Stable and convergent iterative feedback tuning of fuzzy controllers for discrete-time SISO systems

This paper proposes new stability analysis and convergence results applied to the Iterative Feedback Tuning (IFT) of a class of Takagi–Sugeno–Kang proportional-integral-fuzzy controllers (PI-FCs). The stability analysis is based on a convenient original formulation of Lyapunov’s direct method for discrete-time systems dedicated to discrete-time input affine Single Input-Single Output (SISO) systems. An IFT algorithm which sets the step size to guarantee the convergence is suggested. An inequality-type convergence condition is derived from Popov’s hyperstability theory considering the parameter update law as a nonlinear dynamical feedback system in the parameter space and iteration domain. The IFT-based design of a low-cost PI-FC is applied to a case study which deals with the angular position control of a direct current servo system laboratory equipment viewed as a particular case of input affine SISO system. A comparison of the performance of the IFT-based tuned PI-FC and the performance of the PI-FC tuned by an evolutionary-based optimization algorithm shows the performance improvement and advantages of our IFT approach to fuzzy control. Real-time experimental results are included.     

Stable and optimal fuzzy control of linear systems

A number of stable and optimal fuzzy controllers are developed for linear systems. Based on some classical results in control theory, we design the structure and parameters of fuzzy controllers such that the closed-loop fuzzy control systems are stable, provided that the process under control is linear and satisfies certain conditions. It turns out that if stability is the only requirement, there is much freedom in choosing the fuzzy controller parameters. Therefore, a performance criterion is set to optimalize the parameters. Using the Pontryagin minimum principle, we design an optimal fuzzy controller for linear systems with quadratic cost function. Finally, the optimal fuzzy controller is applied to a ball-and-beam system     

Direct adaptive fuzzy control of a class of MIMO non-affine nonlinear systems

An adaptive fuzzy control approach is proposed for a class of multiple-input–multiple-output (MIMO) nonlinear systems with completely unknown non-affine functions. The global implicit function theorem is first used to prove the existence of an unknown ideal implicit controller that can achieve the control objectives. Within this scheme, fuzzy systems are employed the approximate the unknown ideal implicit controller, and robustifying control terms are used to compensate the approximation errors and external disturbances. The adjustable parameters of the used fuzzy systems are deduced from the stability analysis of the closed-loop system in the sense of Lyapunov. To show the efficiency of the proposed controllers, two simulation examples are presented.     

Direct adaptive interval type-2 fuzzy control of multivariable nonlinear systems

A fuzzy logic controller equipped with a training algorithm is developed such that the H^∞ tracking performance should be satisfied for a model-free nonlinear multiple-input multiple-output (MIMO) system, with external disturbances. Due to universal approximation theorem, fuzzy control provides nonlinear controller, i.e., fuzzy logic controllers, to perform the unknown nonlinear control actions and the tracking error, because of the matching error and external disturbance is attenuated to arbitrary desired level by using H^∞ tracking design technique. In this paper, a new direct adaptive interval type-2 fuzzy controller is developed to handle the training data corrupted by noise or rule uncertainties for nonlinear MIMO systems involving external disturbances. Therefore, linguistic fuzzy control rules can be directly incorporated into the controller and combine the H^∞ attenuation technique. Simulation results show that the interval type-2 fuzzy logic system can handle unpredicted internal disturbance, data uncertainties, very well, but the adaptive type-1 fuzzy controller must spend more control effort in order to deal with noisy training data. Furthermore, the adaptive interval type-2 fuzzy controller can perform successful control and guarantee the global stability of the resulting closed-loop system and the tracking performance can be achieved.     

Adaptive sliding mode control for MIMO nonlinear systems based on fuzzy logic scheme

In this study an indirect adaptive sliding mode control (SMC) based on a fuzzy logic scheme is proposed to strengthen the tracking control performance of a general class of multi-input multi-output (MIMO) nonlinear uncertain systems. Combining reaching law approach and fuzzy universal approximation theorem, the proposed design procedure combines the advantages of fuzzy logic control, adaptive control and sliding mode control. The stability of the control systems is proved in the sense of the Lyapunov second stability theorem. Two simulation studies are presented to demonstrate the effectiveness of our new hybrid control algorithm.     

动态不确定非线性系统直接自适应模糊backstepping控制

对一类单输入单输出动态不确定非线性系统,提出一种直接自适应模糊backstepping和小增益相结合的控制方法.设计中,首先用模糊逻辑系统逼近虚拟控制器:其次把自适应模糊控制和backstepping控制设计技术相结合.给出了直接自适应模糊控制设计方法.最后基于Lyapunov函数和小增益方法证明了整个闭环系统的稳定性.仿真实例进一步验证了所提方法的有效性.     

Reliable decentralized PID controller synthesis for two-channel MIMO processes

Reliable stabilization and regulation of two-channel decentralized multi-input multi-output (MIMO) control systems is considered. The system has integral-action due to using proportional + integral + derivative (PID) controllers. Closed-loop stability and asymptotic tracking of step-input references are achieved at each output channel when all controllers are operational. Stability is maintained when one of the controllers fails completely and is set to zero. Controller synthesis procedures are proposed for stable MIMO plants and for several unstable MIMO plant classes that admit PID controllers. These synthesis procedures are applied to various examples of process systems to illustrate the design methodology.     

Fuzzy approximate disturbance decoupling of MIMO nonlinear systems by backstepping and application to chemical processes

Fuzzy approximate disturbance decoupling concept is introduced for a class of multiple-input-multiple-output (MIMO) nonlinear systems with completely unknown nonlinearities. Based on backstepping technique, a fuzzy almost disturbance decoupling control scheme is proposed. The fuzzy controllers guarantee internal uniform ultimate boundedness of the closed-loop adaptive systems and render a bounded approximate L/sub 2/ gain from the disturbance input to the output. The developed design scheme is applied to control a two continuous stirred tank reactor process. The simulation results illustrate the effectiveness of the method proposed in this paper.     

A combination of fuzzy logic and neural network controller for multiple-input multiple-output systems

Generally, the difficulty of multiple-input multiple-output (MIMO) systems control is how to overcome the coupling effects between the degrees of freedom. Owing to the computational burden and dynamic uncertainty of MIMO systems, the model-based decoupling approach is not practical for real-time control. A hybrid fuzzy logic and neural network controller (HFNC) is proposed here to overcome this problem and to improve the control performance. Firstly, a traditional fuzzy controller (TFC) is designed from a single-input single-output (SISO) systems viewpoint for controlling the degrees of freedom of a MIMO system. Secondly, an appropriate coupling neural network controller is introduced into the TFC for compensating the system coupling effects. This control strategy not only can simplify the implementation problem of fuzzy control but also can improve the control performance. The state-space approach for fuzzy control systems stability analysis is employed to evaluate the stability and robustness of this intelligent hybrid controller. In addition, a dynamic absorber with a twolevel mass-spring-damper structure was designed and constructed to verify the stability and robustness of a HFNC by numerical simulation and to investigate the control performance by comparing the experimental results of the HFNC with that of a TFC for this MIMO system.     

Stabilization of an unstable tubular reactor by nonlinear passive output feedback control

The multiple–input multiple–output (MIMO) output feedback (OF) control problem of an exothermic multi-jacket tubular open-loop unstable reactor is addressed. Over its axial length, the reactor has several equally sized cooling jackets. The controller must adjust the jacket temperatures on the basis of per jacket temperature measurements so that the closed-loop system is robustly stable. The problem is solved within a constructive framework, by combining notions and tools from chemical reactor engineering and partial differential equations (PDEs) control systems theory. The result is a MIMO nonlinear OF dynamic control design with (i) a decentralized MIMO passive state feedback (SF) controller implemented with a pointwise observer (PWO), (ii) closed-loop stability conditions in terms of sensor set and control gains, and (iii) efficient late lumping-based on-line implementation. The design is put in perspective with industrial PI and inventory control, and applied to a representative example through numerical simulation with favorable comparison against adaptive controllers.     

Automated synthesis of multivariable QFT controller using interval constraint satisfaction technique

Robust controller synthesis of Multi-Input–Multi-Output (MIMO) systems is of great practical interest and their automation is a key concern in control system design. The synthesis problem consists of obtaining a controller that ensures stability and meets a given set of performance specifications, in spite of the disturbance and model uncertainties. In addition to perform the above tasks, a MIMO controller also has to perform the difficult task of minimizing the interaction between the various control loops.Unlike existing manual or convex optimization based Quantitative Feedback Theory (QFT) design approaches, the proposed method gives a controller which meets all performance requirements in QFT, without going through the conservative and sequential design stages for each of the multivariable sub-systems. In this paper, a new, simple, and reliable automated MIMO QFT controllers design methodology is proposed. A fixed structure MIMO QFT controller has been synthesized by solving QFT quadratic inequalities of robust stability and tracking specifications. The quadratic inequalities (constraints) are posed as Interval Constraint Satisfaction Problem (ICSP). The constraints are solved by constraint solver — RealPaver. The main feature of this method is that the algorithm finds all the solutions to within the user-specified accuracy. The designed MIMO QFT controllers are tested on the experimental setup designed by Educational Control Product (ECP) Magnetic Levitation Setup ECP 730. From the experimental results presented, it is observed that, the designed controller satisfies the desired performance specifications. It is also observed that, the interactions between the loops are within the specified limits. The robustness of the designed controllers are verified by putting extra weights on the magnets.     

Stabilization of singularly perturbed fuzzy systems

This paper presents some novel results for stabilizing singularly perturbed (SP) nonlinear systems with guaranteed control performance. By using Takagi-Sugeno fuzzy model, we construct the SP fuzzy (SPF) systems. The corresponding fuzzy slow and fast subsystems of the original SPF system are also obtained. Two fuzzy control designs are explored. In the first design method, we propose the composite fuzzy control to stabilize the SPF subsystem with H/sup /spl infin// control performance. Based on the Lyapunov stability theorem, the stability conditions are reduced to the linear matrix inequality (LMI) problem. The composite fuzzy control will stabilize the original SP nonlinear systems for all /spl epsiv//spl isin/(0,/spl epsiv//sup */) and the upper bound /spl epsiv//sup */ can be determined. For the second design method, we present a direct fuzzy control scheme to stabilize the SP nonlinear system with H/sup /spl infin// control performance. By utilizing the Lyapunov stability theorem, the direct fuzzy control can guarantee the stability of the original SP nonlinear systems for a given interval /spl epsiv//spl isin/[/spl epsiv/_,/spl epsiv/~]. The stability conditions are also expressed in the LMIs. Two SP nonlinear systems are adopted to demonstrate the feasibility and effectiveness of the proposed control schemes.     

Stability conditions of fuzzy systems and its application to structural and mechanical systems

This paper provided the stability conditions and controller design for a class of structural and mechanical systems represented by Takagi–Sugeno (T–S) fuzzy models. In the design procedure of controller, parallel-distributed compensation (PDC) scheme was utilized to construct a global fuzzy logic controller by blending all local state feedback controllers. A stability analysis was carried out not only for the fuzzy model but also for a real mechanical system. Furthermore, this control problem can be reduced to linear matrix inequalities (LMI) problems by the Schur complements and efficient interior-point algorithms are now available in Matlab toolbox to solve this problem. A simulation example was given to show the feasibility of the proposed fuzzy controller design method.     

Adaptive control of MIMO time-varying systems with indicator function based parametrization

This paper studies a new solution framework for adaptive control of a class of MIMO time-varying systems with indicator function based parametrization, motivated by a general discrete-time MIMO Takagi–Sugeno (T–S) fuzzy system model in an input–output form with unknown parameters. An indicator (membership) function based parametrization has some favorable capacity to deal with certain large parameter variations. A new discrete-time MIMO system prediction model is derived for approximating a nonlinear dynamic system, and its system properties are clarified. An adaptive control scheme is developed, with desired controller parametrization and stable parameter estimation for control of such uncertain MIMO time-varying systems. A control singularity problem is addressed and the closed-loop stability and output tracking properties are analyzed. This work provides a new method for multivariable T–S fuzzy system modeling and adaptive control. An illustrative example and simulation results are presented to demonstrate the proposed novel concepts and to verify the desired adaptive control system performance.     

Fuzzy Constrained Min-Max Model Predictive Control Based on Piecewise Lyapunov Functions

This paper proposes two novel stable fuzzy model predictive controllers based on piecewise Lyapunov functions and the min-max optimization of a quasi-worst case infinite horizon objective function. The main idea is to design state feedback control laws that minimize the worst case objective function based on fuzzy model prediction, and thus to obtain the optimal transient control performance, which is of great importance in industrial process control. Moreover, in both of these predictive controllers, piecewise Lyapunov functions have been used in order to reduce the conservatism of those existent predictive controllers based on common Lyapunov functions. It is shown that the asymptotic stability of the resulting closed-loop discrete-time fuzzy predictive control systems can be established by solving a set of linear matrix inequalities. Moreover, the controller designs of the closed-loop control systems with desired decay rate and input constraints are also considered. Simulations on a numerical example and a highly nonlinear benchmark system are presented to demonstrate the performance of the proposed fuzzy predictive controllers.     

Robust adaptive NN control for a class of uncertain discrete-time nonlinear MIMO systems

A robust adaptive NN output feedback control is proposed to control a class of uncertain discrete-time nonlinear multi-input–multi-output (MIMO) systems. The high-order neural networks are utilized to approximate the unknown nonlinear functions in the systems. Compared with the previous research for discrete-time MIMO systems, robustness of the proposed adaptive algorithm is obvious improved. Using Lyapunov stability theorem, the results show all the signals in the closed-loop system are semi-globally uniformly ultimately bounded, and the tracking errors converge to a small neighborhood of zero by choosing the design parameters appropriately.     

A comparative study of three expert systems for blood pressure control

Regulation of mean arterial pressure (MAP) using sodium nitroprusside (SNP) infusion is common in many hospitals. We comparatively evaluated the performance of three types of expert systems controllers to automate this task: rule-based, fuzzy, and artificial neural network. For meaningful comparisons the three systems were based on the same set of rules. Their performance was tested on a nonlinear blood pressure model derived and scaled from canine data that simulated typical patient responses to the drug. The controllers were tested for differing patient sensitivities, baseline drift, and noisy blood pressure readings. The controllers were able to regulate the MAP in the target region about the set point for more then 90% of the time. The rule-based controller reduced MAP the fastest, while the fuzzy and neural controllers regulated MAP better over longer periods. Overall, the performance of the expert system controllers, while being intuitive and easier to design and implement, was comparable to more traditional controllers.     

Hinfinity controller design of fuzzy dynamic systems based on piecewise Lyapunov functions.

This paper presents a controller design method for fuzzy dynamic systems based on a piecewise smooth Lyapunov function. The basic idea of the proposed approach is to construct controllers for the fuzzy dynamic systems in such a way that a piecewise continuous Lyapunov function can be used to establish the global stability with Hinfinity performance of the resulting closed loop fuzzy control systems. It is shown that the control law can be obtained by solving a set of Linear Matrix Inequalities (LMI) that is numerically feasible with commercially available software. An example is given to illustrate the application of the proposed method.     

Adaptive fuzzy decentralized control for a class of large-scale nonlinear systems.

In this paper, direct and indirect adaptive output-feedback fuzzy decentralized controllers for a class of uncertain large-scale nonlinear systems are developed. The proposed controllers do not need the availability of the state variables. By designing the state observer, the adaptive fuzzy systems, which are used to model the unknown functions, can be constructed using the state estimations, and a new hybrid adaptive fuzzy control methodology is proposed by combining the adaptive fuzzy systems with H infinity control and the sliding mode control techniques. Based on Lyapunov stability theorem, the stability of the closed-loop systems can be verified. Moreover, the proposed overall control schemes guarantee that all the signals involved are bounded and achieve the H infinity-tracking performance. To demonstrate the effectiveness of the proposed methods, simulation results are illustrated in this paper.     

Robust H-infinity fuzzy control for uncertainMarkovian jump nonlinear singular systems withwiener process

This paper deals with the problems of robust stochastic stabilization and H-infinity control for Markovian jump nonlinear singular systems with Wiener process via a fuzzy-control approach. The Takagi-Sugeno (T-S) fuzzy model is employed to represent a nonlinear singular system. The purpose of the robust stochastic stabilization problem is to design a state feedback fuzzy controller such that the closed-loop fuzzy system is robustly stochastically stable for all admissible uncertainties. In the robust H-infinity control problem, in addition to the stochastic stability requirement, a prescribed performance is required to be achieved. Linear matrix inequality (LMI) sufficient conditions are developed to solve these problems, respectively. The expressions of desired state feedback fuzzy controllers are given. Finally, a numerical simulation is given to illustrate the effectiveness of the proposed method.