This correspondence describes a method to achieve deadbeat response in higher-order servo systems using a single switching operation of the input command signal. Specifically:
- The closed-loop transfer function of the system must have distinct real roots for the deadbeat response condition to be satisfied.
- By suitably controlling the input command signal through a single switching operation, the derivatives of the output response can be driven to zero simultaneously, resulting in deadbeat response.
- This is achieved when the real parts of all the roots of the characteristic equation are equal, causing all exponential terms in the output response expression to have the same value and go to zero at the same time.
Sliding Mode Controller Design for Hybrid Synchronization of Hyperchaotic Che...ijcsa
This paper derives new results for the design of sliding mode controller for the hybrid synchronization of identical hyperchaotic Chen systems (Jia, Dai and Hui, 2010). The synchronizer results derived in this paper for the hybrid synchronization of identical hyperchaotic Chen systems are established using Lyapunov stability theory. Since the Lyapunov exponents are not required for these calculations, the sliding mode control method is very effective and convenient to achieve hybrid synchronization of the
identical hyperchaotic Chen systems. Numerical simulations are shown to illustrate and validate the hybrid synchronization schemes derived in this paper for the identical hyperchaotic Chen systems.
SLIDING MODE CONTROLLER DESIGN FOR SYNCHRONIZATION OF SHIMIZU-MORIOKA CHAOTIC...ijistjournal
This paper investigates the global chaos synchronization of identical Shimizhu-Morioka chaotic systems (Shimizu and Morioka, 1980) by sliding mode control. The stability results derived in this paper for the complete synchronization of identical Shimizu-Morioka chaotic systems are established using Lyapunov stability theory. Since the Lyapunov exponents are not required for these calculations, the sliding mode control method is very effective and convenient to achieve global chaos synchronization of the identical Shimizu-Morioka chaotic systems. Numerical simulations are shown to illustrate and validate the synchronization schemes derived in this paper for the identical Shimizu-Morioka systems.
SLIDING MODE CONTROLLER DESIGN FOR GLOBAL CHAOS SYNCHRONIZATION OF COULLET SY...ijistjournal
This paper derives new results for the design of sliding mode controller for the global chaos synchronization of identical Coullet systems (1981). The synchronizer results derived in this paper for the complete chaos synchronization of identical hyperchaotic systems are established using sliding control theory and Lyapunov stability theory. Since the Lyapunov exponents are not required for these calculations, the sliding mode control method is very effective and convenient to achieve global chaos synchronization of the identical Coullet systems. Numerical simulations are shown to illustrate and validate the synchronization schemes derived in this paper for the identical Coullet systems.
HYBRID SYNCHRONIZATION OF HYPERCHAOTIC LIU SYSTEMS VIA SLIDING MODE CONTROLijccmsjournal
This paper derives new results for the hybrid synchronization of identical hyperchaotic Liu systems (Liu,
Liu and Zhang, 2008) via sliding mode control. In hybrid synchronization of master and slave systems,
the odd states of the two systems are completely synchronized, while their even states are anti-
synchronized. The stability results derived in this paper for the hybrid synchronization of identical
hyperchaotic Liu systems have been proved using Lyapunov stability theory. Since the Lyapunov
exponents are not required for these calculations, the sliding mode control method is very effective and
convenient to achieve anti- synchronization of the identical hyperchaotic Liu systems. Numerical
simulations are shown to illustrate and validate the hybrid synchronization schemes derived in this paper
for the identical hyperchaotic Liu systems.
Anti-Synchronization Of Four-Scroll Chaotic Systems Via Sliding Mode Control IJITCA Journal
In this paper, new results are derived for the anti-synchronization of identical Liu-Chen four-scroll chaotic systems (Liu and Chen, 2004) and identical Lü-Chen-Cheng four-scroll chaotic systems (Lü,Chen and Cheng, 2004) by sliding mode control. The stability results derived in this paper for the antisynchronization of identical four-scroll chaotic systems are established using sliding mode control and Lyapunov stability theory. Since the Lyapunov exponents are not required for these calculations, the sliding mode control method is very effective and convenient to achieve anti-synchronization of the identical four-scroll chaotic systems. Numerical simulations are shown to illustrate and validate the antisynchronization schemes derived in this paper for the identical four-scroll systems
Stochastic Modeling Neutral Evolution by an Iambp of Cortisol Secretion of Br...IJERA Editor
Objective Fatigue is one of the most common and distressing symptoms by cancer patients and survivors. To evaluate cortisol responses to an experimental psychologic stressor in fatigued and non fatigued survivors. The focus is the frequency spectrum of the Infinite-Allele Markov branching process (IAMBP), namely the proportion having a given number of copies at a specified time point.
Generalized Laplace - Mellin Integral TransformationIJERA Editor
The main propose of this paper is to generalized Laplace-Mellin Integral Transformation in between the positive regions of real axis. We have derived some new properties and theorems .And give selected tables for Laplace-Mellin Integral Transformation.
Sliding Mode Controller Design for Hybrid Synchronization of Hyperchaotic Che...ijcsa
This paper derives new results for the design of sliding mode controller for the hybrid synchronization of identical hyperchaotic Chen systems (Jia, Dai and Hui, 2010). The synchronizer results derived in this paper for the hybrid synchronization of identical hyperchaotic Chen systems are established using Lyapunov stability theory. Since the Lyapunov exponents are not required for these calculations, the sliding mode control method is very effective and convenient to achieve hybrid synchronization of the
identical hyperchaotic Chen systems. Numerical simulations are shown to illustrate and validate the hybrid synchronization schemes derived in this paper for the identical hyperchaotic Chen systems.
SLIDING MODE CONTROLLER DESIGN FOR SYNCHRONIZATION OF SHIMIZU-MORIOKA CHAOTIC...ijistjournal
This paper investigates the global chaos synchronization of identical Shimizhu-Morioka chaotic systems (Shimizu and Morioka, 1980) by sliding mode control. The stability results derived in this paper for the complete synchronization of identical Shimizu-Morioka chaotic systems are established using Lyapunov stability theory. Since the Lyapunov exponents are not required for these calculations, the sliding mode control method is very effective and convenient to achieve global chaos synchronization of the identical Shimizu-Morioka chaotic systems. Numerical simulations are shown to illustrate and validate the synchronization schemes derived in this paper for the identical Shimizu-Morioka systems.
SLIDING MODE CONTROLLER DESIGN FOR GLOBAL CHAOS SYNCHRONIZATION OF COULLET SY...ijistjournal
This paper derives new results for the design of sliding mode controller for the global chaos synchronization of identical Coullet systems (1981). The synchronizer results derived in this paper for the complete chaos synchronization of identical hyperchaotic systems are established using sliding control theory and Lyapunov stability theory. Since the Lyapunov exponents are not required for these calculations, the sliding mode control method is very effective and convenient to achieve global chaos synchronization of the identical Coullet systems. Numerical simulations are shown to illustrate and validate the synchronization schemes derived in this paper for the identical Coullet systems.
HYBRID SYNCHRONIZATION OF HYPERCHAOTIC LIU SYSTEMS VIA SLIDING MODE CONTROLijccmsjournal
This paper derives new results for the hybrid synchronization of identical hyperchaotic Liu systems (Liu,
Liu and Zhang, 2008) via sliding mode control. In hybrid synchronization of master and slave systems,
the odd states of the two systems are completely synchronized, while their even states are anti-
synchronized. The stability results derived in this paper for the hybrid synchronization of identical
hyperchaotic Liu systems have been proved using Lyapunov stability theory. Since the Lyapunov
exponents are not required for these calculations, the sliding mode control method is very effective and
convenient to achieve anti- synchronization of the identical hyperchaotic Liu systems. Numerical
simulations are shown to illustrate and validate the hybrid synchronization schemes derived in this paper
for the identical hyperchaotic Liu systems.
Anti-Synchronization Of Four-Scroll Chaotic Systems Via Sliding Mode Control IJITCA Journal
In this paper, new results are derived for the anti-synchronization of identical Liu-Chen four-scroll chaotic systems (Liu and Chen, 2004) and identical Lü-Chen-Cheng four-scroll chaotic systems (Lü,Chen and Cheng, 2004) by sliding mode control. The stability results derived in this paper for the antisynchronization of identical four-scroll chaotic systems are established using sliding mode control and Lyapunov stability theory. Since the Lyapunov exponents are not required for these calculations, the sliding mode control method is very effective and convenient to achieve anti-synchronization of the identical four-scroll chaotic systems. Numerical simulations are shown to illustrate and validate the antisynchronization schemes derived in this paper for the identical four-scroll systems
Stochastic Modeling Neutral Evolution by an Iambp of Cortisol Secretion of Br...IJERA Editor
Objective Fatigue is one of the most common and distressing symptoms by cancer patients and survivors. To evaluate cortisol responses to an experimental psychologic stressor in fatigued and non fatigued survivors. The focus is the frequency spectrum of the Infinite-Allele Markov branching process (IAMBP), namely the proportion having a given number of copies at a specified time point.
Generalized Laplace - Mellin Integral TransformationIJERA Editor
The main propose of this paper is to generalized Laplace-Mellin Integral Transformation in between the positive regions of real axis. We have derived some new properties and theorems .And give selected tables for Laplace-Mellin Integral Transformation.
Adaptive Projective Lag Synchronization of T and Lu Chaotic Systems IJECEIAES
In this paper, the synchronization problem of T chaotic system and Lu chaotic system is studied. The parameter of the drive T chaotic system is considered unknown. An adaptive projective lag control method and also parameter estimation law are designed to achieve chaos synchronization problem between two chaotic systems. Then Lyapunov stability theorem is utilized to prove the validity of the proposed control method. After that, some numerical simulations are performed to assess the performance of the proposed method. The results show high accuracy of the proposed method in control and synchronization of chaotic systems.
Differential evolution (DE) algorithm has been applied as a powerful tool to find optimum switching angles for selective harmonic elimination pulse width modulation (SHEPWM) inverters. However, the DE’s performace is very dependent on its control parameters. Conventional DE generally uses either trial and error mechanism or tuning technique to determine appropriate values of the control paramaters. The disadvantage of this process is that it is very time comsuming. In this paper, an adaptive control parameter is proposed in order to speed up the DE algorithm in optimizing SHEPWM switching angles precisely. The proposed adaptive control parameter is proven to enhance the convergence process of the DE algorithm without requiring initial guesses. The results for both negative and positive modulation index (M) also indicate that the proposed adaptive DE is superior to the conventional DE in generating SHEPWM switching patterns.
Granger Causality Test: A Useful Descriptive Tool for Time Series DataIJMER
Interdependency of one or more variables on the other has been in the existence over long
time when it was discovered that one variable has to move or regress toward another following the
work done by Galton (1886); Pearson & Lee (1903); Kendall & Stuart, (1961); Johnston and
DiNardo, (1997); Gujarati, (2004) etc. It was in the light of this dependency over time the researcher
uses Granger Causality as an effective tool in time series Predictive causality using Nigeria GDP and
Money Supply to know the type of causality in existence in the two time series variables under
consideration and which one can statistically predicts the other.
The research work aimed at testing for nature of causality between GDP and money supply for
Federal Republic of Nigeria for the period of thirty years using the data sourced from Central Bank
of Nigeria Statistical Bulletin. After observing the various conditions of Granger causality test such
as ensuring stationarity in the variables under consideration; adding enough number of lags in the
prescribed model before estimation as Granger causality test is sensitive to the number of lags
introduced in the model; and as well as assuming the disturbance terms in the various models are
uncorrelated, the result of the analysis indicates a bilateral relationship between Nigeria GDP and
Money Supply. It implies Nigeria GDP Granger causes money Supply and vice versa. Based on the
result of this study, both Nigeria GDP and money Supply can be successfully model using Vector
Autoregressive Model since changes in one variable has a significant effect on the other variable.
PD plus error dependent integral nonlinear controllers for robot manipulatorsISA Interchange
In framework of traditional PID controllers, there are only three parameters available to tune, as a result, performance of the resulting system is always limited. As for Cartesian regulation of robot manipulators with uncertain Jacobian matrix, a scheme of PID controllers with error-dependent integral action is proposed. Compare with traditional PID controllers, the error-dependent integration is employed in the proposed PID controller, in which more parameters are available to be tuned. It provides additional flexibility for controller characteristics and tuning as well, and hence makes better transient performance. In addition, asymptotic stability of the resulting closed-loop system is guaranteed. All signals in the system are bounded when exogenous disturbances and measurement noises are bounded. Numerical example demonstrates the superior transient performance of the proposed controller over the traditional one via Cartesian space set-point manipulation of two-link robotic manipulator.
Feedback linearization and Backstepping controllers for Coupled Tanksieijjournal
This paper investigates the usage of some sophisticated and advanced nonlinear control algorithms inorder
to control a nonlinear Coupled Tanks System. The first control procedure is called the
Feedbacklinearisation control (FLC), this type of control has been found a successful in achieving a global
exponentialasymptotic stability, with very short time response, no significant overshooting is recordedand with a negligible norm of the error. The second control procedure is the approaches of Backsteppingcontrol (BC) which is a recursive procedure that interlaces the choice of a Lyapunov functionwith the design of feedback control, from simulation results it shown that this method preserves tracking, robust control and it can often solve stabilization problems with less restrictive conditions may beencountered in other methods. Finally both of the proposed control schemes guarantee theasymptoticstability of the closed loop system meeting trajectory tracking objectives
FEEDBACK LINEARIZATION AND BACKSTEPPING CONTROLLERS FOR COUPLED TANKSieijjournal
This paper investigates the usage of some sophisticated and advanced nonlinear control algorithms inorder to control a nonlinear Coupled Tanks System. The first control procedure is called the Feedbacklinearisation control (FLC), this type of control has been found a successful in achieving a global exponentialasymptotic stability, with very short time response, no significant overshooting is recordedand with a negligible norm of the error. The second control procedure is the approaches of Backsteppingcontrol (BC) which is a recursive procedure that interlaces the choice of a Lyapunov functionwith the design of feedback control, from simulation results it shown that this method preserves tracking, robust control and it can often solve stabilization problems with less restrictive conditions may beencountered in other methods. Finally both of the proposed control schemes guarantee the asymptoticstability of the closed loop system meeting trajectory tracking objectives.
FEEDBACK LINEARIZATION AND BACKSTEPPING CONTROLLERS FOR COUPLED TANKSieijjournal
This paper investigates the usage of some sophisticated and advanced nonlinear control algorithms in order to control a nonlinear Coupled Tanks System. The first control procedure is called the Feedback linearisation control (FLC), this type of control has been found a successful in achieving a global exponential asymptotic stability, with very short time response, no significant overshooting is recorded and with a negligible norm of the error. The second control procedure is the approaches of Back stepping control (BC) which is a recursive procedure that interlaces the choice of a Lyapunov function with the design of feedback control, from simulation results it shown that this method preserves tracking, robust control and it can often solve stabilization problems with less restrictive conditions may been countered in other methods. Finally both of the proposed control schemes guarantee the asymptoticstability of the closed loop system meeting trajectory tracking objectives.
HYBRID SYNCHRONIZATION OF HYPERCHAOTIC LIU SYSTEMS VIA SLIDING MODE CONTROLijccmsjournal
This paper derives new results for the hybrid synchronization of identical hyperchaotic Liu systems (Liu, Liu and Zhang, 2008) via sliding mode control. In hybrid synchronization of master and slave systems, the odd states of the two systems are completely synchronized, while their even states are antisynchronized. The stability results derived in this paper for the hybrid synchronization of identical hyperchaotic Liu systems have been proved using Lyapunov stability theory. Since the Lyapunov exponents are not required for these calculations, the sliding mode control method is very effective and convenient to achieve anti- synchronization of the identical hyperchaotic Liu systems. Numerical simulations are shown to illustrate and validate the hybrid synchronization schemes derived in this paper for the identical hyperchaotic Liu systems.
Simulation, bifurcation, and stability analysis of a SEPIC converter control...IJECEIAES
This article presents some results of SEPIC converter dynamics when controlled by a center pulse width modulator controller (CPWM). The duty cycle is calculated using the ZAD (Zero Average Dynamics) technique. Results obtained using this technique show a great variety of non-linear phenomena such as bifurcations and chaos, as parameters associated with the switching surface. These phenomena have been studied in the present paper in numerical form. Simulations were done in MATLAB.
The Polysolenoid Linear Motor (PLM) have been playing a crucial role in many industrial aspects because it provides a straight motion directly without mediate mechanical actuators. Some control methods for PLM based on Rotational Motor are applied to obtain several good performances, but position and velocity constraints which are important in real systems are ignored. In this paper, we analysis control problem of tracking position in PLM under state-independent disturbances via min-max model predictive control. The proposed controller brings tracking position error converge to zero and satisfies state including position and velocity and input constraints. The simulation results validity a good efficiency of the proposed controller.
SLIDING MODE CONTROLLER DESIGN FOR GLOBAL CHAOS SYNCHRONIZATION OF COULLET SY...ijistjournal
This paper derives new results for the design of sliding mode controller for the global chaos synchronization of identical Coullet systems (1981). The synchronizer results derived in this paper for the complete chaos synchronization of identical hyperchaotic systems are established using sliding control theory and Lyapunov stability theory. Since the Lyapunov exponents are not required for these calculations, the sliding mode control method is very effective and convenient to achieve global chaos synchronization of the identical Coullet systems. Numerical simulations are shown to illustrate and validate the synchronization schemes derived in this paper for the identical Coullet systems.
SLIDING CONTROLLER DESIGN FOR THE GLOBAL CHAOS SYNCHRONIZATION OF IDENTICAL H...ijait
This paper establishes new results for the sliding controller design for the global chaos synchronization of identical hyperchaotic Yujun systems (2010). Hyperchaotic systems are chaotic nonlinear systems having more than one positive Lyapunov exponent. Because of the complex dynamics properties of hyperchaotic system such as high capacity, high security and high efficiency, they are very useful in secure
communication devices and data encryption. Using sliding mode control theory and Lyapunov stability theory, a general result has been obtained for the global chaos synchronization of identical chaotic nonlinear systems. As an application of this general result, this paper designs a sliding controller for the
global chaos synchronization of hyperchaotic Yujun systems. Numerical results and simulations are shown to validate the proposed sliding controller design and demonstrate its effectiveness in achieving global chaos synchronization of hyperchaotic Yujun systems.
Hybrid Chaos Synchronization of Hyperchaotic Newton-Leipnik Systems by Slidin...ijctcm
This paper investigates the hybrid chaos synchronization of identical hyperchaotic Newton-Leipnik systems (Ghosh and Bhattacharya, 2010) by sliding mode control. The stability results derived in this paper for the hybrid chaos synchronization of identical hyperchaotic Newton-Leipnik systems are established using Lyapunov stability theory. Hybrid synchronization of hyperchaotic Newton-Leipnik systems is achieved through the complete synchronization of first and third states of the systems and the anti-synchronization of second and fourth states of the master and slave systems. Since the Lyapunov exponents are not required for these calculations, the sliding mode control is very effective and convenient to achieve hybrid chaos synchronization of the identical hyperchaotic Newton-Leipnik systems. Numerical simulations are shown to validate and demonstrate the effectiveness of the synchronization schemes derived in this paper.
Simple Exponential Observer Design for the Generalized Liu Chaotic Systemijtsrd
In this paper, the generalized Liu chaotic system is firstly introduced and the state observation problem of such a system is investigated. Based on the time-domain approach with differential and integral equalities, a novel state observer for the generalized Liu chaotic system is constructed to ensure the global exponential stability of the resulting error system. Besides, the guaranteed exponential convergence rate can be precisely calculated. Finally, numerical simulations are presented to exhibit the effectiveness and feasibility of the obtained results. Yeong-Jeu Sun"Simple Exponential Observer Design for the Generalized Liu Chaotic System" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-2 | Issue-1 , December 2017, URL: http://www.ijtsrd.com/papers/ijtsrd7126.pdf http://www.ijtsrd.com/engineering/engineering-maths/7126/simple-exponential-observer-design-for-the-generalized-liu-chaotic-system/yeong-jeu-sun
SLIDING MODE CONTROLLER DESIGN FOR SYNCHRONIZATION OF SHIMIZU-MORIOKA CHAOTIC...ijistjournal
This paper investigates the global chaos synchronization of identical Shimizhu-Morioka chaotic systems (Shimizu and Morioka, 1980) by sliding mode control. The stability results derived in this paper for the complete synchronization of identical Shimizu-Morioka chaotic systems are established using Lyapunov stability theory. Since the Lyapunov exponents are not required for these calculations, the sliding mode control method is very effective and convenient to achieve global chaos synchronization of the identical Shimizu-Morioka chaotic systems. Numerical simulations are shown to illustrate and validate the synchronization schemes derived in this paper for the identical Shimizu-Morioka systems.
TEST GENERATION FOR ANALOG AND MIXED-SIGNAL CIRCUITS USING HYBRID SYSTEM MODELSVLSICS Design
In this paper we propose an approach for testing time-domain properties of analog and mixed-signal circuits. The approach is based on an adaptation of a recently developed test generation technique for hybrid systems and a new concept of coverage for such systems. The approach is illustrated by its application to some benchmark circuits.
Adaptive Projective Lag Synchronization of T and Lu Chaotic Systems IJECEIAES
In this paper, the synchronization problem of T chaotic system and Lu chaotic system is studied. The parameter of the drive T chaotic system is considered unknown. An adaptive projective lag control method and also parameter estimation law are designed to achieve chaos synchronization problem between two chaotic systems. Then Lyapunov stability theorem is utilized to prove the validity of the proposed control method. After that, some numerical simulations are performed to assess the performance of the proposed method. The results show high accuracy of the proposed method in control and synchronization of chaotic systems.
Differential evolution (DE) algorithm has been applied as a powerful tool to find optimum switching angles for selective harmonic elimination pulse width modulation (SHEPWM) inverters. However, the DE’s performace is very dependent on its control parameters. Conventional DE generally uses either trial and error mechanism or tuning technique to determine appropriate values of the control paramaters. The disadvantage of this process is that it is very time comsuming. In this paper, an adaptive control parameter is proposed in order to speed up the DE algorithm in optimizing SHEPWM switching angles precisely. The proposed adaptive control parameter is proven to enhance the convergence process of the DE algorithm without requiring initial guesses. The results for both negative and positive modulation index (M) also indicate that the proposed adaptive DE is superior to the conventional DE in generating SHEPWM switching patterns.
Granger Causality Test: A Useful Descriptive Tool for Time Series DataIJMER
Interdependency of one or more variables on the other has been in the existence over long
time when it was discovered that one variable has to move or regress toward another following the
work done by Galton (1886); Pearson & Lee (1903); Kendall & Stuart, (1961); Johnston and
DiNardo, (1997); Gujarati, (2004) etc. It was in the light of this dependency over time the researcher
uses Granger Causality as an effective tool in time series Predictive causality using Nigeria GDP and
Money Supply to know the type of causality in existence in the two time series variables under
consideration and which one can statistically predicts the other.
The research work aimed at testing for nature of causality between GDP and money supply for
Federal Republic of Nigeria for the period of thirty years using the data sourced from Central Bank
of Nigeria Statistical Bulletin. After observing the various conditions of Granger causality test such
as ensuring stationarity in the variables under consideration; adding enough number of lags in the
prescribed model before estimation as Granger causality test is sensitive to the number of lags
introduced in the model; and as well as assuming the disturbance terms in the various models are
uncorrelated, the result of the analysis indicates a bilateral relationship between Nigeria GDP and
Money Supply. It implies Nigeria GDP Granger causes money Supply and vice versa. Based on the
result of this study, both Nigeria GDP and money Supply can be successfully model using Vector
Autoregressive Model since changes in one variable has a significant effect on the other variable.
PD plus error dependent integral nonlinear controllers for robot manipulatorsISA Interchange
In framework of traditional PID controllers, there are only three parameters available to tune, as a result, performance of the resulting system is always limited. As for Cartesian regulation of robot manipulators with uncertain Jacobian matrix, a scheme of PID controllers with error-dependent integral action is proposed. Compare with traditional PID controllers, the error-dependent integration is employed in the proposed PID controller, in which more parameters are available to be tuned. It provides additional flexibility for controller characteristics and tuning as well, and hence makes better transient performance. In addition, asymptotic stability of the resulting closed-loop system is guaranteed. All signals in the system are bounded when exogenous disturbances and measurement noises are bounded. Numerical example demonstrates the superior transient performance of the proposed controller over the traditional one via Cartesian space set-point manipulation of two-link robotic manipulator.
Feedback linearization and Backstepping controllers for Coupled Tanksieijjournal
This paper investigates the usage of some sophisticated and advanced nonlinear control algorithms inorder
to control a nonlinear Coupled Tanks System. The first control procedure is called the
Feedbacklinearisation control (FLC), this type of control has been found a successful in achieving a global
exponentialasymptotic stability, with very short time response, no significant overshooting is recordedand with a negligible norm of the error. The second control procedure is the approaches of Backsteppingcontrol (BC) which is a recursive procedure that interlaces the choice of a Lyapunov functionwith the design of feedback control, from simulation results it shown that this method preserves tracking, robust control and it can often solve stabilization problems with less restrictive conditions may beencountered in other methods. Finally both of the proposed control schemes guarantee theasymptoticstability of the closed loop system meeting trajectory tracking objectives
FEEDBACK LINEARIZATION AND BACKSTEPPING CONTROLLERS FOR COUPLED TANKSieijjournal
This paper investigates the usage of some sophisticated and advanced nonlinear control algorithms inorder to control a nonlinear Coupled Tanks System. The first control procedure is called the Feedbacklinearisation control (FLC), this type of control has been found a successful in achieving a global exponentialasymptotic stability, with very short time response, no significant overshooting is recordedand with a negligible norm of the error. The second control procedure is the approaches of Backsteppingcontrol (BC) which is a recursive procedure that interlaces the choice of a Lyapunov functionwith the design of feedback control, from simulation results it shown that this method preserves tracking, robust control and it can often solve stabilization problems with less restrictive conditions may beencountered in other methods. Finally both of the proposed control schemes guarantee the asymptoticstability of the closed loop system meeting trajectory tracking objectives.
FEEDBACK LINEARIZATION AND BACKSTEPPING CONTROLLERS FOR COUPLED TANKSieijjournal
This paper investigates the usage of some sophisticated and advanced nonlinear control algorithms in order to control a nonlinear Coupled Tanks System. The first control procedure is called the Feedback linearisation control (FLC), this type of control has been found a successful in achieving a global exponential asymptotic stability, with very short time response, no significant overshooting is recorded and with a negligible norm of the error. The second control procedure is the approaches of Back stepping control (BC) which is a recursive procedure that interlaces the choice of a Lyapunov function with the design of feedback control, from simulation results it shown that this method preserves tracking, robust control and it can often solve stabilization problems with less restrictive conditions may been countered in other methods. Finally both of the proposed control schemes guarantee the asymptoticstability of the closed loop system meeting trajectory tracking objectives.
HYBRID SYNCHRONIZATION OF HYPERCHAOTIC LIU SYSTEMS VIA SLIDING MODE CONTROLijccmsjournal
This paper derives new results for the hybrid synchronization of identical hyperchaotic Liu systems (Liu, Liu and Zhang, 2008) via sliding mode control. In hybrid synchronization of master and slave systems, the odd states of the two systems are completely synchronized, while their even states are antisynchronized. The stability results derived in this paper for the hybrid synchronization of identical hyperchaotic Liu systems have been proved using Lyapunov stability theory. Since the Lyapunov exponents are not required for these calculations, the sliding mode control method is very effective and convenient to achieve anti- synchronization of the identical hyperchaotic Liu systems. Numerical simulations are shown to illustrate and validate the hybrid synchronization schemes derived in this paper for the identical hyperchaotic Liu systems.
Simulation, bifurcation, and stability analysis of a SEPIC converter control...IJECEIAES
This article presents some results of SEPIC converter dynamics when controlled by a center pulse width modulator controller (CPWM). The duty cycle is calculated using the ZAD (Zero Average Dynamics) technique. Results obtained using this technique show a great variety of non-linear phenomena such as bifurcations and chaos, as parameters associated with the switching surface. These phenomena have been studied in the present paper in numerical form. Simulations were done in MATLAB.
The Polysolenoid Linear Motor (PLM) have been playing a crucial role in many industrial aspects because it provides a straight motion directly without mediate mechanical actuators. Some control methods for PLM based on Rotational Motor are applied to obtain several good performances, but position and velocity constraints which are important in real systems are ignored. In this paper, we analysis control problem of tracking position in PLM under state-independent disturbances via min-max model predictive control. The proposed controller brings tracking position error converge to zero and satisfies state including position and velocity and input constraints. The simulation results validity a good efficiency of the proposed controller.
SLIDING MODE CONTROLLER DESIGN FOR GLOBAL CHAOS SYNCHRONIZATION OF COULLET SY...ijistjournal
This paper derives new results for the design of sliding mode controller for the global chaos synchronization of identical Coullet systems (1981). The synchronizer results derived in this paper for the complete chaos synchronization of identical hyperchaotic systems are established using sliding control theory and Lyapunov stability theory. Since the Lyapunov exponents are not required for these calculations, the sliding mode control method is very effective and convenient to achieve global chaos synchronization of the identical Coullet systems. Numerical simulations are shown to illustrate and validate the synchronization schemes derived in this paper for the identical Coullet systems.
SLIDING CONTROLLER DESIGN FOR THE GLOBAL CHAOS SYNCHRONIZATION OF IDENTICAL H...ijait
This paper establishes new results for the sliding controller design for the global chaos synchronization of identical hyperchaotic Yujun systems (2010). Hyperchaotic systems are chaotic nonlinear systems having more than one positive Lyapunov exponent. Because of the complex dynamics properties of hyperchaotic system such as high capacity, high security and high efficiency, they are very useful in secure
communication devices and data encryption. Using sliding mode control theory and Lyapunov stability theory, a general result has been obtained for the global chaos synchronization of identical chaotic nonlinear systems. As an application of this general result, this paper designs a sliding controller for the
global chaos synchronization of hyperchaotic Yujun systems. Numerical results and simulations are shown to validate the proposed sliding controller design and demonstrate its effectiveness in achieving global chaos synchronization of hyperchaotic Yujun systems.
Hybrid Chaos Synchronization of Hyperchaotic Newton-Leipnik Systems by Slidin...ijctcm
This paper investigates the hybrid chaos synchronization of identical hyperchaotic Newton-Leipnik systems (Ghosh and Bhattacharya, 2010) by sliding mode control. The stability results derived in this paper for the hybrid chaos synchronization of identical hyperchaotic Newton-Leipnik systems are established using Lyapunov stability theory. Hybrid synchronization of hyperchaotic Newton-Leipnik systems is achieved through the complete synchronization of first and third states of the systems and the anti-synchronization of second and fourth states of the master and slave systems. Since the Lyapunov exponents are not required for these calculations, the sliding mode control is very effective and convenient to achieve hybrid chaos synchronization of the identical hyperchaotic Newton-Leipnik systems. Numerical simulations are shown to validate and demonstrate the effectiveness of the synchronization schemes derived in this paper.
Simple Exponential Observer Design for the Generalized Liu Chaotic Systemijtsrd
In this paper, the generalized Liu chaotic system is firstly introduced and the state observation problem of such a system is investigated. Based on the time-domain approach with differential and integral equalities, a novel state observer for the generalized Liu chaotic system is constructed to ensure the global exponential stability of the resulting error system. Besides, the guaranteed exponential convergence rate can be precisely calculated. Finally, numerical simulations are presented to exhibit the effectiveness and feasibility of the obtained results. Yeong-Jeu Sun"Simple Exponential Observer Design for the Generalized Liu Chaotic System" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-2 | Issue-1 , December 2017, URL: http://www.ijtsrd.com/papers/ijtsrd7126.pdf http://www.ijtsrd.com/engineering/engineering-maths/7126/simple-exponential-observer-design-for-the-generalized-liu-chaotic-system/yeong-jeu-sun
SLIDING MODE CONTROLLER DESIGN FOR SYNCHRONIZATION OF SHIMIZU-MORIOKA CHAOTIC...ijistjournal
This paper investigates the global chaos synchronization of identical Shimizhu-Morioka chaotic systems (Shimizu and Morioka, 1980) by sliding mode control. The stability results derived in this paper for the complete synchronization of identical Shimizu-Morioka chaotic systems are established using Lyapunov stability theory. Since the Lyapunov exponents are not required for these calculations, the sliding mode control method is very effective and convenient to achieve global chaos synchronization of the identical Shimizu-Morioka chaotic systems. Numerical simulations are shown to illustrate and validate the synchronization schemes derived in this paper for the identical Shimizu-Morioka systems.
TEST GENERATION FOR ANALOG AND MIXED-SIGNAL CIRCUITS USING HYBRID SYSTEM MODELSVLSICS Design
In this paper we propose an approach for testing time-domain properties of analog and mixed-signal circuits. The approach is based on an adaptation of a recently developed test generation technique for hybrid systems and a new concept of coverage for such systems. The approach is illustrated by its application to some benchmark circuits.
Test Generation for Analog and Mixed-Signal Circuits Using Hybrid System Mode...VLSICS Design
In this paper we propose an approach for testing time-domain properties of analog and mixed-signal circuits. The approach is based on an adaptation of a recently developed test generation technique for hybrid systems and a new concept of coverage for such systems. The approach is illustrated by its application to some benchmark circuits.
The International Journal of Information Technology, Control and Automation (...IJITCA Journal
The International Journal of Information Technology, Control and Automation (IJITCA) is a Quarterly open access peer-reviewed journal that publishes articles which contribute new results in all areas of Information Technology (IT), Control Systems and Automation Engineering. The journal focuses on all technical and practical aspects of IT, Control Systems and Automation with applications in real-world engineering and scientific problems. The goal of this journal is to bring together researchers and practitioners from academia and industry to focus on information technology, control engineering, automation, modeling concepts and establishing new collaborations in these areas.
Authors are invited to contribute to this journal by submitting articles that illustrate research results, projects, surveying works and industrial experiences that describe significant advances in Information Technology, Control Systems and Automation.
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which was proposed by D. Li (2007). First, adaptive control laws are determined to stabilize the Lü-like
attractor to its unstable equilibrium at the origin. These adaptive laws are established using Lyapunov
stability theory. Then adaptive synchronization laws are determined so as to achieve global chaos
synchronization of identical Lü-like attractors with unknown parameters. Numerical simulations are
presented to validate and demonstrate the effectiveness of the proposed adaptive control and
synchronization schemes for the Lü-like attractor.
A Comparative study of controllers for stabilizing a Rotary Inverted Pendulumijccmsjournal
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1966 bristol, e. - on a new measure of interaction for multivariable process control
1. 1966 CORRESPONDENCE 133
where
From ( 2 ) and (6) wecomputetheesti-
mate of s,,, given (butnot Ai,tobe
= {estimator of the form (6! {
.{ LUNV estimate of ~ " - 1 1
= R,,,n-~G?~. (15)
Similarly,we calculate the error variance
d, = L[& - L ) & - &)TI
as givenby (11), notingfrom (2j and (3)
that
Tocompletethetheorem, me dehnethe
conditional random variable A:,= ( . f n - ? z ) ,
and introduce the dataat time t, in the form
A& =zn-..I 2 r L =-.I "A?". Since
it fo!lows (Theorem l j that t_he LUNY
estimate A?,*, given 5,-1 and A&, only de-
pends uponA$.. Thus
EquaLions (9) and (12j follow from (16)
It is interesting to note that the forms
of the estimation and covariance equations
changewhenoneseekstoobtainthecon-
tinuousestimatorbylettingthetimebe-
inPfeiifer [j] it is shownthat the differ-
tween data samples go to zero. In particular,
ence equation for the discrete estimate con-
verges to a linear differential equation which
cont?ins thedataderivativebutnotthe
data itself. The derivationof the continuous
case does not depend upon introducing the
notion of continuouswhitenoise,indeed,
(4)and (5) make no sense if F(t, s) contains
a Dirac delta function.
CARLPFEIFFER
Space Guidance Theory Group
Jet Propulsion Lab.
Pasadena, Calif.
REFERESCES
[l] R. E. Kalman. "A new approach to linear filtering
and nrediction Droblems." 1.Basic EnRra. DD. 35-
i j - k a r c h 1960.
R.' E. Kalman, and R. S. B X ~ .*Kevnresults in
linearfilteringandpredictiontheory, J. Basic
Engrg., pp. 95-10?, March 1961.
linearpredictionandfilteringtheory;.Research
R. E. Kalman.Kewmethodsand,resultsin
Tech. Rept. 61-1. June 1961.
InstituteforAdvancedStudy,Baltimore. Md.,
C. G . Pfeiffer. "Seouential estimationoi correlated
_ _ ..
.. ~
. .
ctnrhastirvariables.' l e t ProuulsionLab.. P a s -..~-...~~ ~ ~ ~ ~~~~
IS] C. G. Pfeiffer. Continuousestimation of x-
dena.Calii.. Tecb Rept,-32-4k. July 196j.
quentiallycorrelatedrandomvariables."Jet
PropulsionLab.,Pasadena.Calii.,Tech.Rept.
[6] J. I,. Doob. Slochaslic Processcs. S e w Vork: !Vile?.
32-524, October 1963.
1953.
On a New Measure of Interaction
for Multivariable ProcessControl
IKTRODUCTIOS
Thiscorrespondencedescribes an inter-
actionmeasureformultivariablecontrol
developed to overcome theoretical and prac-
ticaldeficiencies of thematrixrepresenta-
tion as a toolfordesign of systems. A lin-
earized,time-invariant,multivariablepro-
cess described bya square gain matrix input-
outputrelation is assumed.Simpleexten-
sions of themeasureandits use to handle
dynamics,nonlinearity,andnonsquare
matrices exist. It is usually better, however,
to use the unmodified measure to determine
the initial design structure of control allow-
ingdynamicbehaviorandnonlinearityto
determine later details.
The control problem discussed is shown
inFig. 1 with mj and c; reconnectedwhere
the process is described by the matrix-vector
relation Ac=@Awz with a a processgain
matrixwhoseelementsareindicated as
+if. However, the matrix by itself is a poor
tool for classifying control properties of the
system. I t is highlydependentonscaling
(see Property 2) and choice of units. For in-
stance, the two matrices
10 10 10 10
(0 10) and ( 9 10)
having radically- differentcontrolcharac-
teristics, can be scaled by the same change
of units to apparently similar matrices
(: I:) and lo)
0 9 1
Scalingbecomesmoreconfusingwithlarge
systems.Conventionalproperties of ama-
trix, including norms, the determinant and
the eigenvalues also depend on scaling or on
theordering of rows andcolumnsinthe
matrix.Andthepropertiesthataremost
relatedtocontrolsuch as the eigenvalues
are also most dependent on variable scaling
and ordering,makingthemunsuitable as
measures of process structure.
Fig. 1. Controlledmultivariable system x%ith a n
input-outputpairdisconnected fromcontrol.
Theterminteractionarosebecausein-
dustry has often found it desirable to control
the multivariable process as if it were made
up of isolated single variable processes. The
resultingloops"interact."Xninteraction
measureattemptstoanswerthequestion:
Map 26, and October 8. 1965.
hianuscript received October 16. 1964; revised
How is themeasuredtransferfunctionbe-
tween a given manipulated variable mrz, and
a given controlled variableci affected by the
completecontrol of all othercontrolled
variables, as in Fig. l ?
DEFINITION
The measure taken to answer this ques-
tion is theratio of twogainsrepresenting
first the process gain in an isolated loop and,
second, theapparent processgainin that
sameloopwhenallothercontrolloopsare
closed. In the first case, the gain between ci
and mj is [(Aci/amj)IAwzk =O when k # j ]
=4;i, the openloopgain.Inthesecond
case, thesteady--stategain is
[(Aci/Aml)IAck = 0 when 0 k # i] = l/+ji-l,
where &,-I is anelement in theinverse
matrix.Noticethattheabstractionrepre-
sentedbythesegainsdoesnotdependon
the structure chosenfor the contro:lerex-
cept that it be effective in enforcing steady-
state values of c equal to thedesired values.
The ratio of these gains defines an array-11
with elements:
p..A ,$,..b.-1
i>- ' 1 . 1 % .
Thisdefinition is relatedinstatementand
purposetothe"conditionnumber"sug-
gested by von Neumann and Goldstine [2].
Otherquitedifferentmeasureshavebeen
proposed 131-[5]. Theauthorwas re-
centlyreferredtorelatedwork of Fiedler
and Ptak [6].
PROPERTIES OF THE MEASURE
The following properties are easily shown
1) A n y row or column sums to one.
2) The measure of a matrix is invariant
underscaling.(Scaling of a matrix
correspondstothemultiplication of
thematrixbytwogeneraldiagonal
matrices D' and D so that the scaled
matrix becomes 0'=D'aD.)
3jlThe only effect of altering the order
to be true:
of rowsorcolumnsin 0 is to intro-
duce the same alteration of order in
1M.
Measures much larger than one imply
a "nearly" singular gain matrix.
Thesubmeasure of an effectively
isolated subprocess is the sameas the
measure of thesubprocess. All other
elements of rows andcolumns corn-
mon to the submeasureare zero.
The measure shows up in calculations
of the changes introduced ina control
system caused by changes in process
parameters(andnonlinearit>-);for
instance, the relation
dpij = p<t(d4<1/+ii+d41<-'/4ji-').
The measure is an approximate mea-
sure of its own sensitivity.
Properties 7 and 8 relatetointeraction
induced dynamic behavior. Both properties
are generallytrueand holdrigorously if
integralcontrolactiondominates all other
process and control dynamics. This is not a
2. 134 IEEETR.WSACTIONS ON AUTOMATICCONTROLJANUARY
trivialcasesinceitcorresponds to ''loose''
or "conservative" control and sets the tenor
of practical control.
7 j The transfer function between ci and
m, measuredasinFig. 1 withall
other loops closed will benonmini-
mumphase or unstable if gij is
negative.
8) .-Itwo-by-twoprocesscontrolledby
twonegativefeedbackcontrollers
set loosely as beforein a minimum
loopsystemmustbestable if con-
trollers are assigned to variable pairs
with positive measure. The same sys-
tembutbasedonnegativemeasure
d l bestable only if one loop is in
positivefeedbackandthenonlvfor
certainratios of loopgains xvith the
negativefeedbackloopclosed.Sim-
ilar care is required in more complex
systems. Detailed generalizations can
be proven for three-by-three processes
and,therefore,for all systemsin
Ix-hich two-by-tn-o or three-b>--three
subprocessesdominate.
EX.UPLESASD DISCLXIOS
Figure 2 shows five examples of gain
matrices of two-by-twomultivariablepro-
cesses alongwiththemeasurecalculated
fromthem. In Fig. 2, (a),(b),and(c)
are an>- nonzero numbers and6 is a nonzero
number of absolutevaluemuchlessthan
one.Figure2(a)and(b)bothshow pro-
cesseswithnointeraction.Theprocess of
Fig. 2(c) givesa measure which also appears
toshownoninteractionas x-ould any tri-
angular matrix or matrix obtained by per-
muting rows orcolumns of atriangular
matrix.The scaling
scales Figs. 2(c) to2(a) in the limit as 01 ap-
proaches zero. Any two loop control system
appliedstablytoanydynamic process
whosegain matrix is that of Fig.2(a) will
alsobestable -hen appliedtoFig.2(cj.
Decoupling for this class of effective1)- non-
interacting process amounts to simple feed-
forwardand is alsoneverdestabilizing.
Stability is unchanged because in each case
no new loop is introduced by the interaction.
The process of Fig. 2(d)showsalmost
identical effects of eachmanipulatedvari-
ableoneachcontrolledvariable.Forthis
reason,independentcontrol of eachcon-
trolled variable is difficult to achieve prac-
tically. Sear singularity is shown by Prop-
ertv 1. Existence of negativemeasure is a
necessan-characteristic of nearlysingular
systems by Properties 4 and 1. Other prob-
lemsaremadeclearfromthemensureby
Properties 6, 7, and 8.
I n contrast to Fig. 2(d), Fig. ?(e) shows
aprocess in whicheachmanipulatedvari-
ablehaslargebutdifferingeffects on each
controlledvariable.Controlactions on in-
dependent tu; donot cancelone another,
and the system is moreeasil>-andinsensi-
tivel>- controlledLvith or without decoupling.
The character of thematrix is reflectedin
aninteractionmeasurehavingpositive
values less thanone.
Fig. 2. Table of gainmatrices a i t h theirinteraction
processes.(c) an interactingprocess whose inter-
measuretables for: (aiand(b)noninteracting
action is iree oi feedback paths, (d) a highly inter-
acting process with considerable control difficult,-.
and (e! a highly interacting process. vhose inter-
action iseasily decoupled.
Co~cLusros
The basiccharacter of thesetypes of
interactioncarriesoverintoa-by-npro-
cesses. The measure cat1 serve as a design
tool to selectpreferredprocesses andto
specify the control structure once a process
is selected. This control structureis specified
by a one-to-onepairing of thecontrolled
andmanipulatedvariablesas a basis for
control. Each pair may be closed in a single
loop in a minirnum loop s p t e m or more re-
fined decoupling may be used. In any case,
theprocedureamountstopicking a pre-
ferred principal diagonal to the matrix. The
examplesandpropertiessuggestthatthe
measurecorrespondingtothepairedvari-
ablesbepositiveandas close tooneas
possible. Numbersnegativeormuchlarger
than one are to be avoided and large nega-
tive numbers are particularly undesirable.
This design procedure is hardly complete
but it is simple to use, and it usually gives a
uniquedesignevenwhenstatedinsuch
qualitative terms. It is supported by Prop-
erty 8 as well as the intuitive argument and
hascorrelatedperfectly uithstandardde-
signs of actualindustrialprocesses.The
author hopes to be able to free the support-
ingexperimental data forpublication a t
some time i n the future.
EDGARH. BRISTOL
Foxboro Company
Foxboro, IIass.
REFERESCES
[l] F.B. Hildebrand, Mt-lhods nf.4pplit-d J i a f h r ~ ~ ~ a f i c s .
[ 2 ] J. ran Seumann and H. H. Goldstine. Xumerical
EnnlevoodCliffs. X. J.: Prentice-Hall, 1952.
in-erting of matrices of highorder. Proc. Amt-r.
Mafh. Sac.. vol. 2: ~p.~188-202.1951.
[3] 11. D. hIesaro-lc. A measure of interaction
and its application to control problems.' Systems
ResearchCenter.CaseInstitllte of Technoloy?-.
[41 R. Brocl;ett. "The control of linearmultivariable
Cleveland.Ohio,Rept. A-6-60.
systems. P1l.D. thesis. Case Institute of Technol-
[jl P. C. Clliu and. C . R. Webb. ".Analog computer
oxy. Cleveland. Ohio. 1962.
studv of amultl-ariablecontrolsvstem. Coelrol.
161 M . Fielderand V. Ptak. 'On matrices xvirh now
rX3. no.49. pp. ii-80.
cipalminors." Chekhoslmalskii.fale~nalicheskii
positiwoff-diagonalelementsandpositi-eprin-
Zharnal, vol. 12, PP. 382-400. 1962.
Dead Beat Response of Higher-
Order Servo Systems by Single
Switching Operation
Smithsuggested a method [I] for ob-
taining dead beat responseof lightly damped
second-orderservosystemstostepsignal
inputs. 111this method, the input command
has to be suitably controlled, which can be
effected bysingleswitchingoperation[2],
[3]. By such controlof the input signal it is
possible toobtaindeadbeatresponse of
higher-ordersystemsprovidedthesystems
havesuitabletransferfunctions.Thepur-
pose of thepresentcorrespondence is to
investigatethesetransferfunctions of
higher-ordersystems.
Co:lsider a closed loop transfer function
of annth-ordersystemas
bo--
hnSn+bn.lSn-'+ . . . +bS +bo
(1)
Ivhere the coefficients h are all real constants
and n arepositiveintegers.Thetransform
of the output response C(S),for a unit step
escitation function and for zero initial con-
ditions is
11-eshall assume that the roots of the equa-
tionB(S) =O areall distinct. LetS1S2.. .S,
bethe n distinctroots.Then C(S) canbe
expanded in the follo-ing form
wherethenumerators of thepartialfrac-
tions in (3j areconstants.Theoutput re-
sponse Cit) is given by
~ ( , t )= 1 + .A;exp C-S,~). (4)
The expression for the qth derivative of the
output can be written as
i-L
Sincetheinitialconditionsarezero, it fol-
l0n-s from (5) that the following relation is
satisfied
n
SPAi = 0 (6)
r - 1
for all valuesof q lying between 1 to n -1.
Sow, if at anyfinite time, all the deriva-
tives for the previous values of q are to at-
tain zero values simultaneously. all exponen-
tialtermsin (5) musthavethesame
value at that time. Since the roots are dis-
tinct, this can occur when the real parts of
all therootsareequal,that is, when the
roots lie on a lineparallel to the imaginary
axis of the complex plane. However, for ob-
tainingdeadbeatresponsebythesingle
switchingoperation it is required that all
the previous derivatives should attain zero
valuesbythetimethe firstderivative
Manuscript received August 2, 1965.