(1988), 471-483.
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Adaptive Inverse Dynamics Control of Rigid Robots ,
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92-95.
APPENDIX: PROCESS DESCRIPTION
In the hybrid three-tank system, three tanks of
uniform area (A1, A2 and A3) are connected to each other and
to sump through seven hand valves and two variable speed
pumps as in figure 3. The seven valve discharge coefficients
are represented by k1 to k7. By conducting simple steady state
experiments and necessary calculations, these hand valve
coefficients are found, which are given in table A.1. Now
throughout this study the position of these hand valves should
not be altered (For the simulation results, all the parameter
values are taken from [7])
After calculating ki (where, i =1, 2,…,7), the system
is modeled using volume balance equations as in (A.1) –
(A.3), in which Qi represent the flows through ith
hand valve
and its equations are provided in (A.4) –(A.10). This is used
as the prediction model for calculating a priori state estimates
in the estimation algorithms described in section 2.
1
1 1 3 5
1
1
[ ]
A
dh
Fin Q Q Q
dt
(A.1)
2
2 2 4 7
2
1
[ ]
A
dh
Fin Q Q Q
dt
(A.2)
3
1 2 3 4 6
3
1
[ ]
A
dh
Q Q Q Q Q
dt
(A.3)
1 1 1 3 1 3=k ( - ) 2g -Q sign h h h h (A.4)
2 2 3 2 3=k ( - ) 2g -2Q sign h h h h (A.5)
3 1 1 0 3 0k3 2g ( - h ) ( - h ) Q z a h b h (A.6)
4 2 4 2 0 3 0k 2g ( - h ) ( - h ) Q z c h b h (A.7)
15 5 1 d2g( h ) Q k h (A.8)
6 6 3 z=k 2g( h )Q h (A.9)
27 7 2 d=k 2g( h )Q h (A.10)
The system is modeled as hybrid system because the
model contains both continuous and discrete states in it. The
flow through the middle inter connecting pipes can be better
modeled with the help of discrete variables.
The levels in three tanks (h1, h2 and h3) make the
continuous state and the variables z1 and z2 are the discrete
state. Depending on the flows, Q3 and Q4, discrete state
variables, z1 and z2 may take the values 0, +1 or -1 as given
below.
-1 if Q3 is away from Tank3
z1= 0; if Q3= 0 (A.11)
+1; if Q3 is towards Tank3
Similarly
-1 if Q4 is away from Tank3
z2= 0; if Q4=0 (A.12)
+1; if Q4 is towards Tank3
As Q3 and Q4 are determined by the three levels, it
is obvious that the discrete mode switching depends on the
continuous variables; hence the system comes under the
definition of AHS. The variables, a, b and c in (A.6) and
(A.7) are temporary variables to indicate the levels in three
tanks as below or above threshold level. The threshold level,
h0 is the height between middle interconnecting pipes and the
tank bottom as marked in figure 3. The height difference
between the 5th
, 6th
and 7th
hand valves from the bottom of the
corresponding tanks are given by hd1, hz and hd2 respectively.
The pumps for delivering inflows are variable speed pumps
The International journal of analytical and experimental modal analysis
Volume XII, Issue III, March/2020
ISSN NO:0886-9367
Page No:1918
13. which deliver flow ranges from 0 to rated flow based
on the input signal value (0-5V) given to the pump. The
experimental setup is given in figure A.1, whose
specifications are given in table A.2.
Table A.1
Experimental Values Of Discharge Coefficients Of Hand
Valves
Discharge
coefficient
Value(m2
)
Discharge
coefficient
Value(m2
)
k1 2.6363x10-5
k4 3.4316 x10-5
k2 2.4891 x10-5
k6 2.2538 x10-5
k3 3.7984 x10-5
k5, k7 0
Table A.2
Values Of Different System Parameters
Parameter Value
Tank height 0.60m
Tank over flow height
0.55m
Rated flow rate of pumps 240 lph
Input voltage to pump 0 –5 V
Tank inner diameter 0.15m
Inter connecting pipes inner diameter 0.0125m
Figure A.1: Experimental Setup of autonomous hybrid three –
tank system
The International journal of analytical and experimental modal analysis
Volume XII, Issue III, March/2020
ISSN NO:0886-9367
Page No:1919
14. The International journal of analytical and experimental modal analysis
Volume XII, Issue III, March/2020
ISSN NO:0886-9367
Page No:1920