Parallel Distributed Compensation Controller Research Articles

Linear Consequence-Based Fuzzy Parallel Distributed Compensation Type $L_{1}$ Adaptive Controller for Two Link Robot Manipulator

This paper presents a novel scheme of controller design for a cross-coupled multi-input multi-output (MIMO) two link robot manipulator (TLRM) system having time varying uncertainties, disturbances, and nonlinearity by employing fuzzy parallel distributed compensation (PDC) type ${L}_{1}$ adaptive controller. The combination of linear consequence-based fuzzy subsystems are utilized to represent the nonlinear TLRM system. The components of $ {L}_{1}$ adaptive control framework are also realized by combining linear consequence-based fuzzy systems to incorporate the zone-wise controlling of the TLRM system. A fuzzy PDC control has also been augmented to achieve robust stable transient and steady state performances. The stability of each fuzzy systems as well as the overall proposed control scheme is guaranteed by utilizing fuzzy Lyapunov theory-based analysis. The experimental results demonstrate the usefulness of the proposed control scheme.

Augmented TP model transformation‐based parallel distributed compensation control design

AbstractThe usual sampled hyper grid points of uniform sampling method are distributed equally in the TP model transformation, thus, the sampling results often omit the local extrema when the sampling step is not fine‐tuned. Then the resultant tensor which is used for controller design can not fully cover the state space, although the gain which is the feasible solution of the linear matrix inequalities. In this paper, we proposed a non‐uniform sampling method for tensor product model transformation, local extrema are considered in the sampling step, while the sampling step can vary dynamically for different function entries. In this paper, TP model transformation‐based parallel distributed compensation (PDC) controller is extended in three folds: (i) The existing TP model transformation‐based PDC controller with uniform sampling method is extended to TP model transformation‐based PDC tracking controller with the uniform sampling method and an extended signal. (ii) A new TP model transformation‐based PDC tracking controller is proposed based on a new sampling method, that is, the Hammersley sampling method. (iii) TP model transformation‐based PDC tracking controller is also proposed based on the non‐uniform sampling method. The proposed adaptive TP model transformation‐based PDC tracking controller is able to enhance the performance of the TP model transformation‐based PDC controller, and the adaptive TP model transformation‐based PDC controller obtains the best results due to the nearly exact sampling of the system.

Fuzzy model-based controller for blood glucose control in type 1 diabetes: An LMI approach

This paper deals with designing a robust controller with H∞ performance index criteria for regulating the glucose-insulin level in type 1 diabetes. The proposed approach employs a Takagi-Sugeno (TS) fuzzy modeling and fuzzy model-based parallel distributed compensation (PDC) and non-parallel distributed compensation (non-PDC) schemes to design a stabilizing control law for the injecting insulin in silico. Deploying a non-quadratic Lyapunov function (NQLF) candidate, the stabilization conditions are derived in terms of linear matrix inequalities (LMIs) and solved by convex optimization techniques. Furthermore, based on the convex property of the membership functions, a new null term is defined which increases the degree of freedom of the proposed LMI constraints and reduces the stabilization conditions conservativeness. The diabetes models that are considered are nonlinear minimal Bergman and Tolic models that describe the glucose-insulin process in diabetes type 1. Based on the so-called sector nonlinearity approach (SNA), the equivalent TS fuzzy models of the Bergman and Tolic models are obtained. Then, the stabilization LMI conditions are solved and the PDC and non-PDC controllers are designed. Simulation results are obtained with a single patient testing parameters uncertainties and verify the advantages of the proposed robust control technique in dealing with the effects of external meal disturbance and maintaining the blood glucose concentration in the desired region to avoid the hypoglycemia and hyperglycemia disorders.

Robust fuzzy stabilization of nonlinear time-delay systems subject to impulsive perturbations

This paper is concerned with robust stabilization problem of Takagi–Sugeno (T-S) fuzzy time-delay systems subject to impulsive perturbations. New results on robust stabilization via parallel distributed compensation (PDC) control are derived. First, based on the impulse-type Razumikhin–Lyapunov method combined with the use of an impulse-time-dependent Lyapunov function, a new exponential stability criterion for T-S fuzzy time-delay system with impulsive effects is obtained. The proposed stability criterion removes the restrictive condition on the relationship between the size of time-delay and lower bound of impulse intervals imposed by the previous results. Then, by employing a convex relaxation technique, a sufficient condition for the constructing the PDC controllers is presented, which is expressed in terms of linear matrix inequalities (LMIs). Next, the robust stabilization problem for the T-S system with slowly time-varying delay is studied. A different stabilization condition is derived via an impulse-time-dependent Lyapunov functional, which is less conservative than the former when the state delay is constant. Finally, an illustrative example is provided to demonstrate the effectiveness of the proposed analysis and design techniques.

Robust stabilization for discrete-time Takagi-Sugeno fuzzy system based on N4SID models

PurposeNonlinear systems identification from experimental data without any prior knowledge of the system parameters is a challenge in control and process diagnostic. It determines mathematical model parameters that are able to reproduce the dynamic behavior of a system. This paper aims to combine two fundamental research areas: MIMO state space system identification and nonlinear control system. This combination produces a technique that leads to robust stabilization of a nonlinear Takagi–Sugeno fuzzy system (T-S).Design/methodology/approachThe first part of this paper describes the identification based on the Numerical algorithm for Subspace State Space System IDentification (N4SID). The second part, from the identified models of first part, explains how we use the interpolation of linear time invariants models to build a nonlinear multiple model system, T-S model. For demonstration purposes, conditions on stability and stabilization of discrete time, T-S model were discussed.FindingsStability analysis based on the quadratic Lyapunov function to simplify implementation was explained in this paper. The linear matrix inequalities technique obtained from the linearization of the bilinear matrix inequalities was computed. The suggested N4SID2 algorithm had the smallest error value compared to other algorithms for all estimated system matrices.Originality/valueThe stabilization of the closed-loop discrete time T-S system, using the improved parallel distributed compensation control law, was discussed to reconstruct the state from nonlinear Luenberger observers.

A Gain Scheduling Wide-Area Damping Controller for the Efficient Integration of Photovoltaic Plant

With photovoltaic generation increasing, the wide-area oscillation has a vital influence on the long-distance power transmission of photovoltaic power. For an efficient integration of photovoltaic generation, a gain scheduling wide-area damping controller (WADC) is designed to guarantee system damping performance under a wide-area signal delay and a changing operating condition, which could be aggravated by the fluctuant and uncertain photovoltaic generation. A linear parameter-varying (LPV) model is proposed to represent all possible operating conditions within varying ranges of the photovoltaic generation and the load. Then, a tensor product (TP) model transformation is applied to transform the LPV model into a TP model. Based on the TP model, a parallel distributed compensation controller (PDC) framework is adopted to design the gain scheduling WADC, which is solved by linear matrix inequalities (LMIs) considering the accommodation to the random interval delay. In addition, a staircase basis function method is proposed to reduce the conservatism of LMIs within the PDC framework. The gain of the proposed WADC will be adjusted according to the operating condition acknowledged through the real-time scheduling and control center, once a wide-area oscillation is detected. Finally, the performance of the proposed WADC is verified by a 2-area 4-machine system and a 68-bus 16-machine system.

Decentralized Control Design for Switching Fuzzy Large-Scale T–S Systems by Switched Lyapunov Function with $$H_\infty $$ H ∞ Performance

This paper investigates the $$H_{\infty }$$ control design for switched fuzzy discrete-time interconnected systems. This type of systems contains nonlinear interconnected subsystems. Every subsystem has different switching modes described by a T–S fuzzy model. Less conservative sufficient conditions are proposed and formulated in terms of LMIs obtained using Switched Lyapunov functions and parallel distributed compensation (PDC) controllers. The design is allowed by $$H_{\infty }$$ technique and a relaxed method is presented. Two numerical examples are developed to illustrate the effectiveness of the obtained results.

Robust fault tolerant controller design for Takagi-Sugeno systems under input saturation

ABSTRACTIn this paper, we address the problem of fault tolerant constrained control (FTCC) design with multiobjective requirement for a class of uncertain Takagi-Sugeno systems subject to input and state constraints. An integrated robust FTC strategy is adopted by combining a descriptor approach and a novel structure of parallel distributed compensation control laws. This ensures the closed-loop system stability of the faulty system and respects the given saturation constraints on the control input. The optimisation problem is formulated using fuzzy Lyapunov function, and expressed in terms of linear matrix inequality constraints (LMIs). Numerical examples are given to show the effectiveness of the proposed FTCC approach for both measurable and unmeasurable decision variables cases.

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.

Stability Analysis of Markov Jump Neural Networks With Mixed Delays in Finite Frequency Domain Based on PDC Controller

In this paper, the stability of Markov jumping neural network (MJNN) with mixed delays under the control of finite frequency domain Parallel Distributed Compensation (PDC) controller is studied. By introducing the generalized-KYP lemma, the frequency domain analysis is combined with the neural network. The positive definite and negative definite conditions in Lyapunov stability theory are improved by using Bessel-Legendre inequality method. Sufficient conditions for the stability of the system are given and proved. Finally, numerical examples show that the system can maintain stability under the control of the PDC controller at low, medium and high frequencies.

Improved T‐S Fuzzy Control for Uncertain Time‐Delay Coronary Artery System

This paper is based on the Takagi‐Sugeno (T‐S) fuzzy models to construct a coronary artery system (CAS) T‐S fuzzy controller and considers the uncertainties of system state parameters in CAS. We propose the fuzzy model of CAS with uncertainties. By using T‐S fuzzy model of CAS and the use of parallel distributed compensation (PDC) concept, the same fuzzy set is assigned to T‐S fuzzy controller. Based on this, a PDC controller whose fuzzy rules correspond to the fuzzy model is designed. By constructing a suitable Lyapunov‐Krasovskii function (LKF), the stability conditions of the linear matrix inequality (LMI) are exported. Simulation results show that the method proposed in this paper is correct and effective and has certain practical significance.

Delay dependent stability analysis of Takagi-Sugeno fuzzy time-delays system

Generally, nonlinearities and time-delays are inherent characters for the Takagi-Sugeno fuzzy system. There has been a lot of research works dealing with this type of systems. Most of these researches are based on measurable states but not all states are available in many physical systems. When such case happens, an observer is designed to estimate the system unavailable states. This work addresses the problem of stability analyses and stabilisation for the Takagi-Sugeno fuzzy system with time-delays. Motivated by recent concerns in stability issues, a stabilisation observer controller for Takagi-Sugeno fuzzy time-delay systems is re-evaluated in this paper. Based on the fuzzy weighting dependent Lyapunov-Krasovskii function approach, we provided, in terms of linear matrix inequalities, the sufficient conditions for the existence of a robust state feedback parallel distributed compensation controller that guarantees stability and finding the maximum delay bounds. The effectiveness and the applicability of the designed stabilisation controller are illustrated via the truck trailer systems.

Delay dependent stability analysis of Takagi-Sugeno fuzzy time-delays system

Generally, nonlinearities and time-delays are inherent characters for the Takagi-Sugeno fuzzy system. There has been a lot of research works dealing with this type of systems. Most of these researches are based on measurable states but not all states are available in many physical systems. When such case happens, an observer is designed to estimate the system unavailable states. This work addresses the problem of stability analyses and stabilisation for the Takagi-Sugeno fuzzy system with time-delays. Motivated by recent concerns in stability issues, a stabilisation observer controller for Takagi-Sugeno fuzzy time-delay systems is re-evaluated in this paper. Based on the fuzzy weighting dependent Lyapunov-Krasovskii function approach, we provided, in terms of linear matrix inequalities, the sufficient conditions for the existence of a robust state feedback parallel distributed compensation controller that guarantees stability and finding the maximum delay bounds. The effectiveness and the applicability of the designed stabilisation controller are illustrated via the truck trailer systems.

A new combined actuator fault estimation and accommodation for linear parameter varying system subject to simultaneous and multiple faults: an LMIs approach

This paper proposes a novel fuzzy observer scheme-based active fuzzy fault-tolerant tracking control (FFTTC) combined with a parallel distributed compensation control law for a linear parameter varying system subject to actuator faults and noise measurement. This system consists of a doubly fed induction generator-based wind energy conversion system described by a Takagi–Sugeno fuzzy model. The developed scheme is able to force system states to track their desired reference signal in finite time and obtain a better dynamic response and performance. A fuzzy state observer is also developed to simultaneously estimate the generator states and the actuator faults. Based on the obtained online fault estimation information, the FFTTC will be reconfigured to compensate for the fault impact. The closed-loop stability is established based on a Lyapunov function. Sufficient conditions are formulated for the existence of fuzzy fault-tolerant control parameters in the form of linear matrix inequalities (LMIs), which can be easily solved by means of a standard YALMIP toolbox. The fuzzy observer and fuzzy fault-tolerant tracking control gains can be computed based on the solutions of a set of LMIs. Computer simulations were performed using the MATLAB/Simulink environment to highlight the performance and robustness of the proposed design procedure with respect to actuator fault occurrences.

TS-based sampled-data model predictive controller for continuous-time nonlinear systems

This paper proposes a new fuzzy model predictive control approach for continuous-time nonlinear systems in terms of linear matrix inequalities (LMIs). The proposed approach is based on the Takagi–Sugeno fuzzy modeling, a quadratic Lyapunov function, and a sampled-data parallel distributed compensation controller with constant sampling time. The goal is designing the sampled-data controller such that at each sampling time, the stability of the closed-loop system is guaranteed and an infinite horizon cost function is minimised. The main advantage of the proposed approach is to eliminate the approximations induced from discretizing the original system and cost function upper bound minimisation. Consequently, a lower bound of the cost function is obtained and the performance of the proposed model predictive controller is improved compared to the recently published papers in the same field of interest. In addition, the Euclidean norm constraint of the control input vector is derived in terms of LMIs. To illustrate the merits of the proposed approach, the proposed technique is applied to a continuous stirred tank reactor system.

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.

Improved results on stability analysis and controller synthesis for T-S fuzzy systems

ABSTRACTThis paper is concerned with the stability analysis and synthesis issues for T-S fuzzy systems. By fully using the properties of fuzzy weighting functions and matrix inequalities, two improved sufficient stability conditions are derived based on the common Lyapunov function and fuzzy Lyapunov function, respectively. It is not necessary to require every fuzzy subsystem to be stable in these conditions. Following the analysis, both parallel and non-parallel distributed compensation controllers are obtained by solving linear matrix inequalities. Finally, four examples are given to show the effectiveness of our proposed approach and the advantages of the approach over existing methods.

Functional observer based controller for stabilizing Takagi–Sugeno fuzzy systems with time-delays

This paper investigates the construction of a fuzzy functional observer for nonlinear systems with time-delays, and the application of the observer to estimate the state functions of the parallel distributed compensation controller for stabilizing the system. Two types of time-delays are considered: constant and time-varying delays with bounded time derivative. Stability conditions are obtained using Lyapunov–Krasovskii functional approach; and the conditions are transformed into linear matrix inequalities with equality constraints so that observer parameters can be calculated using the solution of these inequalities. Functional observer construction procedures are presented considering both constant and time-varying time-delays. Two examples, including one for obtaining a power system stabilizer for a single machine infinite bus system, are presented to illustrate effectiveness of the proposed design procedures.

LMI-based 2-DoF control design of a manipulator via T-S descriptor approach

Abstract This paper presents a method for the control design of a manipulator. The design goal is to achieve a guaranteed H∞ model reference tracking performance with respect to bounded reference inputs through a 2-DoF control scheme. To achieve this goal, the manipulator system is represented by a Takagi-Sugeno fuzzy model in descriptor form. The control scheme is based on a parallel distributed compensation controller. Furthermore, the stability of the nonlinear system is also guaranteed. Based on Lyapunov stability theory, the control design is formulated as an LMI optimization problem which can be effectively solved with numerical solvers. Simulation results carried out with the SimMechanics environment clearly demonstrate the effectiveness of the proposed method.