Hybrid fuzzy control of robotics systems

This paper presents a new approach towards optimal design of a hybrid fuzzy controller for robotics systems. The salient feature of the proposed approach is that it combines the fuzzy gain scheduling method and a fuzzy proportional-integral-derivative (PID) controller to solve the nonlinear control problem. The resultant fuzzy rule base of the proposed controller can be decomposed into two layers. In the upper layer, the gain scheduling method is incorporated with a Takagi-Sugeno (TS) fuzzy logic controller to linearize the robotics system for a given reference trajectory. In the lower layer, a fuzzy PID controller is derived for all the locally linearized systems by replacing the conventional PI controller by a linear fuzzy logic controller, which has different gains for different linearization conditions. Within the guaranteed stability region, the controller gains can be optimally tuned by genetic algorithms. Simulation studies on a pole balancing robot and a multilink robot manipulator demonstrate the effectiveness and robustness of the proposed approach.     

Real-time control of a water-gas shift reactor by a model-based fuzzy gain scheduling technique

A model-based fuzzy gain scheduling technique is proposed. Fuzzy gain scheduling is a form of variable gain scheduling which involves implementing several linear controllers over a partitioned process space. A higher-level rule-based controller determines which local controller is executed. Unlike conventional gain scheduling, a controller with fuzzy gain scheduling uses fuzzy logic to dynamically interpolate controller parameters near region boundaries based on known local controller parameters. Model-based fuzzy gain scheduling (MFGS) was applied to PID controllers to control a laboratory-scale water-gas shift reactor. The experimental results were compared with those obtained by PID with standard fuzzy gain scheduling, PID with conventional gain scheduling, simple PID and a nonlinear model predictive control (NMPC) strategy. The MFGS technique performed comparably to the NMPC method. It exhibited excellent control behaviour over the desired operating space, which spanned a wide temperature range. The other three PID-based techniques were adequate only within a limited range of the same operating space. Due to the simple algorithm involved, the MFGS technique provides a low cost alternative to other computationally intensive control algorithms such as NMPC.     

When is adaptive better than optimal?

Given a stationary process, let us predict it using a first-order predictor whose single coefficient is adapted to the current observations using a constant gain identification algorithm. We investigate the prediction error variance as a function of the adaptation gain i.e., the length of the memory (the number of observations) of the identification scheme. An infinite-memory corresponds to the asymptotically constant optimal predictor and a finite memory to a locally adaptive time varying predictor. We show that, in some specified situations, the prediction error variance associated with the finite memory adaptation scheme is smaller that the optimal variance. This can only occur if the model is misspecified i.e., the structure of the optimal predictor is too simple     

Multiobjective evolution based fuzzy PI controller design for nonlinear systems

This work proposes a gain scheduling adaptive control scheme based on fuzzy systems, neural networks and genetic algorithms for nonlinear plants. A fuzzy PI controller is developed, which is a discrete time version of a conventional one. Its data base as well as the constant PI control gains are optimally designed by using a genetic algorithm for simultaneously satisfying the following specifications: overshoot and settling time minimizations and output response smoothing. A neural gain scheduler is designed, by the backpropagation algorithm, to tune the optimal parameters of the fuzzy PI controller at some operating points. Simulation results are shown to demonstrate the efficiency of the proposed structure for a DC servomotor adaptive speed control system used as an actuator of robotic manipulators.     

Un-symmetric input temperature control by using fuzzy sliding mode controller with gain auto-tuning

In order to obtain the desired product quality, temperature is an important control parameter in chemical and semiconductor manufacturing processes. Generally, the temperature control system has nonlinear time-varying, slow response speed, time-delay and un-symmetric control input dynamic characteristics. It is difficult to accurately establish the dynamic model for designing a general purpose temperature controller to achieve good control performance. Here a model-free fuzzy sliding mode control strategy is employed to design an intelligent temperature controller with gain-scheduling scheme or gain auto-tuning algorithm for a closed chamber with heater one-way input only. The concept of gain scheduling is employed to adjust the mapping ranges of the input and output fuzzy membership functions during the control process for improving the transient and steady-state control performances. The experimental results show that the steady state error of the step input response is always less than 0.2°C without overshoot by using this intelligent control schemes. It is suitable for industrial temperature control systems.     

An advanced FMRL controller for FACTS devices to enhance dynamic performance of power systems

The parameters of power system slowly change with time due to environmental effects or may change rapidly due to faults. It is preferable that the control technique in this system possesses robustness for various fault conditions and disturbances. The used flexible alternating current transmission system (FACTS) in this paper is an advanced super-conducting magnetic energy storage (ASMES). Many control techniques that use ASMES to improve power system stability have been proposed. While fuzzy controller has proven its value in some applications, the researches applying fuzzy controller with ASMES have been actively reported. However, it is sometimes very difficult to specify the rule base for some plants, when the parameters change. To solve this problem, a fuzzy model reference learning controller (FMRLC) is proposed in this paper, which investigates multi-input multi-output FMRLC for time-variant nonlinear system. This control method provides the motivation for adaptive fuzzy control, where the focus is on the automatic online synthesis and tuning of fuzzy controller parameters (i.e., using online data to continually learn the fuzzy controller that will ensure that the performance objectives are met). Simulation results show that the proposed robust controller is able to work with nonlinear and nonstationary power system (i.e., single machine-infinite bus (SMIB) system), under various fault conditions and disturbances.     

利用BP算法的一种自适应模糊预测控制器

提出一种由模糊预测器和模糊预测控制器组成的自适应模糊预测控制方案,采用ＢＰ算法训练模糊预测器和模糊预测控制器,并给出这种模糊预测控制器的训练算法。控制系统对于具有纯时延的非线性被控过程有良好的控制性能。     

Discrete-time optimal fuzzy controller design: global conceptapproach

Proposes a systematic and theoretically sound way to design a global optimal discrete-time fuzzy controller to control and stabilize a nonlinear discrete-time fuzzy system with finite or infinite horizon (time). A linear-like global system representation of a discrete-time fuzzy system is first proposed by viewing such a system in a global concept and unifying the individual matrices into synthetic matrices. Then, based on this kind of system representation, a discrete-time optimal fuzzy control law which can achieve a global minimum effect is developed theoretically. A nonlinear two-point boundary-value-problem (TPBVP) is derived as a necessary and sufficient condition for the nonlinear quadratic optimal control problem. To simplify the computation, a multi-stage decomposition of the optimization scheme is proposed, and then a segmental recursive Riccati-like equation is derived. Moreover, in the case of time-invariant fuzzy systems, we show that the optimal controller can be obtained by just solving discrete-time algebraic Riccati-like equations. Based on this, several fascinating characteristics of the resultant closed-loop fuzzy system can easily be elicited. The stability of the closed-loop fuzzy system can be ensured by the designed optimal fuzzy controller. The optimal closed-loop fuzzy system can not only be guaranteed to be exponentially stable, but also stabilized to any desired degree. Also, the total energy of system output is absolutely finite. Moreover, the resultant closed-loop fuzzy system possesses an infinite gain margin, i.e. its stability is guaranteed no matter how large the feedback gain becomes. An example is given to illustrate the proposed optimal fuzzy controller design approach and to demonstrate the proven stability properties     

Modeling, control, and stability analysis for time-delay TLP systems using the fuzzy Lyapunov method

In this study, we present a Takagi–Sugeno (T–S) fuzzy model for the modeling and stability analysis of oceanic structures. We design a nonlinear fuzzy controller based on a parallel distributed compensation (PDC) scheme and reformulate the controller design problem as a linear matrix inequalities (LMI) problem as derived from the fuzzy Lyapunov theory. The robustness design technique is adopted so as to overcome the modeling errors for nonlinear time-delay systems subject to external oceanic waves. The vibration of the oceanic structure, i.e., the mechanical motion caused by the force of the waves, is discussed analytically based on fuzzy logic theory and a mathematical framework. The end result is decay in the amplitude of the surge motion affecting the time-delay tension leg platform (TLP) system. The feedback gain of the fuzzy controller needed to stabilize the TLP system can be found using the Matlab LMI toolbox. This proposed method of fuzzy control is applicable to practical TLP systems. The simulation results show that not only can the proposed method stabilize the systems but that the controller design is also simplified. The effects of the amplitude damping of the surge motion on the structural response are obvious and work as expected due to the control force.     

A retunable PID multi-rate controller for a networked control system

This paper introduces a control strategy based on retuning a multi-rate PID controller in accordance with the variable delays detected in a networked control system, in order to avoid a decreased control performance. The basic idea is minimising the first-order Taylor terms of a performance measure via gain scheduling, i.e., making the controller gains delay dependent. As network delay is time-variant, the stability of this control approach will be proved by means of linear matrix inequalities.     

Optimal fuzzy control system using the cross-entropy method. A case study of a drilling process

This paper focuses on the optimal tuning of fuzzy control systems using the cross-entropy precise mathematical framework. The design of an optimal fuzzy controller for cutting force regulation in a network-based application and applied to the drilling process is described. The key issue is to obtain optimal fuzzy controller parameters that yield a fast and accurate response with minimum overshoot by minimising the integral time absolute error (ITAE) performance index. Simulation results show that the cross-entropy method does find the optimal solution (i.e. input scaling factors) very accurately, and it can be programmed and implemented very easily (few setting parameters). The results of a comparative study demonstrate that optimal tuning with the cross-entropy method provides a good transient response (without overshoot) and a better error-based performance index than simulated annealing [17], the Nelder-Mead method [14] and genetic algorithms [33]. The experimental results demonstrate that the proposed optimal fuzzy control provides outstanding transient response without overshoot, a small settling time and a minimum steady-state error. The application of optimal fuzzy control reduces rapid drill wear and catastrophic drill breakage due to the increasing and oscillatory cutting forces that occur as the drill depth increases.     

A novel intelligent controller for combating stiction in pneumatic control valves

Pneumatic control valve introduces limit cycles in process variables due to stiction nonlinearity. In this paper a novel stiction combating intelligent controller (SCIC) based on fuzzy logic has been proposed. The proposed technique reduces the complexity of the overall control scheme as it does not require any additional compensator. The SCIC controller is a variable gain fuzzy Proportional Integral (PI) controller making use of Takagi-Sugeno (TS) scheme. The performance of the SCIC controller has been investigated and compared with conventional PI controller on a laboratory scale flow process. SCIC controller outperformed PI controller and provided promising performance with lesser aggressive stem movement.     

Modified Smith predictor scheme for periodic disturbance reduction in linear delay systems

This paper presents a disturbance reduction scheme for linear systems with time delays. The linear systems in the study are assumed to be nominally stable, minimum phase, and relative degree one systems. The proposed scheme is a combination of Astrom’s modified Smith predictor with a disturbance reduction controller and a grey predictor. Unlike conventional disturbance rejection methods, the scheme proposed in this study does not require the estimation of disturbance frequencies. The grey prediction method is used to approximate the inverse of the time delay and to enhance the robustness of the disturbance reduction scheme against errors in the estimated delay time. The simulation results demonstrate the successful performance of the proposed disturbance reduction method for controlling a linear system with time delays, subjected to both step and periodic disturbances.     

Incremental Evolutionary Design of TSK Fuzzy Controllers

This paper proposes a novel method for the incremental design and optimization of first order Tagaki-Sugeno-Kang (TSK) fuzzy controllers by means of an evolutionary algorithm. Starting with a single linear control law, the controller structure is gradually refined during the evolution. Structural augmentation is intertwined with evolutionary adaptation of the additional parameters with the objective not only to improve the control performance but also to maximize the stability region of the nonlinear system. From the viewpoint of optimization the proposed method follows a divide-and-conquer approach. Additional rules and their parameters are introduced into the controller structure in a neutral fashion, such that the adaptations of the less complex controller in the previous stage are initially preserved. The proposed scheme is evaluated at the task of TSK fuzzy controller design for the upswing and stabilization of a rotational inverted pendulum. In the first case, the objective is a time optimal controller that upswings the pendulum in to the upper equilibrium point in shortest time. The stabilizing controller is designed as a state optimal controller. In a second application the optimization method is applied to the design of a fuzzy controller for vision-based mobile robot navigation. The results demonstrate that the incremental scheme generates solutions that are similar in control performance to pure parameter optimization of only the gains of a TSK system. Even more important, whereas direct optimization of control systems with more than 35 rules fails to identify a stabilizing control law, the incremental scheme optimizes fuzzy state-space partitions and gains for hundreds of rules.     

A multivariable predictive fuzzy PID control system

In this paper, a novel multivariable predictive fuzzy-proportional-integral-derivative (F-PID) control system is developed by incorporating the fuzzy and PID control approaches into the predictive control framework. The developed control system has two main units referred as adaptation and application parts. The adaptation part consists of a F-PID controller and a fuzzy predictor. The incremental control actions are generated by the F-PID controller. The controller parameters are adjusted with the predictive control approach. The fuzzy predictor provides the multi-step ahead predictions of the plant outputs. Therefore, the F-PID controller parameters are adjusted by minimizing the errors between the predicted plant outputs and reference trajectories over the prediction horizon. The fuzzy predictor is trained with an on-line training procedure in order to adapt the changes in the plant dynamics and improve the prediction accuracy. The Levenberg–Marquardt (LM) optimization method with a trust region approach is used to adjust both the controller and predictor fuzzy systems parameters. In the application part, an identical F-PID controller of the adaptation part is used to control the actual plant. The adjusted parameter values are transferred to this identical controller at each time step. The performance of the proposed control system is tested for both single-input single-output (SISO) and multiple-input multiple-output (MIMO) nonlinear control problems. The adaptation, robustness to noise, disturbance rejection properties together with the tracking performances are examined in the simulations.     

Real Time Implementation of Fuzzy Gain Scheduling of PI Controller for Induction Motor Machine Control

In this work the control of an induction motor using fuzzy gain scheduling of PI controller (adaptive FLC-PI) is presented. Fuzzy rules are utilized on-line to determine the controller parameters based on tracking error and its first time derivative. Simulation and experimental results of the proposed scheme show good performances compared to the PI controller with fixed parameters.     

基于回路成形的鲁棒增益调度控制器设计

针对目前基于线性变参数系统的增益调度控制设计中存在的控制结构复杂性问题，提出一种基于回路成形的简单且易实现的增益调度控制结构.在此基础上，提出一个鲁棒增益调度控制设计方法.设计过程首先采用补偿器函数使得被控对象奇异值具有期望的形状，以保证被控对象的性能要求，然后利用小增益定理设计一个鲁棒控制器，得到具有良好性能的、结构简单的鲁棒增益调度控制器.最后针对一个化工过程，说明此方法的有效性.     

Stabilization of nonlinear nonminimum phase systems: adaptive parallel approach using recurrent fuzzy neural network

In this paper, an adaptive parallel control architecture to stabilize a class of nonlinear systems which are nonminimum phase is proposed. For obtaining an on-line performance and self-tuning controller, the proposed control scheme contains recurrent fuzzy neural network (RFNN) identifier, nonfuzzy controller, and RFNN compensator. The nonfuzzy controller is designed for nominal system using the techniques of backstepping and feedback linearization, is the main part for stabilization. The RFNN compensator is used to compensate adaptively for the nonfuzzy controller, i.e., it acts like a fine tuner; and the RFNN identifier provides the system's sensitivity for tuning the controller parameters. Based on the Lyapunov approach, rigorous proofs are also presented to show the closed-loop stability of the proposed control architecture. With the aid of the RFNN compensators, the parallel controller can indeed improve system performance, reject disturbance, and enlarge the domain of attraction. Furthermore, computer simulations of several examples are given to illustrate the applicability and effectiveness of this proposed controller.     

基于改进量子粒子群算法的NCS模糊控制器参数优化

针对网络化控制系统中模糊控制器的量化因子和比例因子采用传统经验方法难以整定的问题, 提出了一种改进量子粒子群（IQPSO）算法对模糊控制器量化因子和比例因子进行优化。该方法将ABC算法中的搜索算子作为变异算子引入到QPSO算法中, 使得IQPSO算法较好地克服了QPSO算法保持种群多样性差容易早熟收敛的缺陷, 并以ITAE指标作为IQPSO算法的适应度函数对模糊控制器进行优化。典型工业过程仿真结果表明, IQPSO优化的模糊控制器具有比PID控制器和标准QPSO优化的模糊控制器更好的控制性能和适用性。     

Gain scheduling control of nonlinear systems based on approximate input-output linearization

The gain scheduling control mostly has been developed based on Jacobian linearization around the operating points related with scheduling variables. In this paper, We introduce a gain scheduling control method based on approximate input-output linearization. First, the nonlinear system is approximately input-output linearized via a diffeomorphism. Then, a gain scheduling controller with derivative information is developed. The proposed controller consists of two parts. The outer loop controller is like a feedback linearizing controller and the internal controller is a gain scheduling controller. It is shown that the overall resulting controller has a simple structure and at the same time achieves better tracking performance over the existing Jacobian-based gain scheduling controller.