Output Sensitivity Function Research Articles

Epsilon-multiobjective particle swarm optimization-based tuning of sensitivity functions for polynomial control design

In this paper, a novel systematic method for the polynomial controllers (denoted as RST controllers) design and tuning is proposed and successfully implemented based on an epsilon-multiobjective particle swarm optimization (ε-MOPSO) algorithm. The ε-domination concept is used to further improve both properties of the non-premature convergence towards Pareto-optimal sets and the diversity among the found solutions. The RST polynomials coefficients’ computation is formulated as a constrained multiobjective optimization problem under operational frequency-domain constraints. The proposed methodology aims to optimize a desired output sensitivity function satisfying nominal performance and H∞ robustness specifications of the closed-loop system. The use of a suitable fixed parts of the optimized output sensitivity function will provide partial poles placement of the closed-loop dynamics. The inverse of such an optimized desired sensitivity function defines the performance and robustness H∞ weighting filter. Such a proposed ε-MOPSO algorithm is firstly compared with several homologous MOPSO, non-dominated sorting genetic algorithm II (NSGA-II) and multiobjective differential evolution (MODE) algorithms for a benchmark of multiobjective test functions. The algorithms’ performances are evaluated in terms of several metrics in order to show the superiority and the effectiveness of the proposed method. An application to the axis position control of a flexible transmission system with varying loads is then performed. Demonstrative simulations are carried out to show the remarkable superiority and effectiveness of the proposed ε-MOPSO-tuned digital RST controllers compared with several well-known methods available in the literature.

An Easily Understandable Grey Wolf Optimizer and Its Application to Fuzzy Controller Tuning

This paper proposes an easily understandable Grey Wolf Optimizer (GWO) applied to the optimal tuning of the parameters of Takagi-Sugeno proportional-integral fuzzy controllers (T-S PI-FCs). GWO is employed for solving optimization problems focused on the minimization of discrete-time objective functions defined as the weighted sum of the absolute value of the control error and of the squared output sensitivity function, and the vector variable consists of the tuning parameters of the T-S PI-FCs. Since the sensitivity functions are introduced with respect to the parametric variations of the process, solving these optimization problems is important as it leads to fuzzy control systems with a reduced process parametric sensitivity obtained by a GWO-based fuzzy controller tuning approach. GWO algorithms applied with this regard are formulated in easily understandable terms for both vector and scalar operations, and discussions on stability, convergence, and parameter settings are offered. The controlled processes referred to in the course of this paper belong to a family of nonlinear servo systems, which are modeled by second order dynamics plus a saturation and dead zone static nonlinearity. Experimental results concerning the angular position control of a laboratory servo system are included for validating the proposed method.

Grey Wolf Optimizer Algorithm-Based Tuning of Fuzzy Control Systems With Reduced Parametric Sensitivity

This paper proposes an innovative tuning approach for fuzzy control systems (CSs) with a reduced parametric sensitivity using the Grey Wolf Optimizer (GWO) algorithm. The CSs consist of servo system processes controlled by Takagi–Sugeno–Kang proportional-integral fuzzy controllers (TSK PI-FCs). The process models have second-order dynamics with an integral component, variable parameters, a saturation, and dead-zone static nonlinearity. The sensitivity analysis employs output sensitivity functions of the sensitivity models defined with respect to the parametric variations of the processes. The GWO algorithm is used in solving the optimization problems, where the objective functions include the output sensitivity functions. GWO's motivation is based on its low-computational cost. The tuning approach is validated in an experimental case study of a position control for a laboratory nonlinear servo system, and TSK PI-FCs with a reduced process small time constant sensitivity are offered.

Grey Wolf Optimizer-Based Approach to the Tuning of Pi-Fuzzy Controllers with a Reduced Process Parametric Sensitivity

This paper suggests the use of Grey Wolf Optimizer (GWO) algorithms to tune the parameters of Takagi-Sugeno proportional-integral-fuzzy controllers (PI-FCs) for a class of nonlinear servo systems. The servo systems are modelled by second order dynamics plus a saturation and dead zone static nonlinearity. The GWO algorithms solve the optimization problems that minimize discrete-time objective functions expressed as the weighted sum of the squared control error and of the squared output sensitivity function in order to achieve the parametric sensitivity reduction. The output sensitivity function is derived from the sensitivity model with respect to the modification of the process gain, and fuzzy control systems with a reduced process gain sensitivity are offered. Three parameters of Takagi-Sugeno PI-FCs are obtained by a new cost-effective tuning approach. Experimental results related to the angular position control of a laboratory servo system validate the tuning approach.

Methodology for Detecting Model–Plant Mismatches Affecting Model Predictive Control Performance

The model quality for a model predictive control (MPC) is critical for the control loop performance. Thus, assessing the effect of model–plant mismatch (MPM) is fundamental for performance assessment and monitoring the MPC. This paper proposes a method for evaluating model quality based on the investigation of closed-loop data and the nominal output sensitivity function, which facilitates the assessment procedure for the actual closed-loop performances. The effectiveness of the proposed method is illustrated by a multivariable case study, considering linear and nonlinear plants.

IJIREEICE - Electrical, Electronics, Instrumentation and Control

The objective of this paper is to implement the robust polynomial (RST) controller using particle swarm optimization technique and analyze the robustness properties of the closed loop system with the effect of the auxiliary poles on the output sensitivity function. This designing and analysis part is performed by taking design example from literature.

Adaptive attenuation of unknown and time‐varying narrow band and broadband disturbances

SummaryIn many classes of applications like active vibration control and active noise control, the disturbances can be characterized by their frequency content and their location in a specific region in the frequency domain. The disturbances can be of narrow band type (simple or multiple) or of broad band type. A model can be associated to these disturbances. The knowledge of this model allows to design an appropriate control system in order to attenuate (or to reject) their effect upon the system to be controlled. The attenuation of disturbances by feedback is limited by the Bode Integral and the ‘water bed’ effect upon the output sensitivity function. In such situations, the feedback approach has to be complemented by a ‘feedforward disturbance compensation’ requiring an additional transducer for obtaining information upon the disturbance. Unfortunately, in most of the situations, the disturbances are unknown and time‐varying and therefore an adaptive approach should be considered. The generic term for adaptive attenuation of unknown and time‐varying disturbances is ‘adaptive regulation’ (known plant model, unknown, and time‐varying disturbance model).The paper will review a number of recent developments for adaptive feedback compensation of multiple unknown and time‐varying narrow band disturbances and for adaptive feedforward compensation of broad band disturbances in the presence of the inherent internal positive feedback caused by the coupling between the compensator system and the measurement of the image of the disturbance. Some experimental results obtained on a relevant active vibration control system will illustrate the performance of the various algorithms presented. Some open research problems will be mentioned in the conclusion. Copyright © 2015 John Wiley & Sons, Ltd.

Adaptive active vibration isolation – A control perspective

In many classes of applications like active vibration control and active noise control, the disturbances can be characterized by their frequencies content and their location in a specific region in the frequency domain. The disturbances can be of narrow band type (simple or multiple) or of broad band type. A model can be associated to these disturbances. The knowledge of the disturbance model as well as of the compensator system is necessary for the design of an appropriate control system in order to attenuate (or to reject) their effect upon the system to be controlled. The attenuation of disturbances by feedback is limited by the Bode Integral and the water bed effect upon the output sensitivity function. In such situations, the feedback approach has to be complemented by a disturbance requiring an additional transducer for getting information upon the disturbance. Unfortunately in most of the situations the disturbances are unknown and time-varying and therefore an approach should be considered. The generic term for attenuation of unknown and time-varying disturbances is adaptive regulation (known plant model, unknown and time-varying disturbance model). The paper will review a number of recent developments for feedback compensation of multiple unknown and time- varying narrow band disturbances and for feedforward compensation of broad band disturbances in the presence of the inherent internal positive feedback caused by the coupling between the compensator system and the measurement of the image of the disturbance. Some experimental results obtained on a relevant active vibration control system will illustrate the performance of the various algorithms presented.

Adaptive GSA-based optimal tuning of PI controlled servo systems with reduced process parametric sensitivity, robust stability and controller robustness.

This paper suggests a new generation of optimal PI controllers for a class of servo systems characterized by saturation and dead zone static nonlinearities and second-order models with an integral component. The objective functions are expressed as the integral of time multiplied by absolute error plus the weighted sum of the integrals of output sensitivity functions of the state sensitivity models with respect to two process parametric variations. The PI controller tuning conditions applied to a simplified linear process model involve a single design parameter specific to the extended symmetrical optimum (ESO) method which offers the desired tradeoff to several control system performance indices. An original back-calculation and tracking anti-windup scheme is proposed in order to prevent the integrator wind-up and to compensate for the dead zone nonlinearity of the process. The minimization of the objective functions is carried out in the framework of optimization problems with inequality constraints which guarantee the robust stability with respect to the process parametric variations and the controller robustness. An adaptive gravitational search algorithm (GSA) solves the optimization problems focused on the optimal tuning of the design parameter specific to the ESO method and of the anti-windup tracking gain. A tuning method for PI controllers is proposed as an efficient approach to the design of resilient control systems. The tuning method and the PI controllers are experimentally validated by the adaptive GSA-based tuning of PI controllers for the angular position control of a laboratory servo system.

Improving CNC contouring accuracy by robust digital integral sliding mode control

Integral sliding mode control (ISMC) has been employed and shown to improve contouring accuracy in the presence of external disturbances and model uncertainties. An ISMC controller directly reduces the tracking errors of each individual axis, thereby reducing the overall contour errors indirectly. An ISMC controller drives the system dynamics back onto the sliding surface if there exists a deviation from the predefined surface. In the design of an ISMC controller, it is crucial to choose an appropriate sliding surface as this has a great impact on system performance and on chattering. In current approaches, the sliding surface is chosen largely based on a rule of thumb which is only applicable for systems with open-loop poles having imaginary parts. In this paper, an approach is presented to design the sliding surface using principles of robust digital control so that both the regulation and robustness requirements can be satisfied. The natural frequency of the dominant closed-loop poles is chosen such that the modulus of the output sensitivity function lies within the robustness bounds. Resonant pole-zero filters are then used to reshape the output sensitivity function in specific frequency regions. Experiments showed that when the modulus of the output sensitivity function is kept within the robustness bounds, chattering can be avoided and the contour errors resulting from vibrations can be reduced. The introduction of a resonant pole-zero filter also allowed the attenuation band to be expanded so that the low frequency components of the contour errors are attenuated.

Indirect Adaptive Attenuation of Multiple Narrow-Band Disturbances Applied to Active Vibration Control

In this brief, an indirect adaptive control methodology for attenuation of multiple unknown time varying narrow-band disturbances is proposed. This method is based on the real time estimation of the frequency of narrow-band disturbances using adaptive notch filters followed by the design of a controller using adjustable band-stop filters for the appropriate shaping of the output sensitivity function. A Youla-Kučera parametrization of the controller is used for reducing the computation load. This approach is compared on an active vibration control system with the direct adaptive control scheme based on the internal model principle proposed. Real time experimental results are provided.

Novel Adaptive Charged System Search algorithm for optimal tuning of fuzzy controllers

This paper proposes a novel Adaptive Charged System Search (ACSS) algorithm for the optimal tuning of Takagi–Sugeno proportional–integral fuzzy controllers (T–S PI-FCs). The five stages of this algorithm, namely the engagement, exploration, explanation, elaboration and evaluation, involve the adaptation of the acceleration, velocity, and separation distance parameters to the iteration index, and the substitution of the worst charged particles’ fitness function values and positions with the best performing particle data. The ACSS algorithm solves the optimization problems aiming to minimize the objective functions expressed as the sum of absolute control error plus squared output sensitivity function, resulting in optimal fuzzy control systems with reduced parametric sensitivity. The ACSS-based tuning of T–S PI-FCs is applied to second-order servo systems with an integral component. The ACSS algorithm is validated by an experimental case study dealing with the optimal tuning of a T–S PI-FC for the position control of a nonlinear servo system.

Gravitational search algorithm-based design of fuzzy control systems with a reduced parametric sensitivity

This paper proposes the design of fuzzy control systems with a reduced parametric sensitivity making use of Gravitational Search Algorithms (GSAs). The parametric variations of the processes lead to sensitivity models. Objective functions expressed as integral quadratic performance indices, which depend on the control error and squared output sensitivity functions are suggested. GSAs are employed to minimize the objective functions in the appropriately defined optimization problems. This paper also suggests a GSA with improved search accuracy. The new GSA is characterized by the modification of the denominator in the expression of the force acting on an agent from the other agent; the denominator depends not only on the Euclidian distance between the two agents but also on the position of the latter: A design method for Takagi–Sugeno proportional-integral fuzzy controllers (PI-FCs) is proposed. The PI-FCs are dedicated to a class of processes characterized by second-order linear or linearized models with an integral component. Two discrete-time sensitivity models of the fuzzy control systems are derived. An example dealing with the angular position control of direct current (DC) servo system laboratory equipment validates the new controller design. A set of real-time experimental results illustrates the fuzzy control system performance.

Indirect adaptive regulation strategy for the attenuation of time varying narrow-band disturbances applied to a benchmark problem

The paper presents an indirect adaptive regulation algorithm for the attenuation of unknown narrow-band disturbances. The main features of this new scheme are (i) the use of adaptive Band-stop Filters (BSFs) tuned at the frequencies of the disturbance and (ii) a procedure for direct identification of frequencies contained in the disturbance. The use of adaptive BSFs allows one to introduce the desired attenuation of the disturbance (instead of total rejection) and simplifies the shaping of the output sensitivity function (to meet the specification for the tolerated amplification outside the frequencies of the disturbance). The proposed approach is evaluated on the benchmark simulator and on the benchmark active vibration control system.

Adaptive Attenuation of Unknown and Time Varying Disturbances

Abstract In many classes of applications like active vibration control and active noise control the disturbances can be characterized by their frequencies content and their location in a specific region in the frequency domain. The disturbances can be of narrow band type (simple or multiple) or of broad band type. A model can be associated to these disturbances. The knowledge of this model allows to design an appropriate control system in order to attenuate (or to reject) their effect upon the system to be controlled. The attenuation of disturbances by feedback is limited by the Bode Integral and the “water bed” effect upon the output sensitivity function. In such situations the feedback approach has to be complemented by a “feedforward disturbance compensation” requiring an additional transducer for getting information upon the disturbance. Unfortunately in most of the situations the disturbances are unknown and time-varying and therefore an adaptive approach should be considered. The generic term for adaptive attenuation of unknown and time-varying disturbances is “adaptive regulation” (known plant model, unknown and time-varying disturbance model). The paper will review a number of recent developments for adaptive feedback compensation of multiple unknown and time-varying narrowband disturbances and for adaptive feedforward compensation of broad band disturbances in the presence of the inherent internal positive feedback caused by the coupling between the compensator system and the measurement of the image of the disturbance. Some experimental results obtained on a relevant active vibration control system will illustrate the performance of the various algorithms presented. Some open research problems will be mentioned in the conclusion.

An indirect adaptive scheme for attenuation of multiple narrow-band disturbances: stability analysis

In this paper, a stability proof for an indirect adaptive control method used for the attenuation of multiple unknown time varying narrow-band disturbances is presented. The method is based on the real time estimation of the frequency of the unknown narrow-band disturbances using adaptive notch filters (ANF) followed by the design of a controller using adjustable band-stop filters (BSF) for the appropriate shaping of the output sensitivity function. An Youla-Kučera parametrization of the controller is used for reducing the computation load. Sufficient conditions for stability of the full scheme are stated and a stability proof is given. Finally, an experimental comparison with a direct adaptive method based on the internal model principle (IMP) is shown.

Novel Adaptive Gravitational Search Algorithm for Fuzzy Controlled Servo Systems

This paper presents a novel adaptive Gravitational Search Algorithm (GSA) for the optimal tuning of fuzzy controlled servo systems characterized by second-order models with an integral component and variable parameters. The objective functions consist of the output sensitivity functions of the sensitivity models defined with respect to the parametric variations of the processes. The proposed adaptive GSA solves the optimization problems resulting in a new generation of Takagi-Sugeno proportional-integral fuzzy controllers (T-S PI-FCs) with a reduced time constant sensitivity. A design method for T-S PI-FCs is then proposed and experimentally validated in the representative case study of the optimal tuning of T-S PI-FCs for the position control system of a servo system.

Fuzzy Control Systems With Reduced Parametric Sensitivity Based on Simulated Annealing

This paper discusses the design of fuzzy control systems (FCSs) with a reduced parametric sensitivity using simulated-annealing (SA) algorithms. Four generic families of objective functions expressed as integral quadratic performance indexes, which depend on the control error and squared output sensitivity functions, are suggested. SA algorithms are employed to minimize the objective functions in the appropriately defined optimization problems. A design method for Takagi-Sugeno proportional-integral fuzzy controllers (PI-FCs) is proposed. The resulting PI-FCs are intended for a class of plants characterized by second-order linearized models with integral component. A case study dealing with the angular position control of a dc servo system is used as test bed to validate the proposed new controller design. Experimental results illustrate the FCS performance.

Charged System Search Algorithms for Optimal Tuning of PI Controllers

This paper suggests the application of Charged System Search (CSS) algorithms to the optimal tuning of PI controllers. The presentation is focused on a class of second-order processes with an integral component and variable parameters. The CSS algorithms solve the optimization problems which aim the minimization of objective functions expressed as the integral of squared control error augmented by the integral of squared output sensitivity functions. The expressions of the output sensitivity functions are derived from the state sensitivity models of the control systems with respect to process gain variations. The optimal tuning of PI controllers is proposed such that to ensure a reduced sensitivity with respect to process gain variations. A case study is included to illustrate the application of the new CSS algorithms and to compare it with a Particle Swarm Optimization and a Gravitational Search Algorithm.

Evolutionary optimization-based tuning of low-cost fuzzy controllers for servo systems

This paper suggests the optimal tuning of low-cost fuzzy controllers dedicated to a class of servo systems by means of three new evolutionary optimization algorithms: Gravitational Search Algorithm (GSA), Particle Swarm Optimization (PSO) algorithm and Simulated Annealing (SA) algorithm. The processes in these servo systems are characterized by second-order models with an integral component and variable parameters; therefore the objective functions in the optimization problems include the output sensitivity functions of the sensitivity models defined with respect to the parametric variations of the processes. The servo systems are controlled by Takagi–Sugeno proportional-integral-fuzzy controllers (T–S PI-FCs) that consist of two inputs, triangular input membership functions, nine rules in the rule base, the SUM and PROD operators in the inference engine, and the weighted average method in the defuzzification module. The T–S PI-FCs are implemented as low-cost fuzzy controllers because of their simple structure and of the only three tuning parameters because of mapping the parameters of the linear proportional-integral (PI) controllers onto the parameters of the fuzzy ones in terms of the modal equivalence principle and of the Extended Symmetrical Optimum method. The optimization problems are solved by GSA, PSO and SA resulting in fuzzy controllers with a reduced parametric sensitivity. The comparison of the three evolutionary algorithms is carried out in the framework of a case study focused on the optimal tuning of T–S PI-FCs meant for the position control system of a servo system laboratory equipment. Reduced process gain sensitivity is ensured.