Parallel Distributed Compensation Controller Design Research Articles

Parallel distributed compensation controller design for Markovian jump system with time-varying delays using Bessel-Legendre inequality method and improved positive definite rule

In this paper, based on time-varying delay Markovian jump system (MJS), Bessel-Legendre inequality method and improved positive definite condition of Lyapunov function are used, and parallel distributed compensation (PDC) state feedback controller is also introduced. The conservatism of the system is reduced by using this inequality method and positive definite conditions, and further decreases with the increase of the Legendre parameter N. The PDC controller considers two control parameters simultaneously, which can represent the actual system more truthfully. Finally, Example 1 proves the effectiveness of the improved method in this paper. Example 2 considers time-varying probability transition perturbations. Example 3 obtains the parameters of PDC controller with different parameters N. Example 4 illustrates the practical significance of methods in this paper by introducing a time-delay inverted pendulum system with Markovian parameters.

Stability and Stabilization Analysis for T–S Interconnected Fuzzy Systems Using LMIs

This paper deals with both the stability and stabilization problems of large-scale nonlinear systems described by interconnected T–S fuzzy models. Afterward, LMI-based stabilizability conditions for the decentralized parallel distributed compensation controller design are developed. To compare feasibility results for stability analysis, different Lyapunov functions with slack variables are considered. Simulation examples are presented to illustrate and to compare the effectiveness of the proposed stability and stabilization techniques.

Novel Stabilization Criteria for T–S Fuzzy Systems With Affine Matched Membership Functions

This paper presents a new parallel distributed compensation controller design approach for T–S (Takagi–Sugeno) fuzzy control systems with affine matched membership functions in the system and controller. In the new fuzzy control, affine transformed membership functions are adopted by scaling and biasing the original membership functions of the system. Stabilization and performance criterion of the closed-loop T–S fuzzy systems are obtained through a new parameterized linear matrix inequality, which is rearranged by affine matched membership functions. The conservativeness of stabilization condition for the T–S fuzzy system is significantly relaxed by utilizing the constraints condition of the controllers membership functions, which is determined from the difference of each transformed membership function. In addition, the controller gain is reconstructed by a decision variable separation technique with two different free weighting matrices without any scaling parameter. The superiority of proposed method is verified through numerical examples.

Fuzzy Attitude Control of Spacecraft With Fuel Sloshing via Linear Matrix Inequalities

This paper presents and compares two fuzzy controllers for attitude stabilization of a spacecraft with partially filled fuel tank: a fuzzy controller based on the parallel distributed compensation (PDC) technique and a fuzzy controller based on the linear quadratic regulator. Both controllers are built from the Takagi–Sugeno model of the spacecraft. Using the Lyapunov stability theorem, the fuzzy PDC controller design problem was cast as a minimization problem for the upper bound of control input in the form of linear matrix inequalities. In the end, we compare the efficacy and robustness of each controller via numerical simulations.

Uncertain T-S model-based robust controller design with [formula omitted]-stability constraints—A simulation study of quadrotor attitude stabilization

The problem of the attitude stabilization of a quadrotor unmanned aerial vehicle is considered in simulation. An uncertain-like Takagi–Sugeno model of the quadrotor, where the nonlinear entries which depend on the input motor voltages are reported in uncertainties, is proposed to avoid closed-loop algebraic loops. The design of a Parallel Distributed Compensation (PDC) control law is considered with D-stability constraints in order to improve the closed-loop transient response. In this context, new generic and relaxed Linear Matrix Inequality (LMI) conditions are proposed. These new PDC controller design conditions constitute an alternative to previously proposed D-stabilizing non-PDC controller ones. Indeed, non-PDC controllers require online inversions of time-varying matrices, which is a major drawback for embedded applications with low computational capabilities. The conservatism of the proposed LMI conditions with respect to previous results is illustrated through an academic example. Then, simulations of the quadrotor with usual prescribed LMI regions are proposed to show the effectiveness of the proposed conditions.

Improvements on PDC Controller Design for Takagi-Sugeno Fuzzy Systems with State Time-Varying Delays

This paper deals with the controller design for a class of T-S fuzzy model with state time-varying delays. By choosing a convenient augmented Lyapunov-Krasovskii functional and employing a Parallel Distributed Compensation (PDC) control law including both memoryless and delayed state feedback, new delay dependent sufficient conditions for the stabilization of T–S fuzzy model with time-varying delay are derived in terms of linear matrix inequalities (LMIs). By taking into account the bounds of the time varying delays and its maximal rate of variation, the proposed LMI-based conditions guarantee the closed-loop asymptotic stability of the considered class of delayed T-S fuzzy systems. Finally, a numerical example is given to illustrate the effectiveness of the proposed controller design methodology and the conservatism improvement regarding to previous results.

Design of robust‐optimal controllers with low trajectory sensitivity for uncertain Takagi–Sugeno fuzzy model systems using differential evolution algorithm

SUMMARYBy integrating the robust stabilizability condition, the orthogonal‐function approach (OFA) and the Taguchi‐sliding‐based differential evolution algorithm (TSBDEA), an integrative computational approach is presented in this paper to design the robust‐optimal fuzzy parallel‐distributed‐compensation (PDC) controller with low trajectory sensitivity such that (i) the Takagi–Sugeno (TS) fuzzy model system with parametric uncertainties can be robustly stabilized, and (ii) a quadratic finite‐horizon integral performance index for the nominal TS fuzzy model system can be minimized. In this paper, the robust stabilizability condition is proposed in terms of linear matrix inequalities (LMIs). Based on the OFA, an algebraic algorithm only involving the algebraic computation is derived for solving the nominal TS fuzzy feedback dynamic equations. By using the OFA and the LMI‐based robust stabilizability condition, the robust‐optimal fuzzy PDC control problem for the uncertain TS fuzzy dynamic systems is transformed into a static constrained‐optimization problem represented by the algebraic equations with constraint of LMI‐based robust stabilizability condition; thus, greatly simplifying the robust‐optimal PDC control design problem. Then, for the static constrained‐optimization problem, the TSBDEA has been employed to find the robust‐optimal PDC controllers with low trajectory sensitivity of the uncertain TS fuzzy model systems. A design example is given to demonstrate the applicability of the proposed new integrative approach. Copyright © 2011 John Wiley & Sons, Ltd.

PDC Control Design for Non-holonomic Wheeled Mobile Robots with Delayed Outputs

This paper presents a new technique for tracking-error model-based Parallel Distributed Compensation (PDC) control for non-holonomic vehicles where the outputs (measurements) of the system are delayed and the delay is constant. Briefly, this technique consists of rewriting the kinematic error model of the mobile robot tracking problem into a TS fuzzy representation and finding a stabilizing controller by solving LMI conditions for the tracking-error model. The state variables are estimated by nonlinear predictor observer where the outputs are delayed by a constant delay. To illustrate the efficiency of the proposed approach a comparison between the TS fuzzy observer and the nonlinear predictor observer is shown. For this study the reference trajectory is built by taking into account the acceleration limits of the mobile robot. All experiments are implemented on simulation and the real-time platform.

Robust Quadratic-Optimal Control of TS-Fuzzy-Model-Based Dynamic Systems With Both Elemental Parametric Uncertainties and Norm-Bounded Approximation Error

This paper considers the design problem of the robust quadratic-optimal parallel-distributed-compensation (PDC) controllers for Takagi-Sugeno (TS) fuzzy-model-based control systems with both elemental parametric uncertainties and norm-bounded approximation error. By complementarily fusing the robust stabilizability condition, the orthogonal functions approach (OFA), and the hybrid Taguchi genetic algorithm (HTGA), an integrative method is presented in this paper to design the robust quadratic-optimal PDC controllers such that 1) the uncertain TS-fuzzy-model-based control systems can be robustly stabilized, and 2) a quadratic integral performance index for the nominal TS-fuzzy-model-based control systems can be minimized. In this paper, the robust stabilizability condition is proposed in terms of linear matrix inequalities (LMIs). By using the OFA and the LMI-based robust stabilizability condition, the robust quadratic-optimal PDC control problem for the uncertain TS-fuzzy-model-based dynamic systems is transformed into a static constrained-optimization problem represented by the algebraic equations with constraint of LMI-based robust stabilizability condition, thus greatly simplifying the robust optimal PDC control design problem. Then, for the static constrained-optimization problem, the HTGA is employed to find the robust quadratic-optimal PDC controllers of the uncertain TS-fuzzy-model-based control systems. Two design examples of the robust quadratic-optimal PDC controllers for an uncertain inverted pendulum system and an uncertain nonlinear mass-spring-damper mechanical system are given to demonstrate the applicability of the proposed integrative approach.

Stable and Quadratic Optimal Control for TS Fuzzy-Model-Based Time-Delay Control Systems

For the finite-horizon optimal control problem of the Takagi-Sugeno (TS) fuzzy-model-based time-delay control systems, by integrating the delay-dependent stabilizability condition, the shifted-Chebyshev-series approach (SCSA), and the hybrid Taguchi-genetic algorithm (HTGA), an integrative method is presented to design the stable and quadratic optimal parallel distributed compensation (PDC) controllers. In this paper, the delay-dependent stabilizability condition is proposed in terms of linear matrix inequalities (LMIs). Based on the SCSA, an algebraic algorithm only involving the algebraic computation is derived in this paper for solving the TS fuzzy-model-based time-delay feedback dynamic equations. In addition, by using the SCSA, the stable and quadratic optimal PDC control problem for the TS fuzzy-model-based time-delay control systems is replaced by a static parameter optimization problem represented by the algebraic equations with constraint of the LMI-based stabilizability condition, thus greatly simplifying the stable and optimal PDC control design problem. The computational complexity for both differential and integral in the stable and optimal PDC control design of the original dynamic systems may therefore be reduced considerably. Then, for the static constrained optimization problem, the HTGA is employed to find the stable and quadratic optimal PDC controllers of the TS fuzzy-model-based time-delay control systems. A design example of the stable and quadratic optimal PDC controllers for the continuous-stirred-tank-reactor system is given to demonstrate the applicability of the proposed integrative approach.

Robust-stable and quadratic-optimal control for TS-fuzzy-model-based control systems with elemental parametric uncertainties

By integrating the robust stabilisability condition, the shifted-Chebyshev-series approach (SCSA), and the hybrid Taguchi-genetic algorithm (HTGA), an integrative method is presented in this work to design the robust-stable and quadratic-optimal fuzzy parallel distributed compensation (PDC) controller such that: (i) the Takagi-Sugeno (TS) fuzzy-model-based control system with elemental parametric uncertainties can be robustly stabilised, and (ii) a quadratic finite-horizon integral performance index for the nominal TS-fuzzy-model-based control system can be minimised. In this work, the robust stabilisability condition is proposed in terms of linear matrix inequalities (LMIs). Based on the SCSA, an algebraic algorithm only involving the algebraic computation is derived in this work for solving the nominal TS-fuzzy-model-based feedback dynamic equations. By using the SCSA and the LMI-based robust stabilisability condition, the robust-stable and quadratic-finite-horizon-optimal fuzzy PDC control problem for the uncertain TS-fuzzy-model-based dynamic systems is transformed into a static constrained-optimisation problem represented by the algebraic equations with constraint of LMI-based robust stabilisability condition; thus greatly simplifying the robust optimal PDC control design problem. Then, for the static constrained-optimisation problem, the HTGA is employed to find the robust-stable and quadratic-optimal PDC controllers of the uncertain TS-fuzzy-model-based control systems. A design example of the robust-stable and quadratic-optimal PDC controller for the nonlinear mass-spring-damper mechanical system with elemental parametric uncertainties is given to demonstrate the applicability of the proposed new integrative approach.

From differential equations to PDC controller design via numerical transformation

This paper proposes a transformation method capable of transforming analytically given differential equations of dynamic models into Takagi–Sugeno fuzzy inference model (TS fuzzy model), whereupon various parallel distributed compensation (PDC) controller design techniques can readily be executed. Joining the transformation method and the PDC techniques leads to a controller design framework. The transformation method is specialized to minimize the number of fuzzy rules in the resulting TS fuzzy model according to a given acceptable transformation error, the PDC design thus results in a computational complexity minimized controller which is highly desired in many cases of real applications. The paper presents examples to show the effectiveness of the proposed transformation.