Concept Of Parallel Distributed Compensation Research Articles

Pantograph Catenary Contact Force Regulation Based on Modified Takagi-Sugeno Fuzzy Models

In this paper, a new contact force control technique, based on the modified Takagi-Sugeno model and the parallel distributed compensation concept is developed to suppress vibrations between the pantograph and the catenary by regulating the contact force to a reference value, thereby achieving stable current collection. The proposed method uses simple and standard PID and modified Takagi-Sugeno fuzzy controllers. The two controllers guarantee the designed system's robust stability. Furthermore, based on a simplified pantograph–catenary system model, the comparative simulation results show that variations of the contact force can be almost attenuated. As a result, the system stability is guaranteed, and the performance robustness is verified.

Nonfragile H∞ tracking control strategies for classes of linear and bilinear uncertain Takagi-Sugeno fuzzy systems

This paper presents fuzzy tracking control strategies for classes of linear and bilinear Takagi-Sugeno Fuzzy System with Uncertainties and Disturbances (T-S FSUD). For both classes, the Lyapunov direct approach and the parallel distributed compensation concept are used to design nonfragile H∞ tracking controllers, which ensure the robust asymptotic stability of augmented systems despite the presence of parameter uncertainties, external disturbances, and controllers fragility. Besides that, based on the Schur complement, the separation lemma, and through some variable transformations, sufficient stability conditions of each augmented T-S FSUD are established and formulated in terms of linear matrix inequalities. Finally, numerical simulations are carried out to demonstrate the validity and the applicability of designed control schemes on tracking control of an inverted pendulum and a nonlinear mechanical system.

Planning the Yaw Correction Trajectory Based on Current Motor Detection

This paper describes distributed adaptive methods for solving the trajectory distortion control problem of intelligent lawnmowers. The strategy we have chosen is to use the association of motor current changes with changes in the movement patterns of the trajectory to try to modify the relationship between the fuzzy controller and the Proportional Integral Derivative (PID) controller based on the traditional fuzzy PID control theory to design a new low-cost control scheme. The scheme uses the differences between the current detection and the linearised models as data feedback and interpolates these linear models with the Takagi-Sugeno (T-S) fuzzy method to approximate the entire non- linear model. Then, the concept of parallel distributed compensation (PDC) synthesizes a state feedback controller. A Linear Quadratic Regulator (LQR) is used to stabilize the system and achieve the desired response. A PID fuzzy control method is then used to form the control of the intelligent lawnmower motor. This strategy uses data feedback obtained by monitoring the left and the right motor current fluctuations, and it can be seen from the practical results that the proposed method is effective in obtaining an ideal linear path with good tracking behaviour in various situations. This paper uses the current monitoring change control method to determine whether the bias voltage is tested and confirms that the method can achieve stable path control.

Novel Delay-Dependent Stabilization for Fuzzy Stochastic Systems with Multiplicative Noise Subject to Passivity Constraint

A novel delay-dependent stability criterion for Takagi-Sugeno (T-S) fuzzy systems with multiplicative noise is addressed in this paper subject to passivity performance. The general case of interval time-varying delay is considered for the practical control issue. For the criterion, an integral Lyapunov-Krasovskii function is proposed to derive some sufficient relaxed conditions and to avoid the derivative of the membership function. Moreover, a free-matrix inequality is adopted to deal with the delay terms such that the available derivative of time-varying delay is bigger than one. In order to employ a convex optimization algorithm to find the control gain, a projection lemma is applied to acquire the Linear Matrix Inequality (LMI) form of the sufficient conditions. With the obtained gains, a fuzzy controller is designed by the concept of Parallel Distributed Compensation (PDC) such that the delayed T-S fuzzy systems with multiplicative noise are asymptotically stable and passive in the mean square. Finally, a stabilization problem of the ship’s autopilot dynamic system and some comparisons are discussed during the simulation results.

Current Control of the Permanent-Magnet Synchronous Generator Using Interval Type-2 T-S Fuzzy Systems

The current control of the permanent-magnet synchronous generator (PMSG) using an interval type-2 (IT2) Takagi-Sugeno (T-S) fuzzy systems is designed and implemented. PMSG is an energy conversion unit widely used in wind energy generation systems and energy storage systems. Its performance is determined by the current control approach. IT2 T-S fuzzy systems are implemented to deal with the nonlinearity of a PMSG system in this paper. First, the IT2 T-S fuzzy model of a PMSG is obtained. Second, the IT2 T-S fuzzy controller is designed based on the concept of parallel distributed compensation (PDC). Next, the stability analysis can be conducted through the Lyapunov theorem. Accordingly, the stability conditions of the closed-loop system are expressed in Linear Matrix Inequality (LMI) form. The AC power from a PMSG is converted to DC power via a three-phase six-switch full bridge converter. The six-switch full bridge converter is controlled by the proposed IT2 T-S fuzzy controller. The analog-to-digital (ADC) conversion, rotor position calculation and duty ratio determination are digitally accomplished by the microcontroller. Finally, simulation and experimental results verify the performance of the proposed current control.

Design of Takagi-Sugeno Fuzzy Control Scheme for Real World System Control

In this study, a novelty dual Takagi-Sugeno (TS) fuzzy control scheme (DTSFCS) is proposed for real world system control. We propose using a ball robot (BR) system control problem, where the BR has the ability to move omnidirectionally. The proposed control scheme combines two fuzzy control approaches for a BR. In this fuzzy control approach, the TS fuzzy model was adopted for the fuzzy modeling of the BR. The concept of parallel distributed compensation (PDC) was utilized to develop a fuzzy control scheme from the TS fuzzy models. The linear matrix inequalities (LMIs) can formulate sufficient conditions. Moreover, in this study, the motors of the BR were mounted on two orthogonal axes. Then, the dual TS fuzzy controller was designed to independently operate without coupling. Finally, the efficiency of the proposed control scheme is illustrated by the experimental and simulation results that are presented in this study.

Fuzzy observer-based fault tolerant control against sensor faults for proton exchange membrane fuel cells

In this paper, robust fault diagnosis problem of Proton Exchange Membrane Fuel Cells (PEMFC) is presented based on Takagi-Sugeno (TS) Fuzzy Unknown Input Observer (FUIO). TS FUIO based on Linear Matrix Equalities (LMEs) and the Linear Matrix Inequalities (LMIs) are design. Firstly, the nonlinear PEMFC system with sensor faults and disturbance is represented by TS fuzzy model. Then, a FUIO and sensor fault estimation algorithm is developed and then a model based Fuzzy Fault Tolerant Controller design uses the concept of Parallel Distributed Compensation (PDC). Sufficient stability conditions are studied based on LMIs and LMEs. In order to verify the proposed approach, a PEMFC system with return manifold pressure and hydrogen mass sensors fault and disturbance was tested to illustrate the effectiveness of the proposed strategy.

Electronic Throttle Valve Takagi-Sugeno Fuzzy Control Based on Nonlinear Unknown Input Observers

This paper deals with the synthesis of a new fuzzy controller applied to Electronic Throttle Valve (ETV) affected by an unknown input in order to enhance the rapidity and accuracy of trajectory tracking performance. Firstly, the Takagi-Sugeno (T-S) fuzzy model is employed to approximate this nonlinear system. Secondly, a novel Nonlinear Unknown Input Observer (NUIO)-based controller is designed by the use of the concept of Parallel Distributed Compensation (PDC). Then, based on Lyapunov method, asymptotic stability conditions of the error dynamics are given by solving Linear Matrix Inequalities (LMIs). Finally, the effectiveness of the proposed control strategy in terms of tracking trajectory and in the presence of perturbations is verified in comparison with a control strategy based on Unknown Input Observers (UIO) of the ETV described by a switched system for Pulse-Width-Modulated (PWM) reference signal.

$$H_\infty $$ H ∞ tracking adaptive fuzzy integral sliding mode control for a train of self-balancing vehicles

A series of self-balancing vehicles is stabilized and controlled in this research work. The system is composed of several Segway $$\frac{{\mathrm{TM}}}{}$$ type platforms interconnected through flexible links. The system is inherently highly nonlinear and underactuated which makes the tracking task very challenging. In this paper, $$H_\infty $$ tracking adaptive fuzzy integral sliding mode control scheme is proposed for n-self-balancing interconnected vehicles system where uncertainties and disturbances are included. First, a nonlinear dynamic model with uncertainties for the train system with n-vehicles is derived using the Lagrangian method assuming the vehicles moving in tandem on a inclined path. Then, the dynamics of the train system with n-vehicles is formulated as an error dynamics according to a specified reference signal. A fuzzy technique with an on-line estimation scheme is developed to approximate the dynamics of the train system with n-vehicles. The advantage of employing an adaptive fuzzy system is the use of linear analytical results instead of estimating nonlinear uncertain functions in dynamics with an online update law. Using the concept of parallel distributed compensation, the adaptive fuzzy scheme combined with the integral sliding mode control scheme is synthesized to address the system uncertainties and the external disturbances such that $$H_\infty $$ tracking performance is achieved. Simulation results for 2-self-balancing interconnected vehicles system are presented to show the effectiveness and performance of the proposed control scheme.

Intelligent control of grid‐connected AC–DC–AC converters for a WECS based on T–S fuzzy interconnected systems modelling

Control of power converters is undoubtedly an essential issue in wind-energy systems. This study focuses on the development of a control scheme dedicated to a wind-energy conversion system (WECS) based on Takagi-Sugeno (T-S) fuzzy model. The treated system includes a wind turbine followed by a permanent magnet synchronous generator and power electronic converters. After describing the elements constituting the WECS, the main objectives of control are to extract the maximum amount of available power and to control the DC-bus voltage. The proposed approach is based on the concept of decentralised stabilisation. First, as to reduce the complexity of the system, the WECS is divided into two interconnected non-linear subsystems. Then, each subsystem is represented by a T-S fuzzy model. Using the parallel distributed compensation concept, a decentralised fuzzy controller is synthesised for each subsystem. Sufficient conditions are derived from Lyapunov theory and the local feedback gains for each controller are calculated by using linear matrix inequalities tools. Therefore, the whole closed-loop fuzzy system is stable using the elaborated fuzzy control scheme. Simulation results are included to show the performance of the proposed algorithm.

Non-fragile controller design of uncertain saturated polynomial fuzzy systems subjected to persistent bounded disturbance

This paper investigates the problem of designing a non-fragile polynomial fuzzy controller for a class of polynomial fuzzy models subjected to persistent bounded disturbances and system uncertainty. The proposed controller is considered to satisfy the input saturation constraint. Furthermore, the resilient controller is affected by linear fractional uncertainties. The overall structure of the controller is obtained by the polynomial parallel distributed compensation concept. The sufficient conditions guarantee an L1 performance of the perturbed system and exponential stability of the non-perturbed system is achieved in terms of sum-of-squares decomposition conditions. Subsequently, the sum-of-squares-based conditions lead to minimization of the L1 performance such that the above-mentioned hard constraints on the control input and robustness of the closed-loop system against the system and controller uncertainties will be guaranteed. The controller gain matrices will be achieved by numerically solving the sum-of-squares-based conditions with the third-party MATLAB toolbox ‘SOSTOOLS’. Finally, extensive studies and hardware-in-the-loop simulations on a ball-and-beam system are presented, which illustrate the proposed controller can accurately and smoothly track the set point frequency. Furthermore, the proposed control approach is more robust over prior-art controllers for all the simulation scenarios.

ESTIMATED STATE FEEDBACK FUZZY CONTROL FOR PASSIVE DISCRETE TIME-DELAY MULTIPLICATIVE NOISED PENDULUM SYSTEMS

This paper develops a fuzzy controller design method via estimated state feedback scheme for discrete-time nonlinear stochastic time-delay systems which are presented by Takagi-Sugeno fuzzy model with multiplicative noises. The proposed design method is accomplished by the concept of parallel distributed compensation. Using the Lyapunov-Krasovskii function and passivity theory, the stability conditions are derived to guarantee the stability and attenuation performance. An algorithm is proposed in this paper to solve the derived stability conditions that belong to non-strict linear matrix inequality problems. Moreover, the discrete Jensen inequality and free-weighting matrix technique are employed to decrease the conservatism of the proposed design method. Finally, the control of a nonlinear time-delay pendulum system is provided to illustrate the effectiveness and usefulness of the proposed fuzzy control method.

Formula omitted] tracking adaptive fuzzy integral sliding mode control for parallel manipulators

Highly nonlinear coupling phenomenon is an inherently inevitable in parallel manipulators in which limbs/links undergo rotating and sliding with/without fixed base. In this paper, an H∞ tracking adaptive fuzzy integral sliding mode control scheme is proposed for controlling parallel manipulators with nonlinear unmodeled dynamics, external disturbances, and limb-to-limb couples in which each coupled uncertainty is assumed to be bounded by an unknown gain. The dynamics of the parallel manipulator is formulated as an error dynamics according to a specified reference model; then, a fuzzy model is used to approximate the uncertainties. Two on-line estimation schemes are developed to overcome the uncertainties and identify the gains of the unknown coupled uncertainty bounds from limb-to-limb couples, simultaneously. The advantage of employing an adaptive fuzzy system is the use of linear analytical results instead of estimating nonlinear uncertain functions with an on-line update law. By the concept of parallel distributed compensation (PDC), the adaptive fuzzy scheme uses an integral sliding mode control scheme to resolve the system uncertainties, unknown limb-to-limb coupled uncertainties, and the external disturbances such that H∞ tracking performance is achieved. The control laws are derived based on a Lyapunov criterion and the Riccati-inequality such that all states of the system are uniformly ultimately bounded (UUB) and the effect on the tracking error can be attenuated to any prescribed level to achieve H∞ tracking performance. Finally, a numerical example of a planar 2-dof parallel robot system is given to verify the effectiveness of the proposed control scheme.

Passive estimated state feedback fuzzy controller design for discrete perturbed fuzzy systems with multiplicative noises

This article presents an estimated state feedback fuzzy controller design method for uncertain passive discrete-time nonlinear stochastic systems with multiplicative noises. The nonlinear stochastic systems considered in this article are represented by Takagi–Sugeno (T–S) fuzzy models. For describing stochastic behaviors, stochastic differential equations are used to structure the stochastic T–S fuzzy model for representing nonlinear stochastic systems. Besides, the uncertainties of the controlled system are considered for dealing with molding errors and varying parameters. The concept of parallel distributed compensation is employed in this article to construct the estimated state feedback fuzzy controllers. Applying the Lyapunov and passivity theories, the sufficient stability conditions are derived in terms of linear matrix inequality. Finally, a numerical example is provided to show the effectiveness and applicability of the proposed fuzzy controller design approach.

Robust Scheduler Fuzzy Controller of DFIG Wind Energy Systems

This paper addresses the robust fuzzy scheduler controller (RFSC) for nonlinear systems which is robust enough to stabilize a nonlinear system with parametric uncertainties, wind disturbance, and give an acceptable closed-loop performance in the presence of state variables unavailable for measurements. The Takagi-Sugeno (TS) fuzzy model is adopted for fuzzy modeling of the nonlinear system. The concept of parallel distributed compensation (PDC) is employed to design fuzzy control from the TS fuzzy models. Sufficient conditions are formulated in the format of linear matrix inequalities (LMIs). The proposed controller design methodology is finally demonstrated through the model of wind energy systems (WES) with a doubly-fed induction generator (DFIG) to illustrate the effectiveness of the proposed method. The proposed algorithm maximizes the produced power and is able to maintain a stable system during the parameter uncertainties.

On the state observer based stabilization of Takagi-Sugeno systems with immeasurable premise variables

This paper presents two approaches of observer based stabilization for Takagi-Sugeno (T-S) systems with immeasurable premise variables in continuous time case. These approaches are based on the description of the state estimation error by a T-S model. To design the observer based stabilization law, the concept of PDC (Parallel Distributed Compensation) is employed, the sufficient stabilization conditions are proved and expressed in the form of Linear Matrix Inequalities (LMI). The performances of these approaches are tested by simulation for an illustrate example and a physical system representing a two-link robot.

Robust fault tolerant control of DFIG wind energy systems with unknown inputs

This paper proposes a Fuzzy Dedicated Observers (FDOS) method using a Nonlinear Unknown Input Fuzzy Observer (UIFO) with a Fuzzy Scheduler Fault Tolerant Control (FSFTC) algorithm for fuzzy Takagi-Sugeno (TS) systems subject to sensor faults, parametric uncertainties, and time varying unknown inputs. FDOS provide residuals for detection and isolation of sensor faults which can affect a TS model. The TS fuzzy model is adopted for fuzzy modeling of the uncertain nonlinear system and establishing fuzzy state observers. The concept of Parallel Distributed Compensation (PDC) is employed to design FSFTC and fuzzy observers from the TS fuzzy models. TS fuzzy systems are classified into three families based on the input matrices and a FSFTC synthesis procedure is given for each family. In each family, sufficient conditions are derived for robust stabilization, in the sense of Taylor series stability and Lyapunov method, for the TS fuzzy system with parametric uncertainties, sensor faults, and unknown inputs. The sufficient conditions are formulated in the format of Linear Matrix Inequalities (LMIs). The effectiveness of the proposed controller design methodology is finally demonstrated through a wind energy system with Doubly Fed Induction Generators (DFIG) to illustrate the effectiveness of the proposed method.

Robust control for a class of T-S fuzzy systems with interval time-varying delay

The problem of delay-dependent stability analysis and controller design for a class of T-S fuzzy systems with interval state time-varying delay is considered. Based on Lyapunov stability theory, defining a new Lyapunov-Krasovskii functional and introducing some free-weighting matrices, a new delay-dependent criterion is given to ensure the systems asymptotically stable. The merit of the proposed conditions lies in the less conservativeness than the existing ones, which is achieved by considering the mean of time-delay interval and the introduction of the free variables. By the concept of parallel distributed compensation (PDC), a delay-dependent condition for the existence of a fuzzy state feedback control law with memory is proposed. Another merit is the consideration of the memory of the controller. All conditions are shown in terms of linear matrix inequalities (LMIs), which can be solved efficiently by using the LMI optimization techniques. Two numerical examples are given to illustrate the feasibility and validity of the proposed approach.

Fuzzy sliding PDC control for some non-linear systems

This paper develops a new design method of fuzzy sliding parallel distributed compensation (PDC) controller applied to deal with some non-linear systems subject to unpredictable but bounded disturbances. A new fuzzy integral sliding surface vector based on the PDC concept is defined for the proposed fuzzy sliding PDC control. The Lyapunov stability condition is guaranteed in this design to develop strictly robust sliding PDC gains F i . This fuzzy sliding PDC controller is applied to control the ecological system and pendulum system. The simulation results of this controller demonstrate that the performance and robustness are better than that with state feedback control and fuzzy PDC control.

Fuzzy control with robust and passive properties for discrete-time Takagi–Sugeno fuzzy systems with multiplicative noises

This paper deals with the problem of robust fuzzy control for uncertain passive discrete-time non-linear stochastic systems with multiplicative noise. In this paper the non-linear stochastic system is represented by a Takagi–Sugeno fuzzy model. Using that approach the concept of parallel distributed compensation is applied to construct the fuzzy controller. Sufficient stability conditions are derived in terms of a linear matrix inequality by applying the Lyapunov theory. In addition, the passivity theory and robust technique are used to guarantee strict input passivity and robust asymptotical stability of the closed-loop system with admissible parameter uncertainties. Finally, a numerical example concerning the control of a truck–trailer system is provided to demonstrate the validity of the proposed fuzzy controller design method.