Model Reference Adaptive Fuzzy Control

Fuzzy control is a model-free linguistic control (if-then rules), which is easy to understand and provides nonlinear controllers for nonlinear systems. In recent years, some fuzzy controllers with an adaptive mechanism for unknown systems have been studied. In these studies, the parameters of a fuzzy controller are adjusted by some experience of human opereators or adaptive lows with some if-then rules. But the stability of the control system which is constructed by the plant and the fuzzy controller has not been analysed in most of these studies In this paper, we propose a class of Model Reference Adaptive Fuzzy Controllers for nonlinear systems. This class of controllers are the fuzzy controllers with the structure of the direct adaptive control system which can directly stabilize tracking error e. Finally, we derive the stability conditions (the adaptive laws) for the fuzzy controller for nonlinear systems by taking quadratic parameter error φ_i as the Lyapunov function V

Adaptive fuzzy sliding mode control for uncertain nonlinear underactuated mechanical systems

Sliding mode control has been shown to be a robust and effective control approach for stabilization of nonlinear systems. However the dynamic performance of the controller is a complex function of the system parameters, which is often uncertain or partially known. This paper presents an adaptive fuzzy sliding mode control for a class of underactuated nonlinear mechanical systems. An adaptive fuzzy system is used to approximate the uncertain parts of the underactuated system. The adaptive law is designed based on the Lyapunov method. The proof for the stability and the convergence of the system is presented. Robust performance of the adaptive fuzzy sliding mode control is illustrated using a gantry crane system. Simulation results demonstrate that the system output can track the reference signal in the presence of modelling uncertainties, external disturbances and parameter variation. © 2013 IEEE

Adaptive fuzzy tracking control for a class of uncertain MIMO nonlinear systems using disturbance observer

In this paper, the adaptive fuzzy tracking control is proposed for a class of multi-input and multioutput (MIMO) nonlinear systems in the presence of system uncertainties, unknown non-symmetric input saturation and external disturbances. Fuzzy logic systems (FLS) are used to approximate the system uncertainty of MIMO nonlinear systems. Then, the compound disturbance containing the approximation error and the time-varying external disturbance that cannot be directly measured are estimated via a disturbance observer. By appropriately choosing the gain matrix, the disturbance observer can approximate the compound disturbance well and the estimate error converges to a compact set. This control strategy is further extended to develop adaptive fuzzy tracking control for MIMO nonlinear systems by coping with practical issues in engineering applications, in particular unknown non-symmetric input saturation and control singularity. Within this setting, the disturbance observer technique is combined with the FLS approximation technique to compensate for the effects of unknown input saturation and control singularity. Lyapunov approach based analysis shows that semi-global uniform boundedness of the closed-loop signals is guaranteed under the proposed tracking control techniques. Numerical simulation results are presented to illustrate the effectiveness of the proposed tracking control schemes

Design of stable adaptive fuzzy control.

by John Tak Kuen Koo.Thesis (M.Phil.)--Chinese University of Hong Kong, 1994.Includes bibliographical references (leaves 217-[220]).Chapter 1 --- Introduction --- p.1Chapter 1.1 --- Introduction --- p.1Chapter 1.2 --- "Robust, Adaptive and Fuzzy Control" --- p.2Chapter 1.3 --- Adaptive Fuzzy Control --- p.4Chapter 1.4 --- Object of Study --- p.10Chapter 1.5 --- Scope of the Thesis --- p.13Chapter 2 --- Background on Adaptive Control and Fuzzy Logic Control --- p.17Chapter 2.1 --- Adaptive control --- p.17Chapter 2.1.1 --- Model reference adaptive systems --- p.20Chapter 2.1.2 --- MIT Rule --- p.23Chapter 2.1.3 --- Model Reference Adaptive Control (MRAC) --- p.24Chapter 2.2 --- Fuzzy Logic Control --- p.33Chapter 2.2.1 --- Fuzzy sets and logic --- p.33Chapter 2.2.2 --- Fuzzy Relation --- p.40Chapter 2.2.3 --- Inference Mechanisms --- p.43Chapter 2.2.4 --- Defuzzification --- p.49Chapter 3 --- Explicit Form of a Class of Fuzzy Logic Controllers --- p.51Chapter 3.1 --- Introduction --- p.51Chapter 3.2 --- Construction of a class of fuzzy controller --- p.53Chapter 3.3 --- Explicit form of the fuzzy controller --- p.57Chapter 3.4 --- Design criteria on the fuzzy controller --- p.65Chapter 3.5 --- B-Spline fuzzy controller --- p.68Chapter 4 --- Model Reference Adaptive Fuzzy Control (MRAFC) --- p.73Chapter 4.1 --- Introduction --- p.73Chapter 4.2 --- "Fuzzy Controller, Plant and Reference Model" --- p.75Chapter 4.3 --- Derivation of the MRAFC adaptive laws --- p.79Chapter 4.4 --- "Extension to the Multi-Input, Multi-Output Case" --- p.84Chapter 4.5 --- Simulation --- p.90Chapter 5 --- MRAFC on a Class of Nonlinear Systems: Type I --- p.97Chapter 5.1 --- Introduction --- p.98Chapter 5.2 --- Choice of Controller --- p.99Chapter 5.3 --- Derivation of the MRAFC adaptive laws --- p.102Chapter 5.4 --- Example: Stabilization of a pendulum --- p.109Chapter 6 --- MRAFC on a Class of Nonlinear Systems: Type II --- p.112Chapter 6.1 --- Introduction --- p.113Chapter 6.2 --- Fuzzy System as Function Approximator --- p.114Chapter 6.3 --- Construction of MRAFC for the nonlinear systems --- p.118Chapter 6.4 --- Input-Output Linearization --- p.130Chapter 6.5 --- MRAFC with Input-Output Linearization --- p.132Chapter 6.6 --- Example --- p.136Chapter 7 --- Analysis of MRAFC System --- p.140Chapter 7.1 --- Averaging technique --- p.140Chapter 7.2 --- Parameter convergence --- p.143Chapter 7.3 --- Robustness --- p.152Chapter 7.4 --- Simulation --- p.157Chapter 8 --- Application of MRAFC scheme on Manipulator Control --- p.166Chapter 8.1 --- Introduction --- p.166Chapter 8.2 --- Robot Manipulator Control --- p.170Chapter 8.3 --- MRAFC on Robot Manipulator Control --- p.173Chapter 8.3.1 --- Part A: Nonlinear-function feedback fuzzy controller --- p.174Chapter 8.3.2 --- Part B: State-feedback fuzzy controller --- p.182Chapter 8.4 --- Simulation --- p.186Chapter 9 --- Conclusion --- p.199Chapter A --- Implementation of MRAFC Scheme with Practical Issues --- p.203Chapter A.1 --- Rule Generation by MRAFC scheme --- p.203Chapter A.2 --- Implementation Considerations --- p.211Chapter A.3 --- MRAFC System Design Procedure --- p.215Bibliography --- p.21

A New Approach to Nonlinear Tracking Control Based on Fuzzy Approximation

The problem of tracking control is addressed for a class of nonlinear systems with uncertainties. The original nonlinear systems are approximated by a fuzzy T-S model based on which a state-feedback controller is constructed by using the linear matrix inequalities. The approximating error is eliminated by an adaptive compensator based on fuzzy logic systems. The effectiveness of the proposed control scheme is demonstrated by a simulation example. The main advantage is that the designer makes milder constraint assumption for the approximation error and the uncertainties in nonlinear systems

Prescribed Performance Fuzzy Adaptive Output-Feedback Control for Nonlinear Stochastic Systems

A prescribed performance fuzzy adaptive output-feedback control approach is proposed for a class of single-input and single-output nonlinear stochastic systems with unmeasured states. Fuzzy logic systems are used to identify the unknown nonlinear system, and a fuzzy state observer is designed for estimating the unmeasured states. Based on the backstepping recursive design technique and the predefined performance technique, a new fuzzy adaptive output-feedback control method is developed. It is shown that all the signals of the resulting closed-loop system are bounded in probability and the tracking error remains an adjustable neighborhood of the origin with the prescribed performance bounds. A simulation example is provided to show the effectiveness of the proposed approach

Global Feed-Forward Adaptive Fuzzy Control of Uncertain MIMO Nonlinear Systems

This study proposes a novel adaptive control approach using a feedforward Takagi-Sugeno (TS) fuzzy approximator for a class of highly unknown multi-input multi-output (MIMO) nonlinear plants. First of all, the design concept, namely, feedforward fuzzy approximator (FFA) based control, is introduced to compensate the unknown feedforward terms required during steady state via a forward TS fuzzy system which takes the desired commands as the input variables. Different from the traditional fuzzy approximation approaches, this scheme allows easier implementation and drops the boundedness assumption on fuzzy universal approximation errors. Furthermore, the controller is synthesized to assure either the disturbance attenuation or the attenuation of both disturbances and estimated fuzzy parameter errors or globally asymptotic stable tracking. In addition, all the stability is guaranteed from a feasible gain solution of the derived linear matrix inequality (LMI). Meanwhile, the highly uncertain holonomic constrained systems are taken as applications with either guaranteed robust tracking performances or asymptotic stability in a global sense. It is demonstrated that the proposed adaptive control is easily and straightforwardly extended to the robust TS FFA-based motion/force tracking controller. Finally, two planar robots transporting a common object is taken as an application example to show the expected performance. The comparison between the proposed and traditional adaptive fuzzy control schemes is also performed in numerical simulations. Keywords: Adaptive control; Takagi-Sugeno (TS) fuzzy system; holonomic systems; motion/force control

Robust Adaptive Fuzzy Output Tracking Control for a Class of Twin-Roll Strip Casting Systems

This paper is concerned with the adaptive fuzzy control problem for a class of twin-roll strip casting systems. By using fuzzy logic systems (FLSs) to approximate the compounded nonlinear functions, a novel robust output tracking controller with adaptation laws is designed based on the high gain observer. First, the nonlinear dynamic equations for the roll gap and the molten steel level are constructed, respectively. Then, the mean value theorem is employed to transform the nonaffine nonlinear systems to the corresponding affine nonlinear systems. Moreover, it is also proved that all the closed-loop signals are bounded and the systems output tracking errors can converge to the desired neighborhoods of the origin via the Lyapunov stability analysis. Finally, simulation results, based on semiexperimental system dynamic model and parameters, are worked out to show the effectiveness of the proposed adaptive fuzzy design method

Intelligent control of a class of nonlinear systems

The objective of this study is to improve and propose new fuzzy control algorithms for a class of nonlinear systems. In order to achieve the objectives, novel stability theorems as well as modeling techniques are also investigated. Fuzzy controllers in this work are designed based on the fuzzy basis function neural networks and the type-2 Takagi-Sugeno fuzzy models. For a class of single-input single-output nonlinear systems, a new stability condition is derived to facilitate the design process of proportional-integral Mamdani fuzzy controllers. The stability conditions require a new technique to calculate the dynamic gains of nonlinear systems represented by fuzzy basis function network models. The dynamic gain of a fuzzy basis function network can be approximated by finding the maximum of norm values of the locally linearized systems or by solving a non-smooth optimal control problem. Based on the new stability theorem, a multilevel fuzzy controller with self-tuning algorithm is proposed and simulated in a tower crane control system. For a class of multi-input multi-output nonlinear systems with measurable state variables, a new method for modeling unstructured uncertainties and robust control of unknown nonlinear dynamic systems is proposed by using a novel robust Takagi-Sugeno fuzzy controller. First, a new training algorithm for an interval type-2 fuzzy basis function network is presented. Next, a novel technique is derived to convert the interval type-2 fuzzy basis function network to an interval type-2 Takagi-Sugeno fuzzy model. Based on the interval type-2 Takagi-Sugeno and type-2 fuzzy basis function network models, a robust controller is presented with an adjustable convergence rate. Simulation results on an electrohydraulic actuator show that the robust Takagi-Sugeno fuzzy controller can reduce steady-state error under different conditions while maintaining better responses than the other robust sliding mode controllers can. Next, the study presents an implementation of type-2 fuzzy basis function networks and robust Takagi-Sugeno fuzzy controllers to data-driven modeling and robust control of a laser keyhole welding process. In this work, the variation of the keyhole diameter during the welding process is approximated by a type-2 fuzzy-basis-function network, while the keyhole penetration depth is modelled by a type-1 fuzzy basis function network. During the laser welding process, a CMOS camera integrated with the welding system was used to provide a feedback signal of the keyhole diameter. An observer was implemented to estimate the penetration depth in real time based on the adaptive divided difference filter and the feedback signal from the camera. A robust Takagi-Sugeno fuzzy controller was designed based on the fuzzy basis function networks representing the welding process with uncertainties to adjust the laser power to ensure that the penetration depth of the keyhole is maintained at a desired value. Experimental results demonstrated that the fuzzy models provided an accurate estimation of both the welding geometry and its variations due to uncertainties, and the robust Takagi-Sugeno fuzzy controller successfully reduced the penetration depth variation and improved the quality of the welding process