Parallel Distributed Compensation Research Articles

Sampled-Data Fuzzy Stabilization of Nonlinear Systems Under Nonuniform Sampling

This paper investigates the sampled-data fuzzy stabilization problem for a class of nonlinear systems that is exactly modeled in Takagi–Sugeno fuzzy form at least locally. A new method for designing parallel distribution compensation fuzzy controller is proposed, which just requires that the nonlinear function is locally Lipschitz. By considering the sample-and-hold behavior of the system and using Jensen's integral inequality, an inequality constrain condition is derived from the locally Lipschitz property. Further, by defining a time-dependent Lyapunov–Krasovskii functional term, a new technique instead of the use of S-procedure is developed, and stabilization conditions for state feedback and observer-based output feedback under nonuniform sampling are obtained. Compared with the existing ones, the new design method not only avoids the difficulty of finding exact upper bounds of asynchronous errors of mismatch membership functions, but contains less conservatism and less numerical complexity as well. Finally, some illustrative examples are given to show the effectiveness of the proposed design method and the significant improvement over the existing results.

Reliable fuzzy H∞ control for active suspension of in-wheel motor driven electric vehicles with dynamic damping

A fault-tolerant fuzzy H∞ control design approach for active suspension of in-wheel motor driven electric vehicles in the presence of sprung mass variation, actuator faults and control input constraints is proposed. The controller is designed based on the quarter-car active suspension model with a dynamic-damping-in-wheel-motor-driven-system, in which the suspended motor is operated as a dynamic absorber. The Takagi-Sugeno (T-S) fuzzy model is used to model this suspension with possible sprung mass variation. The parallel-distributed compensation (PDC) scheme is deployed to derive a fault-tolerant fuzzy controller for the T-S fuzzy suspension model. In order to reduce the motor wear caused by the dynamic force transmitted to the in-wheel motor, the dynamic force is taken as an additional controlled output besides the traditional optimization objectives such as sprung mass acceleration, suspension deflection and actuator saturation. The H∞ performance of the proposed controller is derived as linear matrix inequalities (LMIs) comprising three equality constraints which are solved efficiently by means of MATLAB LMI Toolbox. The proposed controller is applied to an electric vehicle suspension and its effectiveness is demonstrated through computer simulation.

Industrial Internet of Things: Design and Stabilization of Nonlinear Automation Systems

A fuzzy model-based method for Internet-based control of nonlinear automation systems is presented, here. In this way, the nonlinear system is decomposed to a set of fuzzy-blended locally linearized subsystems, and further the previously proposed variable selective control methodology is applied to each subsystem. In order to deal with Internet effects, real-time control signals are constructed for every entry of pre-specified vector of time delays, which is chosen based on the presumed upper-bound of the network time delay. Using the idea of parallel distributed compensation strategy and by solving linear matrix inequalities, the closed-loop stability of the overall Internet-based control system is guaranteed. Simulation studies on two well-known benchmark problems demonstrate the effectiveness of the proposed method.

A robust L1 controller design for continuous-time TS systems with persistent bounded disturbance and actuator saturation

This paper proposes a novel approach for L1 performance controller design of saturated input nonlinear systems described by Takagi-Sugeno (TS) fuzzy systems. The proposed method utilizes parallel distributed compensation (PDC) approach to minimize the effect of persistent bounded disturbances on the system output and the design conditions are formulated in terms of linear matrix inequalities (LMIs) and a generalized eigenvalue problem (GEVP). The novelty of this paper is to design a saturated robust L1 PDC controller whose procedure comprises new techniques for both minimizing the L1 performance gain and handling actuator saturation constraint. These techniques lead to less conservative results compared to recently published papers in the viewpoint of L1 performance criterion gain as well as the control input saturation. The advantages of the proposed approach in each above-mentioned viewpoint are shown via numerical examples by comparing our results with the existing literatures. Finally, a nonlinear electromagnetic suspension (EMS) system is considered to verify the applicability and efficiency of this novel design method.

Imperfect premise matching controller design for T-S fuzzy systems under network environments

This paper focuses on an imperfect premise matching controller design for T-S fuzzy systems under network environments. Different with the traditional parallel distribution compensation (PDC) method, the same premises between the PDC controller and the T-S fuzzy systems are no longer needed again in the proposed method. Under consideration of the unmatched grades of membership in the networked T-S fuzzy systems, a unified T-S fuzzy model is firstly proposed, in which a networked state-feedback fuzzy controller with communication delays is used to reconstruct the system. Then, based on the constructed model and by use of the Wirtinger-based inequality technique to deal with the cross items, two less conservative stability and stabilization criteria are derived to enhance the design flexibility. Finally, two numerical examples are used to show the effectiveness of proposed method.

Design of new fuzzy sliding mode controller based on parallel distributed compensation controller and using the scalar [formula omitted] function

This paper presents a new design of fuzzy sliding mode controller based on parallel distributed compensation and using a scalar sign function. The proposed fuzzy sliding mode controller (FSMC) uses the parallel distributed compensation (PDC) scheme to design the state feedback control law. The controller gains are determined in offline mode via linear quadratic regulator technique. Moreover, the fuzzy sliding surface of the system is designed using stable eigenvectors and the scalar sign function in order to overcome the discontinuous switching. This later is obtained by a sign function of the standard FSMC. The advantages of the proposed design are a minimum energy control effort, faster response and zero steady-state error. Finally, the validity of the proposed design strategy is demonstrated through the simulation of a flexible joint robot.

T-S Fuzzy Observer and Controller of Doubly-Fed Induction Generator

This paper aims to ensure a stability and observability of doubly fed induction generator DFIG of a wind turbine based on the approach of fuzzy control type T-S PDC (Parallel Distributed Compensation) which determines the control laws by return state and fuzzy observers. First, the fuzzy TS model is used to precisely represent a nonlinear model of DFIG proposed and adopted in this work. Then, the stability analysis is based on the quadratic Lyapunov function to determine the gains that ensure the stability conditions. The fuzzy observer of DFIG is built to estimate non-measurable state vectors and the estimated states converging to the actual statements. The gains of observatory and of stability are obtained by solving a set of linear matrix inequality (LMI). Finally, numerical simulations are performed to verify the theoretical results and demonstrate satisfactory performance.

T-S fuzzy model based adaptive fuzzy current tracking control of three-phase active power filter

This paper proposed an adaptive fuzzy state feedback controller for a three-phase active power filter (APF) based on a Takagi-Sugeno (T-S) fuzzy model. The T-S fuzzy model is based on the APF dynamic model in the dq frame, which ensures that the current control dynamic and DC capacitor voltage dynamic become decoupled. By using the parallel distributed compensation (PDC), local linear state feedback controller could be designed for each T-S fuzzy sub-model. To deal with the parametric uncertainties and external disturbances, a parameter estimation scheme for tuning the parameters of T-S fuzzy model is designed and the parameters are adjusted online by the adaptive law derived from the Lyapunov stability analysis. Simulation studies demonstrate that the proposed control method exhibit excellent performance in both steady state and transient operation during balanced and unbalanced load, and source voltage.

Decentralized Fuzzy MPC on Spatial Power Control of a Large PHWR

Reliable power control for stabilizing the spatial oscillations is quite important for ensuring the safe operation of a modern pressurized heavy water reactor (PHWR), since these spatial oscillations can cause “flux tilting” in the reactor core. In this paper, a decentralized fuzzy model predictive control (DFMPC) is proposed for spatial control of PHWR. Due to the load dependent dynamics of the nuclear power plant, fuzzy modeling is used to approximate the nonlinear process. A fuzzy Lyapunov function and “quasi-min-max” strategy is utilized in designing the DFMPC, to reduce the conservatism. The plant-wide stability is achieved by the asymptotically positive realness constraint (APRC) for this decentralized MPC. The solving optimization problem is based on a receding horizon scheme involving the linear matrix inequalities (LMIs) technique. Through dynamic simulations, it is demonstrated that the designed DFMPC can effectively suppress spatial oscillations developed in PHWR, and further, shows the advantages over the typical parallel distributed compensation (PDC) control scheme.

An Observer-Based Robust Fuzzy Stabilization Control Design for Switched Nonlinear Systems with Immeasurable Premise Variables

This paper investigates the output feedback robust stabilization problem for a class of switched nonlinear fuzzy systems, in which the premise variables depend on the state variables and do not measured directly. A switched state observer is designed to obtain the estimation of the immeasurable states. By using the parallel distributed compensation (PDC) design method and the multiple Lyapunov function approach, an output feedback controller and the switching laws are developed. To obtain the feasible solutions of the control and observer gain matrixes, a novel decoupled method is proposed, and the sufficient conditions of guaranteeing the stability of the control system conditions can be transformed into some linear matrix inequalities (LMIs), which can be easily solved. Two simulation examples are provided to show the effectiveness of the suggested theoretical results.

Robust H∞ control of Magnetic Levitation system based on parallel distributed compensator

Abstract This paper concerns with designing of a robust H ∞ controller for Magnetic Levitation system exposed to external disturbances. First, the Maglev is modeled in a discrete form of Takagi–Sugeno fuzzy (TSF) system. Then the nonlinear fuzzy controller is synthesized based on such a technique called Parallel Distributed Compensation (PDC) schemes and sufficient conditions are developed to control and guarantee the robust stabilization of a complex nonlinear system. So the proposed algorithm is used to enhance the performance and to ensure the stability of the system. Furthermore, the design conditions and criteria for quadratic stability of the TSF system are formulated as a Linear Matrix Inequality (LMI) to robustly stabilize the position of the iron ball in a Maglev system in the existence of disturbances. The proposed technique will guarantee H ∞ performance to be less than one and attenuate the effect of exogenous disturbances. Moreover, the comparison results for the control of Maglev will show the capability of the proposed approach.

New time-varying fuzzy sets based on a PSO midpoint of the universe of discourse

The paper presents a robust parallel distributed compensation (PDC) fuzzy controller for a nonlinear and certain system in continuous time described by the Takagi-Sugeno (T-S) fuzzy model. This controller is based on a new type of time-varying fuzzy sets (TVFS). These fuzzy sets are characterized by displacement of the kernels to the right or left of the universe of discourse, and they are directed by a well-defined criterion. In this work, we only focused on the movement of midpoint of the universe. The movements of this midpoint are optimized by particle swarm optimization (PSO) approach.

Robust H∞ control for uncertain singular discrete T–S fuzzy time-delay systems with actuator saturation

In this paper, the problem of robust H∞ control for uncertain singular discrete T–S fuzzy time-delay systems with actuator saturation is addressed. Based on singular value decomposition approach, a delay-dependent sufficient condition for the H∞ control problem is obtained by constructing multiple Lyapunov–Krasovskii function and a latest difference inequality. Meanwhile, a parallel-distributed compensation (PDC) state feedback H∞ controller design problem is solved by linear matrices inequalities (LMIs) to guarantee the closed-loop system not only is admissible but also possesses H∞ performance index γ. Moreover, the problem of estimating the domain of attraction for the discrete T–S fuzzy closed-loop system is formulated and solved as a LMI optimization problem. Finally, numerical examples demonstrate the obtained estimation of the domain of attraction and H∞ performance index γ less conservative than some result reported in the literature.

Basis-dependent and delay-dependent results on robust L1 filtering for networked control systems

Persistent and amplitude-bounded disturbances are nowadays considered for various engineering applications. Whereas the traditional H∞ and L2–L∞ filtering methods under the energy-bounded external disturbances assumption cannot receive good noise suppression effect. To effectively reflect the capability of disturbances suppression, this paper proposes a robust L1 filtering approach for a class of nonlinear networked control systems (NNCSs) described by Takagi–Sugeno (T–S) fuzzy model. According to the analysis of the typical time-delay issue induced by communication network and the parallel distributed compensation (PDC) technique, a fuzzy filtering error system is established. Attention is focused on designing the robust L1 filter that guarantees the fuzzy filtering error system to be asymptotically stable and to have a prescribed L1 noise attenuation level γ with respect to all persistent and amplitude-bounded disturbances. In particular, we concentrate on the delay-dependent case, using a basis-dependent Lyapunov–Krasovskii functional which refers to reducing the conservatism, the peak-to-peak performance criterion is first proposed. The integral inequality method and linear matrix inequality (LMI) technique are adopted during the process of robust L1 stability analysis. Finally, two numerical examples are presented to demonstrate the effectiveness of the proposed method.

H 2 control of a one-quarter semi-active ground vehicle suspension

Magneto-rheological (MR) dampers are effective solutions in improving vehicle stability and passenger comfort. However, handling these dampers implies a strong effort in modeling and control. This research proposes an H2 controller, based on a Takagi-Sugeno (T-S) fuzzy model, for a two-degrees-of-freedom (2-DOF) one-quarter vehicle semi-active suspension with an MR damper; a system with important applications in automotive industry. Regarding performance criteria (in frequency domain) handled herein, the developed controller considerably improves the passive suspension's efficiency. Moreover, nonlinear actuator dynamics usually avoided in reported work, is included in controller's synthesis; improving the relevance of research outcomes because the controller is synthesized from a closer-to-reality suspension model. Going further, outcomes of this research are compared (based on frequency domain performance criteria and a common time domain test) with reported work to highlight the outstanding results. H2 controller is given in terms of quadratic Lyapunov stability theory and carried out by means of Linear Matrix Inequalities (LMI), and the command signal is applied via the Parallel Distributed Compensation (PDC) approach. A case of study, with real data, is developed and simulation work supports the results. The methodology applied herein can be extended to include other vehicle suspension's dynamics towards a general chassis control

Robust-Optimal Fuzzy Model-Based Control of Flexible Spacecraft With Actuator Constraint

This paper presents a robust-optimal fuzzy controller for position and attitude stabilization and vibration suppression of a flexible spacecraft during antenna retargeting maneuver. The fuzzy controller is based on Takagi–Sugeno (T–S) fuzzy model and uses the parallel distributed compensator (PDC) technique to quadratically stabilize the closed-loop system. The proposed controller is robust to parameter and unstructured uncertainties of the model. We improve the performance and the efficiency of the controller by minimizing the upper bound of the actuator's amplitude and maximizing the uncertainties terms included in the T–S fuzzy model. In addition to actuator amplitude constraint, a fuzzy model-based observer is considered for estimating unmeasurable states. Using Lyapunov stability theory and linear matrix inequalities (LMIs), we formulate the problem of designing an optimal-robust fuzzy controller/observer with actuator amplitude constraint as a convex optimization problem. Numerical simulation is provided to demonstrate and compare the stability, performance, and robustness of the proposed fuzzy controller with a baseline nonlinear controller.

Exponentially stable guaranteed cost control for continuous and discrete-time Takagi–Sugeno fuzzy systems

This paper investigates exponentially stable guaranteed cost control (GCC) for a class of nonlinear systems which is represented by Takagi–Sugeno (T–S) fuzzy systems. State feedback controllers of parallel distributed compensation (PDC) structure are designed by the means of GCC for continuous and discrete-time T–S fuzzy systems respectively. GCC methods in this paper adopt quadratic performance functions, which take effects of control efforts, regulation errors and convergence rates into consideration simultaneously, to provide desirable performance and fast response for closed-loop systems. Sufficient design conditions that guarantee exponential stabilities of resulting closed-loop systems with predefined convergence rates are presented. By setting different convergence rates, response speed of the closed-loop nonlinear system can be adjusted. The proposed design procedures are eventually converted into linear matrix inequalities (LMIs) problems of minimizing upper bounds of the guaranteed cost functions. Finally, a well-known nonlinear benchmark control example and a truck–trailer example demonstrate the effectiveness and feasibility of all the proposed methods.

Delay-dependent exponential stabilization of nonlinear fuzzy impulsive systems with time-varying delay

This paper investigates the problem of exponential stabilization for a class of nonlinear fuzzy impulsive systems with time-varying delay. Firstly, the systems are expressed by the extended Takagi–Sugeno (T–S) fuzzy model. Secondly, the combination of Lyapunov–Krasovskii type functionals and the parallel distributed compensation (PDC) idea is employed to design a state feedback controller such that the closed-loop systems are globally exponentially stable. The corresponding sufficient delay-dependent conditions are derived in terms of linear matrix inequalities (LMIs). Finally, two examples are presented to demonstrate the effectiveness of the theoretical contribution.

A new method for control of nonlinear networked systems

Networked control of a class of nonlinear systems is considered. For this purpose, the previously proposed variable selective control (VSC) methodology is extended to the nonlinear systems. This extension is based upon the decomposition of the nonlinear system to a set fuzzy-blended locally linearized subsystems, and further application of the VSC methodology to each subsystem. Using the idea of parallel distributed compensation (PDC) method, the closed-loop stability of the overall networked system is guaranteed, using new linear matrix inequalities (LMIs). For the real-time implementation, real-time control signals are constructed for every entry of pre-specified vector of time delays, which is selected based on the presumed upper-bound of the network time delay. Similar to the traditional packet-base control methodology, such control signals are then packed as a control-side packet and transmitted back to a time delay compensator (TDC) located on the plant-side of the network. According to the most recent network time delay, the TDC selects just one entry of the control vector and applies it to the actuator through a zero order hold element. A sufficient condition for closed-loop asymptotic stability is determined. Simulation studies on nonlinear benchmark problems demonstrate the effectiveness of the proposed method.

An Optimal Divisioning Technique to Stabilization Synthesis of T-S Fuzzy Delayed Systems.

This paper investigates the problem of stability analysis and stabilization for Takagi-Sugeno (T-S) fuzzy systems with time-varying delay. By using appropriately chosen Lyapunov-Krasovskii functional, together with the reciprocally convex a new sufficient stability condition with the idea of delay partitioning approach is proposed for the delayed T-S fuzzy systems, which significantly reduces conservatism as compared with the existing results. On the basis of the obtained stability condition, the state-feedback fuzzy controller via parallel distributed compensation law is developed for the resulting fuzzy delayed systems. Furthermore, the parameters of the proposed fuzzy controller are derived in terms of linear matrix inequalities, which can be easily obtained by the optimization techniques. Finally, three examples (one of them is the benchmark inverted pendulum) are used to verify and illustrate the effectiveness of the proposed technique.