The purpose of this paper is to present a novel technique for analyzing the behavior of an industrial system stochastically by utilizing vague, imprecise, and uncertain data. In the present study two important tools namely Lambda-Tau methodology and particle swarm optimization are combinedly used to present a novel technique named as particle swarm optimization based Lambda-Tau (PSOBLT) for analyzing the behavior of a complex repairable system stochastically up to a desired degree of accuracy. Expressions of reliability indices like failure rate, repair time, mean time between failures (MTBF), expected number of failures (ENOF), reliability and availability for the system are obtained by using Lambda-Tau methodology and particle swarm optimization is used to construct their member- ship function. The interaction among the working units of the system is modeled with the help of Petri nets. The feeding unit of a paper mill situated in a northern part of India, producing approximately 200 ton of paper per day, has been considered to demonstrate the proposed approach. Sensitivity analysis of system’s behavior has also been done. The behavior analysis results computed by PSOBLT technique have a reduced region of prediction in comparison of existing technique region, i.e. uncertainties involved in the analysis are reduced. Thus, it may be a more useful analysis tool to assess the current system conditions and involved uncertainties.]]>

The purpose of this paper is to present a novel technique for analyzing the behavior of an industrial system stochastically by utilizing vague, imprecise, and uncertain data. In the present study two important tools namely Lambda-Tau methodology and particle swarm optimization are combinedly used to present a novel technique named as particle swarm optimization based Lambda-Tau (PSOBLT) for analyzing the behavior of a complex repairable system stochastically up to a desired degree of accuracy. Expressions of reliability indices like failure rate, repair time, mean time between failures (MTBF), expected number of failures (ENOF), reliability and availability for the system are obtained by using Lambda-Tau methodology and particle swarm optimization is used to construct their member- ship function. The interaction among the working units of the system is modeled with the help of Petri nets. The feeding unit of a paper mill situated in a northern part of India, producing approximately 200 ton of paper per day, has been considered to demonstrate the proposed approach. Sensitivity analysis of system’s behavior has also been done. The behavior analysis results computed by PSOBLT technique have a reduced region of prediction in comparison of existing technique region, i.e. uncertainties involved in the analysis are reduced. Thus, it may be a more useful analysis tool to assess the current system conditions and involved uncertainties.]]>

X–Z inverted pendulum is a new kind of inverted pendulum which can move with the combination of the vertical and horizontal forces. Through a new transformation, the X–Z inverted pendulum is decomposed into three simple models. Based on the simple models, sliding-mode control is applied to stabilization and tracking control of the inverted pendulum. The performance of the sliding mode control is compared with that of the PID control. Simulation results show that the design scheme of sliding-mode control is effective for the stabilization and tracking control of the X–Z inverted pendulum.]]>

X–Z inverted pendulum is a new kind of inverted pendulum which can move with the combination of the vertical and horizontal forces. Through a new transformation, the X–Z inverted pendulum is decomposed into three simple models. Based on the simple models, sliding-mode control is applied to stabilization and tracking control of the inverted pendulum. The performance of the sliding mode control is compared with that of the PID control. Simulation results show that the design scheme of sliding-mode control is effective for the stabilization and tracking control of the X–Z inverted pendulum.]]>

This paper considers the control problem of a class of uncertain switched systems deﬁned on polyhedral sets known as piecewise linear systems where, instead of the conventional Caratheodory solutions, Filippov solutions are studied. In other words, in contrast to the previous studies, solutions with inﬁnite switching in ﬁnite time along the facets and on faces of arbitrary dimensions are also taken into account. Firstly, established upon previous studies, a set of linear matrix inequalities are brought forward which determines the asymptotic stability of piecewise linear systems with Filippov solutions. Subsequently, bilinear matrix inequality conditions for synthesizing a robust controller with a guaranteed H1 performance are presented. Furthermore, these results has been generalized to the case of piecewise afﬁne systems. Finally, a V–K iteration algorithm is proposed to deal with the aforementioned bilinear matrix inequalities. The validity of the proposed method is veriﬁed through the analysis of two simulation examples.]]>

This paper considers the control problem of a class of uncertain switched systems deﬁned on polyhedral sets known as piecewise linear systems where, instead of the conventional Caratheodory solutions, Filippov solutions are studied. In other words, in contrast to the previous studies, solutions with inﬁnite switching in ﬁnite time along the facets and on faces of arbitrary dimensions are also taken into account. Firstly, established upon previous studies, a set of linear matrix inequalities are brought forward which determines the asymptotic stability of piecewise linear systems with Filippov solutions. Subsequently, bilinear matrix inequality conditions for synthesizing a robust controller with a guaranteed H1 performance are presented. Furthermore, these results has been generalized to the case of piecewise afﬁne systems. Finally, a V–K iteration algorithm is proposed to deal with the aforementioned bilinear matrix inequalities. The validity of the proposed method is veriﬁed through the analysis of two simulation examples.]]>

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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.]]>

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.]]>

This paper presents an improved reinforcement learning method to minimize electricity costs on the premise of satisfying the power balance and generation limit of units in a microgrid with grid- connected mode. Firstly, the microgrid control requirements are analyzed and the objective function of optimal control for microgrid is proposed. Then, a state variable ‘‘Average Electricity Price Trend’’ which is used to express the most possible transitions of the system is developed so as to reduce the complexity and randomicity of the microgrid, and a multi-agent architecture including agents, state variables, action variables and reward function is formulated. Furthermore, dynamic hierarchical reinforcement learning, based on change rate of key state variable, is established to carry out optimal policy exploration. The analysis shows that the proposed method is beneﬁcial to handle the problem of ‘‘curse of dimensionality’’ and speed up learning in the unknown large-scale world. Finally, the simulation results under JADE (Java Agent Development Framework) demonstrate the validity of the presented method in optimal control for a microgrid with grid-connected mode.]]>

This paper presents an improved reinforcement learning method to minimize electricity costs on the premise of satisfying the power balance and generation limit of units in a microgrid with grid- connected mode. Firstly, the microgrid control requirements are analyzed and the objective function of optimal control for microgrid is proposed. Then, a state variable ‘‘Average Electricity Price Trend’’ which is used to express the most possible transitions of the system is developed so as to reduce the complexity and randomicity of the microgrid, and a multi-agent architecture including agents, state variables, action variables and reward function is formulated. Furthermore, dynamic hierarchical reinforcement learning, based on change rate of key state variable, is established to carry out optimal policy exploration. The analysis shows that the proposed method is beneﬁcial to handle the problem of ‘‘curse of dimensionality’’ and speed up learning in the unknown large-scale world. Finally, the simulation results under JADE (Java Agent Development Framework) demonstrate the validity of the presented method in optimal control for a microgrid with grid-connected mode.]]>

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In this paper we propose sliding mode control strategies for the point-to-point motion control of a hoisting crane. The strategies employ time-varying switching lines (characterized by a constant angle of inclination) which move either with a constant deceleration or a constant velocity to the origin of the error state space. An appropriate design of these switching lines results in non-oscillatory convergence of the regulation error in the closed-loop system. Parameters of the lines are selected optimally in the sense of two criteria, i.e. integral absolute error (IAE) and integral of the time multiplied by the absolute error (ITAE). Furthermore, the velocity and acceleration constraints are explicitly taken into account in the optimization process. Theoretical considerations are veriﬁed by experimental tests conducted on a laboratory scale hoisting crane.]]>

In this paper we propose sliding mode control strategies for the point-to-point motion control of a hoisting crane. The strategies employ time-varying switching lines (characterized by a constant angle of inclination) which move either with a constant deceleration or a constant velocity to the origin of the error state space. An appropriate design of these switching lines results in non-oscillatory convergence of the regulation error in the closed-loop system. Parameters of the lines are selected optimally in the sense of two criteria, i.e. integral absolute error (IAE) and integral of the time multiplied by the absolute error (ITAE). Furthermore, the velocity and acceleration constraints are explicitly taken into account in the optimization process. Theoretical considerations are veriﬁed by experimental tests conducted on a laboratory scale hoisting crane.]]>

This paper presents an adaptive terminal sliding mode control (ATSMC) strategy for DC–DC buck converters. The idea behind this strategy is to use the terminal sliding mode control (TSMC) approach to assure ﬁnite time convergence of the output voltage error to the equilibrium point and integrate an adaptive law to the TSMC strategy so as to achieve a dynamic sliding line during the load variations. In addition, the inﬂuence of the controller parameters on the performance of closed-loop system is investigated. It is observed that the start up response of the output voltage becomes faster with increasing value of the fractional power used in the sliding function. On the other hand, the transient response of the output voltage, caused by the step change in the load, becomes faster with decreasing the value of the fractional power. Therefore, the value of fractional power is to be chosen to make a compromise between start up and transient responses of the converter. Performance of the proposed ATSMC strategy has been tested through computer simulations and experiments. The simulation results of the proposed ATSMC strategy are compared with the conventional SMC and TSMC strategies. It is shown that the ATSMC exhibits a considerable improvement in terms of a faster output voltage response during load changes.]]>

This paper presents an adaptive terminal sliding mode control (ATSMC) strategy for DC–DC buck converters. The idea behind this strategy is to use the terminal sliding mode control (TSMC) approach to assure ﬁnite time convergence of the output voltage error to the equilibrium point and integrate an adaptive law to the TSMC strategy so as to achieve a dynamic sliding line during the load variations. In addition, the inﬂuence of the controller parameters on the performance of closed-loop system is investigated. It is observed that the start up response of the output voltage becomes faster with increasing value of the fractional power used in the sliding function. On the other hand, the transient response of the output voltage, caused by the step change in the load, becomes faster with decreasing the value of the fractional power. Therefore, the value of fractional power is to be chosen to make a compromise between start up and transient responses of the converter. Performance of the proposed ATSMC strategy has been tested through computer simulations and experiments. The simulation results of the proposed ATSMC strategy are compared with the conventional SMC and TSMC strategies. It is shown that the ATSMC exhibits a considerable improvement in terms of a faster output voltage response during load changes.]]>

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Traditionally, in the redundancy allocation problem (RAP), two general classes of optimization problems are considered; reliability optimization and availability optimization. Contrary to reliability optimization, fewer researchers have studied availability optimization to find out the optimal combination of components type and redundancy levels for each subsystem in a system for maximizing (or minimizing) the objectives. In each problem it is assumed that either the entire components are repairable or they are non-repairable. However, in real world situations, systems usually consist of both repairable and non-repairable components. In this paper a new Mixed Integer Nonlinear Programming (MINLP) model is presented to analyze the availability optimization of a system with a given structure, using both repairable and non-repairable components, simultaneously. To find the solution of the introduced MINLP, an efficient Genetic Algorithm (GA) is also developed. Furthermore, to show the efficiency of the proposed GA, a numerical example is presented. Experimental results demonstrate that the proposed GA has a better performance compared to one of the most recommended algorithm in the literature.]]>

Traditionally, in the redundancy allocation problem (RAP), two general classes of optimization problems are considered; reliability optimization and availability optimization. Contrary to reliability optimization, fewer researchers have studied availability optimization to find out the optimal combination of components type and redundancy levels for each subsystem in a system for maximizing (or minimizing) the objectives. In each problem it is assumed that either the entire components are repairable or they are non-repairable. However, in real world situations, systems usually consist of both repairable and non-repairable components. In this paper a new Mixed Integer Nonlinear Programming (MINLP) model is presented to analyze the availability optimization of a system with a given structure, using both repairable and non-repairable components, simultaneously. To find the solution of the introduced MINLP, an efficient Genetic Algorithm (GA) is also developed. Furthermore, to show the efficiency of the proposed GA, a numerical example is presented. Experimental results demonstrate that the proposed GA has a better performance compared to one of the most recommended algorithm in the literature.]]>

This paper introduces a numerical method to estimate the region of attraction for polynomial nonlinear systems using sum of squares programming. This method computes a local Lyapunov function and an invariant set around a locally asymptotically stable equilibrium point. The invariant set is an estimation of the region of attraction for the equilibrium point. In order to enlarge the estimation, a subset of the invariant set defined by a shape factor is enlarged by solving a sum of squares optimization problem. In this paper, a new algorithm is proposed to select the shape factor based on the linearized dynamic model of the system. The shape factor is updated in each iteration using the computed local Lyapunov function from the previous iteration. The efficiency of the proposed method is shown by a few numerical examples.]]>

This paper introduces a numerical method to estimate the region of attraction for polynomial nonlinear systems using sum of squares programming. This method computes a local Lyapunov function and an invariant set around a locally asymptotically stable equilibrium point. The invariant set is an estimation of the region of attraction for the equilibrium point. In order to enlarge the estimation, a subset of the invariant set defined by a shape factor is enlarged by solving a sum of squares optimization problem. In this paper, a new algorithm is proposed to select the shape factor based on the linearized dynamic model of the system. The shape factor is updated in each iteration using the computed local Lyapunov function from the previous iteration. The efficiency of the proposed method is shown by a few numerical examples.]]>

This paper addresses the problem of global output feedback control for a class of nonlinear time-delay systems. The nonlinearities are dominated by a triangular form satisfying linear growth condition in the unmeasurable states with an unknown growth rate. With a change of coordinates, a linear-like controller is constructed, which avoids the repeated derivatives of the nonlinearities depending on the observer states and the dynamic gain in backstepping approach and therefore, simplifies the design procedure. Using the idea of universal control, we explicitly construct a universal-type adaptive output feedback controller which globally regulates all the states of the nonlinear time-delay systems.]]>

This paper addresses the problem of global output feedback control for a class of nonlinear time-delay systems. The nonlinearities are dominated by a triangular form satisfying linear growth condition in the unmeasurable states with an unknown growth rate. With a change of coordinates, a linear-like controller is constructed, which avoids the repeated derivatives of the nonlinearities depending on the observer states and the dynamic gain in backstepping approach and therefore, simplifies the design procedure. Using the idea of universal control, we explicitly construct a universal-type adaptive output feedback controller which globally regulates all the states of the nonlinear time-delay systems.]]>

This paper deals with the problem of forbidden states in discrete event systems based on Petri net models. So, a method is presented to prevent the system from entering these states by constructing a small number of generalized mutual exclusion constraints. This goal is achieved by solving three types of Integer Linear Programming problems. The problems are designed to verify the constraints that some of them are related to verifying authorized states and the others are related to avoiding forbidden states. The obtained constraints can be enforced on the system using a small number of control places. Moreover, the number of arcs related to these places is small, and the controller after connecting them is maximally permissive.]]>

This paper deals with the problem of forbidden states in discrete event systems based on Petri net models. So, a method is presented to prevent the system from entering these states by constructing a small number of generalized mutual exclusion constraints. This goal is achieved by solving three types of Integer Linear Programming problems. The problems are designed to verify the constraints that some of them are related to verifying authorized states and the others are related to avoiding forbidden states. The obtained constraints can be enforced on the system using a small number of control places. Moreover, the number of arcs related to these places is small, and the controller after connecting them is maximally permissive.]]>

This paper considers a single sensor and single actuator approach to the static feedback stabilization of nonlinear systems. This is essentially a remote control problem that is present in many engineering applications. The proposed method solves this problem that is less expensive to implement and more reliable in practice. Significant results are obtained on the design of controllers for stabilizing the nonlinear systems. Important issues on control implementation are also discussed. The proposed design method is validated through its application to nonlinear control of aircraft engines.]]>

This paper considers a single sensor and single actuator approach to the static feedback stabilization of nonlinear systems. This is essentially a remote control problem that is present in many engineering applications. The proposed method solves this problem that is less expensive to implement and more reliable in practice. Significant results are obtained on the design of controllers for stabilizing the nonlinear systems. Important issues on control implementation are also discussed. The proposed design method is validated through its application to nonlinear control of aircraft engines.]]>

In this paper, a fast terminal sliding mode control (FTSMC) scheme with double closed loops is proposed for the spacecraft attitude control. The FTSMC laws are included both in an inner control loop and an outer control loop. Firstly, a fast terminal sliding surface (FTSS) is constructed, which can drive the inner loop tracking-error and the outer loop tracking-error on the FTSS to converge to zero in finite time. Secondly, FTSMC strategy is designed by using Lyaponov’s method for ensuring the occurrence of the sliding motion in finite time, which can hold the character of fast transient response and improve the tracking accuracy. It is proved that FTSMC can guarantee the convergence of tracking-error in both approaching and sliding mode surface. Finally, simulation results demonstrate the effectiveness of the proposed control scheme.]]>

In this paper, a fast terminal sliding mode control (FTSMC) scheme with double closed loops is proposed for the spacecraft attitude control. The FTSMC laws are included both in an inner control loop and an outer control loop. Firstly, a fast terminal sliding surface (FTSS) is constructed, which can drive the inner loop tracking-error and the outer loop tracking-error on the FTSS to converge to zero in finite time. Secondly, FTSMC strategy is designed by using Lyaponov’s method for ensuring the occurrence of the sliding motion in finite time, which can hold the character of fast transient response and improve the tracking accuracy. It is proved that FTSMC can guarantee the convergence of tracking-error in both approaching and sliding mode surface. Finally, simulation results demonstrate the effectiveness of the proposed control scheme.]]>

This paper presents a method to model and design servo controllers for flexible ball screw drives with dynamic variations. A mathematical model describing the structural flexibility of the ball screw drive containing time-varying uncertainties and disturbances with unknown bounds is proposed. A mode-compensating adaptive backstepping sliding mode controller is designed to suppress the vibration. The time-varying uncertainties and disturbances represented in finite-term Fourier series can be estimated by updating the Fourier coefficients through function approximation technique. Adaptive laws are obtained from Lyapunov approach to guarantee the convergence and stability of the closed loop system. The simulation results indicate that the tracking accuracy is improved considerably with the proposed scheme when the time-varying parametric uncertainties and disturbances exist.]]>

This paper presents a method to model and design servo controllers for flexible ball screw drives with dynamic variations. A mathematical model describing the structural flexibility of the ball screw drive containing time-varying uncertainties and disturbances with unknown bounds is proposed. A mode-compensating adaptive backstepping sliding mode controller is designed to suppress the vibration. The time-varying uncertainties and disturbances represented in finite-term Fourier series can be estimated by updating the Fourier coefficients through function approximation technique. Adaptive laws are obtained from Lyapunov approach to guarantee the convergence and stability of the closed loop system. The simulation results indicate that the tracking accuracy is improved considerably with the proposed scheme when the time-varying parametric uncertainties and disturbances exist.]]>

A modified nonlinear autoregressive moving average with exogenous inputs (NARMAX) model-based state-space self-tuner with fault tolerance is proposed in this paper for the unknown nonlinear stochastic hybrid system with a direct transmission matrix from input to output. Through the off-line observer/Kalman filter identification method, one has a good initial guess of modified NARMAX model to reduce the on-line system identification process time. Then, based on the modified NARMAX-based system identification, a corresponding adaptive digital control scheme is presented for the unknown continuous-time nonlinear system, with an input–output direct transmission term, which also has measurement and system noises and inaccessible system states. Besides, an effective state space self-turner with fault tolerance scheme is presented for the unknown multivariable stochastic system. A quantitative criterion is suggested by comparing the innovation process error estimated by the Kalman filter estimation algorithm, so that a weighting matrix resetting technique by adjusting and resetting the covariance matrices of parameter estimate obtained by the Kalman filter estimation algorithm is utilized to achieve the parameter estimation for faulty system recovery. Consequently, the proposed method can effectively cope with partially abrupt and/or gradual system faults and input failures by the fault detection.]]>

A modified nonlinear autoregressive moving average with exogenous inputs (NARMAX) model-based state-space self-tuner with fault tolerance is proposed in this paper for the unknown nonlinear stochastic hybrid system with a direct transmission matrix from input to output. Through the off-line observer/Kalman filter identification method, one has a good initial guess of modified NARMAX model to reduce the on-line system identification process time. Then, based on the modified NARMAX-based system identification, a corresponding adaptive digital control scheme is presented for the unknown continuous-time nonlinear system, with an input–output direct transmission term, which also has measurement and system noises and inaccessible system states. Besides, an effective state space self-turner with fault tolerance scheme is presented for the unknown multivariable stochastic system. A quantitative criterion is suggested by comparing the innovation process error estimated by the Kalman filter estimation algorithm, so that a weighting matrix resetting technique by adjusting and resetting the covariance matrices of parameter estimate obtained by the Kalman filter estimation algorithm is utilized to achieve the parameter estimation for faulty system recovery. Consequently, the proposed method can effectively cope with partially abrupt and/or gradual system faults and input failures by the fault detection.]]>

This paper shows how to apply generalized eigenvalue minimization to processes that can be described by a first-order plus time-delay model with uncertain gain, time constant and delay. An algorithm to transform the uncertain first-order plus time delay model into a state-space model with uncertainty polyhedron is firstly described. The accuracy of the transformation is studied using numerical examples. Then, the uncertainty polyhedron is rewritten as a linear-matrix-inequality constraint and generalized eigenvalue minimization is adopted to calculate a feedback control law. Case studies show that even if uncertainties associated with the first-order plus time delay model are significant, a stable feedback control law can be found. The proposed control is tested by comparing with a robust internal model control. It is also tested by applying it to the temperature control of air-handing units.]]>

This paper shows how to apply generalized eigenvalue minimization to processes that can be described by a first-order plus time-delay model with uncertain gain, time constant and delay. An algorithm to transform the uncertain first-order plus time delay model into a state-space model with uncertainty polyhedron is firstly described. The accuracy of the transformation is studied using numerical examples. Then, the uncertainty polyhedron is rewritten as a linear-matrix-inequality constraint and generalized eigenvalue minimization is adopted to calculate a feedback control law. Case studies show that even if uncertainties associated with the first-order plus time delay model are significant, a stable feedback control law can be found. The proposed control is tested by comparing with a robust internal model control. It is also tested by applying it to the temperature control of air-handing units.]]>

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