Parallel Distributed Compensation Research Articles

Experimental Evaluation of a Takagi–Sugeno Fuzzy Controller for an EV3 Ballbot System

In this paper, experimental results about the performance of a Takagi–Sugeno Fuzzy Controller (TSFC) for an EV3 Ballbot Robotic System (EV3BRS) are reported. The physical configuration of the EV3BRS has the form of an inverted pendulum mounted on a ball. The EV3BRS is an underactuated robotic system with four outputs and two control torques. In this work, following the Takagi–Sugeno (TS) fuzzy control design methodology, the Parallel Distributed Compensation (PDC) approach is used in the design of the TSFC. The EV3BRS’s TS Fuzzy Model (TSFM) design comes from linearization of the nonlinear model around two operation points near the upright position of EV3BRS’s body. The Linear Matrix Inequality (LMI) approach was used to obtain the feedback gains for every local linear controller, guaranteeing, via a conservative stability condition, the global asymptotic stability of the overall fuzzy control system. The main goal of the control task consists of maintaining the EV3BRS’s body at its upright position. Measurement and control data from and to the EV3BRS are transferred via telecontrol and telemetry. The appropriate performance of the controller design is corroborated via experimentation.

Fuzzy Modeling Framework Using Sector Non-Linearity Techniques for Fixed-Wing Aircrafts

This paper presents a mathematical modeling approach utilizing a fuzzy modeling framework for fixed-wing aircraft systems with the goal of creating a highly desirable mathematical representation for model-based control design applications. The starting point is a mathematical model comprising fifteen non-linear ordinary differential equations representing the dynamic and kinematic behavior applicable to a wide range of fixed-wing aircraft systems. Here, the proposed mathematical modeling framework is applied to the AIRBUS A310 model developed by ONERA. The proposed fuzzy modeling framework takes advantage of sector non-linearity red techniques to recast all the non-linear terms from the original model to a set of combined fuzzy rules. The result of this fuzzification is a more suitable mathematical description from the control system design point of view. Therefore, the combination of this fuzzy model and the wide range of control techniques available in the literature for such kind of models, like parallel and non-parallel distributed compensation control laws using linear matrix inequality optimization, enables the development of control algorithms that guarantee stability conditions for a wide range of operations points, avoiding the classical gain scheduling schemes, where the stability issues can be extremely challenging.

The positivity and event-triggered stabilization of Takagi-Sugeno fuzzy systems with actuator saturation

The positivity and event-triggered stabilization of Takagi-Sugeno fuzzy systems with actuator saturation are investigated in this paper. Different from the existing quadratic event-triggered mechanism (ETM), a linear ETM is constructed, which can be reduced to a time-triggered mechanism (TTM). Based on parallel distribution compensation, an event-triggered fuzzy controller is designed, and sufficient conditions under the estimation of a certain domain of attraction are proposed to ensure the ETM-based and TTM-based closed-loop systems are positive and stable. The controller gain is solved directly by the proposed conditions. And then these sufficient conditions are extended to the conditions under the estimation of the largest domain of attraction by establishing an optimization problem. Furthermore, the linear ETM is proved to exclude the Zeno behavior of the system. Finally, two simulation examples are utilized to verify the effectiveness of the proposed event-triggered control scheme.

Robust Observer-Based Proportional Derivative Fuzzy Control Approach for Discrete-Time Nonlinear Descriptor Systems with Transient Response Requirements

This paper proposes an observer-based proportional Derivative (O-BPD) fuzzy controller for uncertain discrete-time nonlinear descriptor systems (NDSs). Representing NDSs with the Takagi–Sugeno fuzzy model (T-SFM), the proportional derivative (PD) feedback method can be utilized in the fuzzy controller design via the Parallel Distributed Compensation (PDC) concept, such that the noncausal problem and impulse behavior are avoided. A fuzzy observer is proposed to obtain unmeasured states to fulfill the PD fuzzy controller. Moreover, uncertainties and transient response performances are taken into account for the NDSs. Then, a stability analysis process and corresponding stability conditions are derived from the Lyapunov theory with the robust control method and the pole constraint. Different from existing research, the Singular Value Decomposition (SVD) and the projection lemma are utilized to transfer the stability conditions into the Linear Matrix Inequation (LMI) form. Because of this reason, the conservatism of the analysis process can be reduced by eliminating the restriction on the positive definite matrix in the Lyapunov function. By giving the proper center and radius parameters of the pole constraint in the O-BPD fuzzy controller design process, the expected transient responses can be obtained for different designers and different practical applications. Finally, the effectiveness and applicability of the proposed O-BPD fuzzy controller are demonstrated by two examples of the simulation.

Enhanced robust adaptive flight control for a convertible VTOL UAV

In this paper, we propose less conservative formulations for candidate controllers of robust adaptive mixing control (RAMC) strategies. The RAMCs are employed to solve the trajectory tracking problem throughout the full flight envelope, with guaranteed stability, of a convertible plane (CP) vertical take-off and landing (VTOL) unmanned aerial vehicle (UAV). Initially, the multi-body nonlinear dynamic model of the CP VTOL UAV is obtained using the Euler–Lagrange formalism, from which a linear parameter-varying (LPV) model is derived to be used in the design of the RAMC candidate controllers. The new formulations of the candidate controllers are proposed considering two approaches: a (i) Parallel Distributed Compensation (PDC); and (ii) a parameter-dependent Lyapunov function. Hardware-In-the-Loop (HIL) experiments are performed in a high-fidelity flight simulator to verify the fulfillment of real-time constraints, ensuring a computationally lightweight control strategy ready for implementation in a low-cost embedded computational system.

Robust H2 nonlinear fuzzy decentralized control design for a VSC‐HVDC link

SummaryA Robust Nonlinear Fuzzy Decentralized Controller ( RNFDC) is proposed to improve the overall robustness and tracking ability of a VSC‐HVDC link. The studied system is considered as composed by two overlapping nonlinear subsystems. The nonlinear interaction between the two subsystems is treated as a disturbance rejection problem by fuzzy control techniques. First, the Takagi Sugeno (TS) fuzzy model is adopted for fuzzy modeling of the uncertain nonlinear system. Next, new stability conditions for a generalized class of uncertain HVDC systems are derived from robust control techniques based on Linear Matrix Inequalities (LMIs). The design method employs the so‐called Parallel Distributed Compensation (PDC) to obtain RNFDC gains based on LMIs.The efficiency and robustness of the proposed controllers are analytically proven and tested through validation simulations. The main contributions of this paper are: (i) resilience: in case of failure of one converter or loss of measures or controls, the control of the other converter is not affected; (ii) robustness is improved in order to provide good responses in case of network variations and HVDC line parameters changes; (iii) fuzzy techniques are adopted to handle nonlinearities and changes of operating conditions. The proposed RNFDC is compared with Fuzzy H Decentralized State Feedback Control ( NFDC) and Linear Decentralized Control ( LDC) in simulation to illustrate the control synthesis and its effectiveness.

$H_{\infty }$ Asynchronous Admissibilization for Nonlinear Singular Delayed Hybrid Hydraulic Turbine Governing Systems With Impulsive Perturbations

This article researches <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> asynchronous admissibilization for nonlinear singular delayed hybrid hydraulic turbine governing systems with impulsive perturbations. By exploiting Takagi-Sugeno (T-S) fuzzy technique, the fuzzy singular delayed hybrid hydraulic turbine governing system with impulsive perturbations is built, which can not only accurately and concisely describe the dynamic behaviors of the pipeline, but also resist damages for the hydraulic turbine system caused by sudden reasons. Then, the asynchronous fuzzy state feedback controller (FSFC) is designed by using parallel distributed compensation (PDC) technique, and the asynchronous mechanism (AM) between the modes of FSFC and the modes of controlled plant is depicted by a hidden Markovian model. By constructing an improved timer-dependent (T-D) Lyapunov-Krasovskii (L-K) functional, the new criteria about <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> admissibilization for fuzzy singular delayed hybrid hydraulic turbine governing systems with impulsive perturbations can be acquired. The gains of asynchronous FSFC are expressed by solving linear matrix inequalities (LMIs). Impulsive operators are successfully generalized and extended from <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathbb {R}$</tex-math></inline-formula> to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathbb {R}^{n\times n}$</tex-math></inline-formula> , which makes the approach presented in this article more universal. Finally, the simulation results prove the correctness and availability of the method provided in this article.

Dynamic Output Feedback-Based Tracking Control Design With Input Time-Varying Delay for Fuzzy Systems

The prime purpose of this study is to design an output tracking control law in the perspective of compensating the effects induced by time-varying input delays and disturbances. In particular, the control protocol is developed for nonlinear systems, where the nonlinearities are effectively represented as a convex summation of linear subsystems using membership functions, which is precisely referred by fuzzy model approach. Accordingly, with the aid of parallel distributed compensation strategy and extended Smith predictor approach, the fuzzy-dependent dynamic control law is formulated. Moreover, the improved-equivalent-input-disturbance estimator approach is implemented to estimate the disturbance signals, whose output are tied to the resultant dynamic output feedback controller. On such circumstances, the controller gain matrices that assures the asymptotic tracking performance of the addressed system is calculated by solving the derived set of sufficient conditions. Conclusively, the effectiveness of the developed theoretical outcomes is validated by virtue of numerical simulations.

Passive Stabilization of Static Output Feedback of Disturbed Nonlinear Stochastic System

This paper investigates the Static Output (SO) control issue of the disturbed nonlinear stochastic system, which achieves passivity. Through the application of fuzzy sets and the stochastic differential equation, a Takagi–Sugeno (T-S) fuzzy model with the terms of multiplicative noise and external disturbance can be constructed to describe the considered systems. Furthermore, the Parallel Distributed Compensation (PDC) concept is used to design a fuzzy controller exhibiting an SO feedback scheme structure. To attenuate the effect of external disturbance, the PDC-based SO fuzzy controller is designed to exhibit passivity. During the derivation of some sufficient conditions, a line-integral Lyapunov function is utilized to avoid the conservative term produced using the derivative membership function. Using converting technologies, a stability criterion belonging to Linear Matrix Inequality (LMI) forms is proposed such that the derived conditions are convex hull problems and are solved through an optimization algorithm. Then, the proposed criterion is used to discuss the problem of SO controller design of ship fin stabilizing systems with added disturbance and noise.

Improved stabilization condition of delayed T-S fuzzy systems via an extended quadratic function negative-determination lemma

This paper focuses on the stability and stabilization problems of continuous-time T-S fuzzy systems (TSFS) with variable delay. A new augmented Lyapunov–Krasovskii functional (LKF) is established by combining the negative quadratic term with the alterable delay-product-integral term. To further improve the results, an extended quadratic function negative-determination (QFND) lemma is proposed to deal with δ(t)-related quadratic function in the LKF derivative. Subsequently, based on the parallel distributed compensation (PDC) technique, a bounded delay correlation stabilization criterion is derived. Finally, the proposed methods are applied to a numerical example and an inverted pendulum system to verify their effectiveness and superiority.

Fuzzy optimal tracking control for nonlinear underactuated unmanned surface vehicles

In this paper, a reinforcement Q-learning fuzzy optimal tracking control method is investigated for nonlinear underactuated unmanned surface vehicles (USVs) with external disturbances. Firstly, the motion dynamics of USVs are described by the Takagi–Sugeno (T–S) fuzzy discrete-time systems. Secondly, by applying parallel distributed compensation (PDC) method and constructing cost function, the existence condition of optimal solutions is derived and reduced to the algebraic Riccati equations (AREs). To solve the solutions of the GAREs, a Q-learning value iteration (VI) algorithm is further developed, which can be implemented by eliminating the demand of initial allowable control policy and system information. The developed strategy has the advantage that the optimal control policy can ensure the USV to be stable and the desired reference signal can also be well tracked by the USV output. Finally, the proposed fuzzy optimal control algorithm is applied to control the USV, the simulation results verify the feasibility of the proposed optimal control algorithm.

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.

Dual asynchronous control for T‐S fuzzy semi‐Markov jump systems: A finite‐time design

AbstractThis paper addresses the control problem of Takagi–Sugeno fuzzy semi‐Markov jump systems (TFSMJSs) under the finite‐time analysis and synthesis framework. Due to the commonly used networked communication structure, the semi‐Markovian jumping modes and fuzzy premise variables cannot always perfectly match for system and controller among the whole system operation. More precisely, both asynchronous phenomena in fuzzy membership and jumping mode are taken into account, and then, mode‐dependent finite‐time controllers are developed with these features. By utilizing stochastic analysis and Lyapunov–Krasovskii stability theory, sufficient criteria are first established for the closed‐loop system in the context of mean‐square sense. Furthermore, feedback controller gains are captured by the matrix technique and parallel distributed compensation (PDC)‐related arguments. Eventually, a simulation example of an unmanned marine vehicle (UMV) is utilized to demonstrate the validity of the developed results.

Robust Preview Path Tracking Control of Autonomous Vehicles Under Time-Varying System Delays and Saturation

Realistic uncertainties and disturbances cannot be ignored when striving towards high-performance autonomous driving. Meanwhile, advanced vehicular sensing technology enables more and more self-driving techniques to come out. Against this backdrop, this paper aims to holistically address the system uncertainties and disturbances in the path tracking control of autonomous vehicles (AVs) by the preview control theory to achieve superior control performance. First, unmeasureable multi-uncertainties and the external disturbance are considered simultaneously into the robust gain-scheduling framework with variable longitudinal velocity. Then, by the equivalent delay approach, ineluctable time-varying system delays are effectively handled. Next, the physical constraints of the steering system and direct yaw moment control (DYC) system are considered for practical implementation through robust set invariance theory. The parallel distributed compensation (PDC) technique and auxiliary feedback matrices approach are introduced for reducing design conservatism. After that, by incorporating the road curvature into the augmented system state, the path tracking preview control problem can be solved without online optimization. Thereafter, the closed-loop system stability and guaranteed performance have been proved through the Lyapunov- Krasovski approach. The proposed controller design is finally reformulated as the optimization problem based on linear matrix inequalities (LMIs) via specific convexification techniques. Finally, to verify the validity of the proposed controller, Software in Loop (SIL) tests with Carsim full-vehicle model under different dynamic conditions have been implemented.

Design a robust and optimal fuzzy logic controller to stabilize the speed of an electric vehicle in the presence of uncertainties and external disturbances

In the nonlinear dynamic equations of the electric vehicle, parameters such as the coefficient of friction between the tires and the road, the coefficient of traction, the resistance of the anchor, and so on have ambiguities. Designing a controller that is robust to the existence of these parametric ambiguities and also to external disturbances, while still satisfying the optimality criteria, is a challenging task. In practical applications, in addition to the problems mentioned above, the computing load of the control input should also be taken into account and a sensible interaction between the performance desired by the controller and the computing volume should be offered. In the present work, a robust, optimally stable fuzzy controller based on parallel distributed compensation is designed using the Takagi–Sugeno fuzzy model of the electric vehicle. The fuzzy model stabilizer feedback gains, the upper bound of uncertainties, the upper bound of disturbance effect, and the upper bound of the cost function are obtained completely offline by solving a minimization problem based on the linear matrix inequality. Therefore, the calculation volume of the control input is extremely small. This allows the proposed control to be put into practice. The good performance of the proposed controller is demonstrated in five-stage simulations.

Observer-Based Fuzzy Control of Uncertain Nonlinear Singular Systems under Multi-Performance Requirements

This paper discusses an observer-based fuzzy control problem for uncertain nonlinear singular systems under Multi-Performance Requirements (MPRs). The approach used in the paper is to model the system using a Takagi–Sugeno (T-S) fuzzy model that can be analyzed using linear control theories. The proposed control scheme is based on the Parallel Distributed Compensation (PDC) approach and Proportional Derivative (PD) control scheme. The goal is to design an observer-based fuzzy controller that achieves stability of the system and also satisfies the Guarantee Cost Control (GCC) constraint while maintaining a desired passive constraint. The stability analysis is performed using Lyapunov theory, and the sufficient conditions are transformed into a Linear Matrix Inequality (LMI) form using a Shur Complement, free-weighting matrix method and Singular Value Decomposition (SVD) techniques. The LMI conditions are then solved using convex optimization algorithms. Finally, the proposed control method is validated using a bio-economic system to demonstrate its effectiveness.

Fractal control and synchronization of population competition model based on the T–S fuzzy model

It is of great significance to study the law of population change in species protection, resource utilization, ecological stability, and so on. The fractal behavior of the population competition model is discussed from the fractal viewpoint. By using the sector nonlinear method, the Takagi–Sugeno (T–S) fuzzy model of the population competition model is established, and the Julia set of the population competition model based on the T–S fuzzy model is introduced. The parallel distributed compensation (PDC) is used to design the corresponding fuzzy controller, and sufficient conditions for the stability of the system are given in the form of linear matrix inequalities (LMIs). The parameters of controller gain are obtained by solving LMIs, and the control of the Julia set of the population competition model based on the T–S fuzzy model is carried out. Using the exact linearization technique, the synchronization of the Julia sets of the population competition models is realized based on the T–S fuzzy model by the linear control method, and the Julia set diagram of the corresponding population competition model is analyzed.

Practical stability of fractional-order nonlinear fuzzy systems

In this paper, we present a practical Mittag–Leffler stability for a new class of fractional-order nonlinear Takagi–Sugeno fuzzy uncertain systems. Based on fractional-order Lyapunov stability theory and the parallel distributed compensation (PDC) controller techniques, we show the convergence of the solutions of the closed-loop considered system toward a neighborhood of the origin. Furthermore, a numerical example is given to show the applicability of the main result.

Designing a Switched Takagi-Sugeno Fuzzy controller for CDC semi-active suspensions with current input constraint

To prevent the degradation of control performance resulting from the use of the clipped approach, this paper presents a novel control strategy for CDC (continuous damping control) semi-active suspensions using the Takagi-Sugeno (T-S) fuzzy method based on a piecewise affine (PWA) vertical dynamics model. First, to account for the significant tension-compression asymmetry and dissipative constraint of CDC damper force, a piecewise damping-force model is developed with current serving as input. Due to the nonlinear terms, T-S fuzzy system is then utilized to describe the suspension system via the sector nonlinearity approach. Finally, a fuzzy state feedback controller considering the asymmetry saturation of the control current is designed for the obtained switched T–S fuzzy model with optimized H∞ performance for suspension system by using the parallel distributed compensation (PDC) scheme. Simulation and experimental results under sinusoidal, random and transient excitations show significant improvements of the proposed approach on ride comfort and road handling while guaranteeing the performance under the input current constraint.