Parallel Distributed Compensation Fuzzy Controller Research Articles

Takagi–Sugeno Fuzzy Parallel Distributed Compensation Control for Low-Frequency Oscillation Suppression in Wind Energy-Penetrated Power Systems

In this paper, a Takagi–Sugeno fuzzy parallel distributed compensation control (TS-PDCC) is proposed for low-frequency oscillation (LFO) suppression in wind energy-penetrated power systems. Firstly, the fuzzy C-mean algorithm (FCMA) is applied to cluster the daily average wind speed of the wind farm, and the obtained wind speed clustering center is used as the premise variable of TS-PDCC, which increases the freedom of parameter setting of the TS fuzzy model and is closer to the actual working environment. Secondly, based on the TS fuzzy model, the TS-PDCC is designed to adjust the active power output of the wind turbine for LFO suppression. To facilitate the computation of controller parameters, the stability conditions are transformed into a set of Linear Matrix Inequalities (LMIs) via the Schur complement. Subsequently, a Lyapunov function is designed to verify the stability of the wind energy-penetrated power system and obtain the parameter ranges. Simulation cases are conducted to verify the validity and superior performance of the proposed TS-PDCC under different operating conditions.

Modeling and Control of Delayed, Nonlinear, Uncertain, and Disturbed Air Heater Employing Fuzzy PDC-L 1 Adaptive Scheme

In this article, we proposed a scheme of modeling an air heater system with a long airflow duct, predominantly available in many industrial plants to maintain the desired temperature by simultaneously befitting the transport delay, nonlinearities, model uncertainties, and nonuniform disturbances. At first, the nonlinear delayed air heater system is formulated by combining linear fuzzy system models utilizing fuzzy parallel distributed compensation (PDC) logic. Then, a newly developed L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> adaptive control strategy is modified by replacing its conventional state feedback controller with fuzzy PDC control logic to maintain the desired temperature by nullifying nonlinearities, transport delays, uncertainties, and disturbances. The novelty of the proposed work lies in the fact that the proposed fuzzy PDC law augmented L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> adaptive scheme explicitly deals with the delays and nonlinearities by means of fuzzy PDC logic as well as eliminates time-varying uncertainties and disturbances utilizing L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> adaptive control strategy. The results obtained from real-life laboratory-scale experiments suitably demonstrate the usefulness of the proposed approach.

Observer-based proportional derivative fuzzy control for singular Takagi-Sugeno fuzzy systems

This study investigates the issue of stability analysis and controller synthesis for nonlinear singular systems . Via applying a fuzzy modeling approach, the nonlinear singular system is expressed by a Takagi-Sugeno (T-S) fuzzy model composed of several linear subsystems. Furthermore, the parallel distributed compensation fuzzy controller is designed such that the controlled singular system is stable. Employing Proportional Derivative (PD) control method, the regularity and impulse-free property of the singular systems can be held. However, the PD control method is challengable because the state signals of singular systems are not always measurable. Therefore, a novel fuzzy observer is designed to ensure the existence of estimated states. For the observer-based PD control issue, some sufficient stability conditions are derived for T-S fuzzy singular systems. Moreover, the control gains and observer gains can be conveniently calculated using the Linear Matrix Inequality (LMI) calculation. Finally, two numerical examples are presented to verify the availability and applicability of the proposed design method.

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

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

Robust Fuzzy Control with Transient and Steady-State Performance Constraints for Ship Fin Stabilizing Systems

This paper studies the robust fuzzy controller design problem for the nonlinear ship fin stabilizing systems. By considering the perturbations, the nonlinear ship fin stabilizing system is represented by the perturbed Takagi–Sugeno fuzzy model. According to the perturbed Takagi–Sugeno fuzzy model, the parallel distributed compensation technique is used to design a model-based robust fuzzy controller. The purpose of the parallel distributed compensation fuzzy controller is to derive linear controllers such that each fuzzy rule of the Takagi–Sugeno fuzzy model can be compensated. In addition to the robust stability performance, the variance constraint and transient performance constraint are also considered in this paper. According to these performance constraints, the linear matrix inequality technique is employed to solve the sufficient conditions developed in this paper. At last, some simulations for the control of nonlinear ship fin stabilizing systems are made to show the usefulness and effectiveness of the proposed design method.

Fuzzy Attitude Control of Spacecraft With Fuel Sloshing via Linear Matrix Inequalities

This paper presents and compares two fuzzy controllers for attitude stabilization of a spacecraft with partially filled fuel tank: a fuzzy controller based on the parallel distributed compensation (PDC) technique and a fuzzy controller based on the linear quadratic regulator. Both controllers are built from the Takagi–Sugeno model of the spacecraft. Using the Lyapunov stability theorem, the fuzzy PDC controller design problem was cast as a minimization problem for the upper bound of control input in the form of linear matrix inequalities. In the end, we compare the efficacy and robustness of each controller via numerical simulations.

Fuzzy-logic control of an inverted pendulum on a cart

The inverted pendulum on a cart is an under actuated, unstable non-linear system that is used as a benchmarking problems in control theory. The non-linear nature of the system makes linear controllers, such as the proportional integral derivative (PID) controllers, possibly unfeasible as they only guarantee stability of a linear system. A fuzzy-logic controller provides many different stable controllers applicable to inverted pendulum on a cart. In this paper, the fuzzy parallel distributed compensation (PDC) controller is introduced and implemented on an unstable system, and the performance is demonstrated in MATLAB Simulink. The fuzzy PDC controller is dependent on the Takagi–Sugeno (TS) fuzzy model to obtain the state feedback gains required by solving the linear matrix inequalities (LMI). The LMI produced satisfactory results for all initial pendulum positions simulated even under uniformed disturbance. Our results have been compared against two other works to reveal the effectiveness of the proposed model.

To Transmit or Not to Transmit: A Discrete Event-Triggered Communication Scheme for Networked Takagi–Sugeno Fuzzy Systems

This paper first proposes a discrete event-triggered communication scheme for a class of networked Takagi-Sugeno (T-S) fuzzy systems. This scheme has two main features: 1) Whether or not the sampled state should be transmitted is determined by the current-sampled state and the error between the current-sampled state and the latest transmitted state. Compared with those in a periodic time-triggered communication scheme, the communication bandwidth utilization is considerably reduced while preserving the desired control performance; and 2) it is a discrete event-triggered communication scheme due to the fact that the triggered conditions are only measured and checked at a constant sampling period. Compared with a continuous event-triggered communication scheme, the special hardware for continuous measurement and computation is no longer needed. Second, a networked T-S fuzzy model is delicately constructed, which not only considers nonuniform time scales in the networked T-S fuzzy model and the parallel distributed compensation fuzzy control rules but includes the aforementioned state error as well. Third, a stability criterion and a stabilization criterion about the networked T-S fuzzy system are derived, respectively. The stability criterion and stabilization criterion can provide a tradeoff to balance the required communication resource and the desired performance: Lowering the desired performance allows the network to allocate more limited bandwidth to other nodes in need. Finally, a numerical example is given to show the effectiveness of the proposed method.

Parallel Distributed Compensation Fuzzy Controller Design for Dynamic Positioning

Parallel Distributed Compensation Fuzzy Controller Design for Dynamic Positioning

Thermal Control of a Greenhouse by Variation in Ventilation Rate using a Fuzzy Parallel Distributed Compensation Controller with an RST Regulator in Each Rule

Problem statement: The greenhouse has uncontrollable inputs that affect its climate, which arises the difficulty to regulate its inside temperature. The solution can be found using a multi-system approach like the Takagi-Sugeno System from which a design of a Parallel Distributed Compensation (PDC) controller is performed. However, a stability problem arises and was negotiatesd in general based on a Lyapunov criterion. The latter isn’t appropriate in our case because of the great number of rules describing the greenhouse. Approach: An alternative solution is proposed using a PDC controller with a local RST regulator in each rule. The synthesis of each one is determined using pole placement avoiding the cross-coupling (that may cause instability) between the local regulators and the sub-models related to differents rules. Results: The proposed fuzzy controller was applied to an experimental greenhouse and was able to lead the inside temperature to the desired value despite the externals perturbations. Conclusion: The presented study offer a simple solution to the stability problem when using PDC controller and so can be mush more implementable than the others stabilization methods presented in the literature. In the agriculture field, it can replace the on-off control action that is widely used in the greenhouses because of the processus complexity.

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.

Design of robust‐optimal controllers with low trajectory sensitivity for uncertain Takagi–Sugeno fuzzy model systems using differential evolution algorithm

SUMMARYBy integrating the robust stabilizability condition, the orthogonal‐function approach (OFA) and the Taguchi‐sliding‐based differential evolution algorithm (TSBDEA), an integrative computational approach is presented in this paper to design the robust‐optimal fuzzy parallel‐distributed‐compensation (PDC) controller with low trajectory sensitivity such that (i) the Takagi–Sugeno (TS) fuzzy model system with parametric uncertainties can be robustly stabilized, and (ii) a quadratic finite‐horizon integral performance index for the nominal TS fuzzy model system can be minimized. In this paper, the robust stabilizability condition is proposed in terms of linear matrix inequalities (LMIs). Based on the OFA, an algebraic algorithm only involving the algebraic computation is derived for solving the nominal TS fuzzy feedback dynamic equations. By using the OFA and the LMI‐based robust stabilizability condition, the robust‐optimal fuzzy PDC control problem for the uncertain TS fuzzy dynamic systems is transformed into a static constrained‐optimization problem represented by the algebraic equations with constraint of LMI‐based robust stabilizability condition; thus, greatly simplifying the robust‐optimal PDC control design problem. Then, for the static constrained‐optimization problem, the TSBDEA has been employed to find the robust‐optimal PDC controllers with low trajectory sensitivity of the uncertain TS fuzzy model systems. A design example is given to demonstrate the applicability of the proposed new integrative approach. Copyright © 2011 John Wiley &amp; Sons, Ltd.

Fuzzy Tracking Control for Indirect Field-oriented Induction Machine Using Integral Action Performance

This paper deals with the synthesis of fuzzy controller applied to the induction motor with a guaranteed H∞ tracking performance. First, the Takagi-Sugeno fuzzy model is employed to approximate a nonlinear system in the synchronous d-q frame rotating with electromagnetic field-oriented. Next, a fuzzy observer-based fuzzy tracking controller is designed to stabilize the induction motor and guaranteed a minimum disturbance attenuation level for the closed-loop system. The rotor flux is unavailable for measurement and it is estimated by a fuzzy observer. An integral action is added to the new parallel distributed compensation fuzzy controller related to the tracking to avoid static errors. The gains of fuzzy control and fuzzy observer are obtained by solving a set of Linear Matrix Inequality. Finally, simulation result is given to demonstrate the controller’s effectiveness.

Stabilization Using a Discrete Fuzzy PDC Control with PID Controllers and Pole Placement: Application to an Experimental Greenhouse

This paper proposes a control strategy for complex and nonlinear systems, based on a parallel distributed compensation (PDC) controller. A solution is presented to solve a stability problem that arises when dealing with a Takagi‐Sugeno discrete system with great numbers of rules. The PDC controller will use a classical controller like a PI, PID, or RST in each rule with a pole placement strategy to avoid causing instability. The fuzzy controller presented combines the multicontrol approach and the performance of the classical controllers to obtain a robust nonlinear control action that can also deal with time‐variant systems. The presented method was applied to a small greenhouse to control its inside temperature by variation in ventilation rate inside the process. The results obtained will show the efficiency of the adopted method to control the nonlinear and complex systems.

Modeling and Fuzzy PDC Control and Its Application to an Oscillatory TLP Structure

An analytical solution is derived to describe the wave‐induced flow field and surge motion of a deformable platform structure controlled with fuzzy controllers in an oceanic environment. In the controller design procedure, a parallel distributed compensation (PDC) scheme is utilized to construct a global fuzzy logic controller by blending all local state feedback controllers. The Lyapunov method is used to carry out stability analysis of a real system structure. The corresponding boundary value problems are then incorporated into scattering and radiation problems. These are analytically solved, based on the separation of variables, to obtain a series of solutions showing the harmonic incident wave motion and surge motion. The dependence of the wave‐induced flow field and its resonant frequency on wave characteristics and structural properties including platform width, thickness and mass can thus be drawn with a parametric approach. The wave‐induced displacement of the surge motion is determined from these mathematical models. The vibration of the floating structure and mechanical motion caused by the wave force are also discussed analytically based on fuzzy logic theory and the mathematical framework to find the decay in amplitude of the surge motion in the tension leg platform (TLP) system. The expected effects of the damping in amplitude of the surge motion due to the control force on the structural response are obvious.

Parallel-Distributed Compensation Fuzzy Controller for Nonlinear Control of a Series Dc Motor

Based on parallel-distributed compensation (PDC ) technique to stabilize the nonlinear systems, this paper presents the design of fuzzy logic controllers (FLCs) for series DC motor. A nonlinear mathematical model of a series-connected DC motor is proposed. Finally, the proposed designed controller is demonstrated through numerical simulation and compared with feedback linearization and conventional linearization technique.

A Novel Stabilization Criterion for Large-Scale T–S Fuzzy Systems

This correspondence studies the stabilization problem of large-scale Takagi-Sugeno fuzzy systems. A novel stabilization criterion with decentralized parallel distributed compensation (PDC) fuzzy controller is proposed. The criterion contains two inequalities and one negative definite matrix to be satisfied. The effects of all interconnection terms and all decentralized PDC gains are entirely included in the negative definite matrix. The size of the matrix depends on the number of subsystems; the more the number of subsystems is, the larger the size of the matrix is. By using the linear matrix inequality method, the inequalities in the criterion can be solved to synthesize the local feedback gain of each PDC fuzzy controller such that the whole closed-loop large-scale fuzzy system is asymptotically stable. Finally, we give a practical example to illustrate the effectiveness of the proposed criterion.

Robust-stable and quadratic-optimal control for TS-fuzzy-model-based control systems with elemental parametric uncertainties

By integrating the robust stabilisability condition, the shifted-Chebyshev-series approach (SCSA), and the hybrid Taguchi-genetic algorithm (HTGA), an integrative method is presented in this work to design the robust-stable and quadratic-optimal fuzzy parallel distributed compensation (PDC) controller such that: (i) the Takagi-Sugeno (TS) fuzzy-model-based control system with elemental parametric uncertainties can be robustly stabilised, and (ii) a quadratic finite-horizon integral performance index for the nominal TS-fuzzy-model-based control system can be minimised. In this work, the robust stabilisability condition is proposed in terms of linear matrix inequalities (LMIs). Based on the SCSA, an algebraic algorithm only involving the algebraic computation is derived in this work for solving the nominal TS-fuzzy-model-based feedback dynamic equations. By using the SCSA and the LMI-based robust stabilisability condition, the robust-stable and quadratic-finite-horizon-optimal fuzzy PDC control problem for the uncertain TS-fuzzy-model-based dynamic systems is transformed into a static constrained-optimisation problem represented by the algebraic equations with constraint of LMI-based robust stabilisability condition; thus greatly simplifying the robust optimal PDC control design problem. Then, for the static constrained-optimisation problem, the HTGA is employed to find the robust-stable and quadratic-optimal PDC controllers of the uncertain TS-fuzzy-model-based control systems. A design example of the robust-stable and quadratic-optimal PDC controller for the nonlinear mass-spring-damper mechanical system with elemental parametric uncertainties is given to demonstrate the applicability of the proposed new integrative approach.

Nonlinear Model Following Control via Takagi-Sugeno Fuzzy Model

This paper presents a unified approach toward regulation and servocontrol problems as special cases of a nonlinear model following control via the Takagi-Sugeno fuzzy model. New parallel distributed compensation (PDC) is presented for realizing a nonlinear model following control. The new PDC fuzzy controller mirrors the structures of two Takagi-Sugeno fuzzy models representing a nonlinear system and nonlinear reference model. First, we derive linear matrix inequality (LMI) conditions to linearize the error system between the feedback system and the nonlinear reference model. A controller is designed using LMI conditions. Design examples verify the usefulness of nonlinear model following control.