Parallel Distributed Compensation Method Research Articles

PD Control-Based Reachable Set Synthesis for Singular Takagi-Sugeno Fuzzy Systems With Time-Varying Delay.

This article focuses on the reachable set synthesis problem for singular Takagi-Sugeno fuzzy systems with time-varying delay. The main contribution is that we design a proportional plus derivative state feedback controller to ensure that the singular fuzzy system is normal and the system states are bounded by a derived ellipsoid. In the light of the Lyapunov stability theory and the parallel distributed compensation method, the sufficient criteria are shown in the format of linear matrix inequalities. Furthermore, we investigate another case of reachable set synthesis, where the reachable set to be found is contained in a given ellipsoid. Finally, we use two examples to exhibit the usefulness of the proposed method.

Actuator fault and Bernoulli random delay-based H∞ reliable fuzzy control of singular hybrid vehicle suspension systems with impulsive perturbations

The problem of actuator fault and Bernoulli random delay-based H∞ reliable fuzzy state feedback control of singular hybrid vehicle suspension systems (SHVSSs) with impulsive perturbations is studied in this paper. By taking the acceleration of each part of the suspension as the component of the system state, the vehicle suspension system is successfully extended to a singular vehicle suspension system. The regularity and non-impulsiveness of the time-varying delays SHVSSs with impulsive perturbations are proved via singular value decomposition (SVD) method. By means of constructing a novel Lyapunov-Krasovskii (L-K) functional embodied with Markovian jump modes and impulse times information, neoteric conditions are smoothly concluded under linear matrix inequalities (LMIs) framework, which guarantee that the closed-loop SHVSS acquires H∞ stochastic admissibilization. By exploiting Takagi-Sugeno (T-S) fuzzy technique and parallel-distributed compensation (PDC) method, a reliable Bernoulli random delay-based fuzzy mode-dependent feedback (FMDF) controller is proposed to handle the change of sprung mass and actuator fault of the controlled time-varying delays SHVSSs. Simulation results verify the validity of the method and riding comfort level of the vehicle.

Anti-disturbance observer-based finite-time reliable control design for fuzzy switched systems

This study proposes a finite-time anti-disturbance observer-based reliable (Q,S,R)−θ dissipative feedback control technique for a class of Takagi-Sugeno fuzzy switched systems in conjunction with time-varying state/input delays and multiple disturbances. In contrast to previous findings, the external disturbances in this study are considered to be multiple disturbances, which are classified into matched and mismatched disturbances since the underlying system can be affected by various forms of disturbances [21], [25]. In order to deal with the matched disturbances that are brought about by exogenous systems, an anti-disturbance observer has been established. As well, (Q,S,R)−θ dissipative performance handles the mismatched part, which includes the concepts of H∞, passivity, mixed H∞ and passivity performance in a unified structure. In addition, unlike previous works in which the failure of the actuator is assumed to be deterministic [37], [38], the failure probability of the actuator in this work is determined using a distinct random variable with a probabilistic distribution in the range of [0,1]. Furthermore, in accordance with parallel distributed compensation method and reliable control design with stochastic theory, the desired fuzzy-rule based control protocol is developed. Moreover, distinct from the asymptotic and exponential stability that are defined over an infinite interval of time [4], [14], the finite-time notion is considered in this work, where it prevents the states from exceeding a specific range within a fixed interval. A set of adequate requirements are derived utilising the Lyapunov stability theory and average dwell time technique to ensure the finite-time boundedness of the system under consideration. In the end, effectiveness of the theoretical findings is validated by means of simulation results.

Disturbance observer-based fuzzy fault-tolerant control for high-speed trains with multiple disturbances

Abstract The fault-tolerant control problem is investigated for high-speed trains with actuator faults and multiple disturbances in this paper. Based on the novel train model resulting from Takagi and Sugeno fuzzy theory, a sliding-mode fault-tolerant control strategy is proposed. The norm bounded disturbances which are composed of interactive forces among adjacent carriages and basis running resistances are rearranged by the fuzzy linearity technique. The modeled disturbances described as an exogenous system are compensated by a disturbance observer. Moreover, a sliding mode surface is constructed, which can transform the stabilization problem of position and velocity into the stabilization problem of position errors and velocity errors, i.e., the tracking problem of position and velocity. Based on the parallel distributed compensation method and the disturbance observer, the fault-tolerant controller is solved. Lyapunov theory is used to prove the stability of the closed-loop system. The feasibility and effectiveness of the proposed fault-tolerant control strategy are illustrated by simulation results.

Fuzzy robust non-fragile control for nonlinear active suspension systems with time varying actuator delay

The active suspension systems have attracted increasing attentions because of its advantages in improving automotive dynamic performance. This paper focuses on the fuzzy robust non-fragile [Formula: see text] control problem for the nonlinear active suspension system with the time-varying actuator delay and control uncertainty. Firstly, a Takagi-Sugeno fuzzy suspension model is established to describe the highly nonlinear components in the suspension system. Then, a series of linear matrix inequalities are derived based on a novel parameter Lyapunov function to guarantee the asymptotic stability of the suspension systems. Also, a fuzzy [Formula: see text] controller is derived for the proposed fuzzy suspension model with the parallel distributed compensation method. Thirdly, a co-design criterion is proposed to obtain the fuzzy controller with the time varying delay and control uncertainty simultaneously. Finally, both simulations and experiments are carried out to demonstrate the effectiveness and robustness of the proposed controller.

Admissibility and admissibilization for T–S fuzzy descriptor systems with partially unknown membership functions

In this paper, the admissibility analysis and controller design issues for a class of nonlinear descriptor systems described by the T–S descriptor fuzzy model with partially unknown membership functions are discussed. New sufficient conditions are first given to ensure the admissibility of such fuzzy descriptor systems. To fully utilise the information of membership functions, the known and unknown parts of membership functions are handled by staircase functions and the bounds of the unknown part, respectively. Different from the traditional parallel distribution compensation (PDC) method, the state-feedback controller design condition is given under an imperfect premise matching method via linear matrix inequalities (LMIs). Some examples are given to show the validity of the proposed methods.

Control of Time Delay in Magnetic Levitation Systems

The high-performance control of magnetic levitation (maglev) vehicles has encountered challenges in the form of time delays. In this letter, we model a reliable control method based on a Takagi-Sugeno fuzzy model aimed at solving the problem of air gap control of a magnetic levitation system for a maglev vehicle under time-delay conditions. The key idea is based on the global fuzzy model derived through sector nonlinearity to design a global controller utilizing the parallel distributed compensation method and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${H_\infty }$</tex-math></inline-formula> method. As a result, the stability of the system is guaranteed under conditions of mass parameter uncertainty, disturbance, and time delay. The theoretical analysis, numerical simulations, and experimental results consistently show the effectiveness of the control method.

Distributed control of nonlinear conductivity heat transfer equation in a thick functionally graded plate

In this paper, distributed control of nonhomogeneous nonlinear conductivity heat transfer equation on a single plate is studied. The inhomogeneity of the equation is due to the use of functionally graded materials. In the proposed method, the governing equation of the system, which is a nonlinear partial differential equation, is represented as some linear partial differential equation using the Takagi-Sugeno linearization technique; so that their fuzzy combination accurately retrieve the original nonlinear equation. This process is done to prevent the phenomenon of frequency disorder or aliasing. Then, the modified wavenumber method is utilized to convert the obtained linear partial differential equations to a set of ordinary differential equations. In this way, a combination of fast Fourier transform and finite difference methods is implemented. Consequently, by combining Takagi-Sugeno and the modified wavenumber strategies, several ordinary differential equations are obtained for each grid point. In this regard, the parallel distributed compensation method is used to stabilize each grid point. The second method of Lyapunov is implemented to study the stability of the proposed control strategy. Numerical Simulations have been used to demonstrate the efficacy of the proposed control scheme and also its relative robustness with respect to measurement noises and parametric uncertainties.

Intelligent Fuzzy Control with State-Derivative Feedback for Takagi-Sugeno Fuzzy Stochastic Singular Systems

This document deals with the problem of passive fuzzy controller design with the state-derivative feedback approach for the nonlinear stochastic singular systems. Recently, the singular systems have a greater focus on literature because they can keep more physical system characteristics than conventional systems. At first, the Takagi-Sugeno fuzzy stochastic singular models are used to represent the nonlinear stochastic singular systems. Then, the state-derivative feedback approach and parallel distributed compensation method are employed to design the passive fuzzy controllers. In the design process, the Lyapunov stability conditions are developed subject to multiple performance constraints, including the passivity constraint and decay rate constraint. According to these Lyapunov stability conditions, the proposed fuzzy control problem can be effectively shifted into the linear matrix inequality problem that can be solved by using the convex optimal programming algorithm. At last, two examples are provided to verify the applicability and effectivity of the proposed passive fuzzy controller design approach.

Fuzzy controller design for nonlinear singular systems with external noises subject to passivity constraints

AbstractThis paper applies the state derivative feedback method and proportional plus derivative state feedback method to design the fuzzy controllers for the nonlinear singular systems with external noises. The Takagi‐Sugeno fuzzy modeling technology is employed in this paper to represent the nonlinear singular systems with external noise. Considering the singular Takagi‐Sugeno fuzzy model, the passivity constraint is chosen to treat the external noises for the controlled systems. By using the parallel distributed compensation method, the fuzzy controller is designed to satisfy the Lyapunov stability conditions and passivity constraints simultaneously. These sufficient conditions can be effectively solved in terms of linear matrix inequalities, which can be solved via the convex optimization technique. At last, some numerical examples are provided to verify the applicability and effectivity of the proposed fuzzy controller design methods.

Fuzzy Control with Pole Assignment and Variance Constraints for Continuous-time Perturbed Takagi-Sugeno Fuzzy Models: Application to Ship Steering Systems

The stability analysis and controller design of stochastic systems have become much more important because the stochastic behaviors usually exist in practical nonlinear systems. In this paper, a robust fuzzy controller design approach is proposed with multiple constraints, including state variance constraints, output variance constraints, and pole placement constraints. At first, nonlinear systems are expressed as the Takagi-Sugeno fuzzy model, and the parallel distributed compensation method is applied to design the robust fuzzy controllers. Next, considering the stability analysis and the performance constraints of perturbed Takagi-Sugeno fuzzy models, Lyapunov conditions are developed based on covariance control theory, pole placement theory and robust control theory. By constructing the stability conditions with multiple constraints, the proposed fuzzy control problem can be effectively transferred into the linear matrix inequality problem. It can be solved by the convex optimal programming algorithm. At last, a nonlinear ship steering system is selected to verify the effectiveness and applicability of the proposed robust fuzzy controller design method.

Impulsive observer‐based output control for PMSG‐based Wind Energy Conversion System

The main intention of this study is to design the fuzzy impulsive observer-based output controller scheme for hybrid Takagi–Sugeno (T–S) fuzzy permanent magnet synchronous generator (PMSG) model. Initially, the non-linearities of the PMSG differential model is equivalently transformed into linear sub-models via T–S fuzzy approach. Then, the theoretical sufficient conditions are derived by utilising the Lyapunov stability theory. Distinct to the existing studies, the overall contributions of the present work is summarised as follows: (i) the paper proposes the impulsive controller, which is a combination of both continuous and discontinuous factors that can handle the uncertainties in a complex T–S fuzzy PMSG model. (ii) The time-dependent Lyapunov functional (based on parallel distributed compensation method) has introduced for the given model, and then the sufficient conditions are proposed as solvable linear matrix inequalities. The simulation concerning the industrial problem of PMSG model is validated with the proposed theoretical conditions that guarantee the global asymptotic stability performance of the chaotic model.

Fault-Tolerant Control for Actuator Faults of Wind Energy Conversion System

The problem of robust fault-tolerant control for actuators of nonlinear systems with uncertain parameters is studied in this paper. Takagi–Sugeno (T-S) fuzzy model is used to describe the wind energy conversion system (WECS). Fuzzy dedicated observer (FDO) and fuzzy proportional integral observer (FPIO) are established to reconstruct the system state and actuator fault, respectively. Fuzzy Robust Scheduling Fault-Tolerant Controller (FRSFTC) is designed by parallel distributed compensation (PDC) method, so as to realize the purpose of active fault tolerance for actuator faults and ensure the robust stability of the system. The stability of the closed-loop system is proved by Taylor series, Lyapunov function, and Linear Matrix Inequalities (LMIs). Finally, the simulation results verify that the proposed method is feasible and effective applied to WECS with doubly fed induction generators (DFIG).

Event-triggered H∞ control for active semi-vehicle suspension system with communication constraints

This paper addresses the event-triggered H∞ control problem for an active semi-vehicle suspension (SVS) system with communication constraints. Firstly, the active SVS system is modeled as a networked T-S fuzzy system with limited communication bandwidth, and an event-triggered communication scheme (ETCS) is proposed after the sensor to lower the size of transmitted sampled-data. Since the fully different premises are used in the fuzzy controller and the T-S fuzzy plant, the requirement of the synchronous premises between them in the traditional parallel distribution compensation (PDC) method is no longer needed again. Moreover, by use of the Lyapunov theory and imperfect premise matching method, an event-triggered stability criterion and an event-triggered stabilization condition are derived which ensure the asymptotical stability of the studied system with an H∞ performance. Thanks to the consideration of imperfect premise matching when deducing the criteria above, less conservative results can be derived while enhancing the design flexibility.

Robust functional observer for stabilising uncertain fuzzy systems with time-delay

This paper presents a new technique for stabilising a Takagi–Sugeno (T-S) fuzzy system with time-delay and uncertainty. A robust fuzzy functional observer is employed to design a controller when the system states are not measurable. The model uncertainty is norm bounded, and the time-delay is time-varying but bounded. The parallel distributed compensation method is applied for defining the fuzzy functional observer to design this controller. The proposed procedure reduces the observer order to the dimension of the control input. Improved stability conditions are provided for the observer compared with the existing results of functional observer-based stabilisation of T-S fuzzy models. Lyapunov–Krasovskii functionals are used to construct delay-dependent stability conditions as linear matrix inequalities. The solution of these inequalities is used for calculating the observer parameters. The sensitivity of the estimation error to the model uncertainty is reduced by minimising the $$L_2$$ gain. The new design method developed is illustrated and verified using two examples.

Event-Triggered Predictive Control for Networked Nonlinear Systems With Imperfect Premise Matching

This paper investigates the event-triggered predictive control problem for networked nonlinear systems with imperfect premise matching. First, a model of networked nonlinear system is well constructed, which has integrated the event-triggered communication scheme (ETCS) and the predictive control together, in which, an ETCS is introduced to alleviate the communication burden by reducing the number of transmitted packets; and a fuzzy predictive controller is designed to predict future states and control signals between two successfully transmitted instants. Therefore, the data dropout induced by the networks can be actively compensated. Second, by using a common Lyapunov theory, a stability criterion and two stabilization criteria are deduced to ensure the asymptotical stability of the studied system and find the controller gains, respectively. Different from the traditional parallel distributed compensation method, the synchronous premise variables between the T–S fuzzy system and the fuzzy event-triggered predictive controller (FETPC) are no longer needed again. Since the imperfect premise matching condition is well considered in the derivation of the main results, the design flexibility and low cost of the FETPC implementation can be expected. Finally, the validity of the method proposed in this paper is demonstrated by a nonlinear mass-spring example.

Iterative Learning Control for Network Data Dropout in Nonlinear System

The paper presents iterative learning control for data dropout in nonlinear system. The parallel distribution compensation method is used to determine the T-S nonlinear model and the nonlinear model is converted into local linear model. Assuming the probability of data loss is known. It is assumed that the probability of data loss is known, and the loss of data is described using a sequence that satisfies the Bernoulli distribution. The design of the learning control controller for linear discrete systems with data loss is studied. The iterative learning controller for data dropout is designed with the T-S model. The iterative learning controller designed has expected convergence characteristics and quadratic performance index. The simulation results show that the design method is effective.

Neural-network-based fuzzy logic control of a 3D rigid pendulum

This paper concerns the attitude control problem of a 3D rigid pendulum based on dynamic T-S fuzzy neural model. A generalized 3D rigid pendulum subjected to a constant gravitational force consists of a rigid body supported by a fixed and frictionless pivot with three degrees of freedom. There exist two equilibriums of the 3D rigid pendulum characterized with unstable manifolds near the inverted equilibrium and stable manifolds near the hanging equilibrium. For the attitude control problem at the equilibrium position, T-S fuzzy neural model is adopted to approximate the nonlinear part of the 3D rigid pendulum. The method of parallel distributed compensation is used to form the angular velocity feedback controller to cope with the nonlinearity. Moreover, an attitude feedback controller is designed for the linear part so as to guarantee the overall system’s stability. Numerical simulations are performed to illustrate the validity of the proposed method.

T-S Fuzzy Model Based H-Infinity Control for 7-DoF Automobile Electrohydraulic Active Suspension System

This paper presents a double loop controller for a 7-DoF automobile electrohydraulic active suspension via T-S fuzzy modelling technique. The outer loop controller employs a modified H-infinity feedback control based on a T-S fuzzy model to provide the actuation force needed to ensure better riding comfort and handling stability. The resulting optimizing problem is transformed into a linear matrix inequalities solution issue associated with stability analysis, suspension stroke limit, and force constraints. Integrating these via parallel distributed compensation method, the feedback gains are derived to render the suspension performance dependent on the perturbation size and improve the efficiency of active suspensions. Adaptive Robust Control (ARC) is then adopted in the inner loop design to deal with uncertain nonlinearities and improve tracking accuracy. The validity of improvements attained from this controller is demonstrated by comparing with conventional Backstepping control and a passive suspension on a 7-DoF simulation example. It is shown that the T-S fuzzy model based controller can achieve favourable suspension performance and energy conservation under both mild and malevolent road inputs.

Output-Feedback Control Design for a Class of Switched Stochastic Nonlinear Systems with Input Delay

An output-feedback control problem is investigated for a class of T-S fuzzy switched stochastic systems with input delay in the paper. The considered fuzzy switched stochastic systems consist of several switched stochastic models, and each is described by T-S fuzzy system. Based on the parallel distributed compensation method, a fuzzy output-feedback controller is developed. Furthermore, the sufficient conditions are derived to guarantee the fuzzy switched stochastic system with input delay pth moment is exponentially stable. Finally, two examples are given to illustrate the effectiveness of the proposed control method.