Petr Hušek

Adaptive fuzzy sliding mode control for electro-hydraulic servo mechanism

An innovative approach to adaptive fuzzy sliding mode control for a class of SISO continuous nonlinear systems with unknown dynamics and bounded disturbances is introduced in this paper. The main idea of the presented method consists in the introduction of the fuzzy self-tuning mechanism for adaptation of the sliding mode control parameters - extended feedback and switching gains. Such modification reduces the well-known chattering problem in classical sliding mode control. In comparison with the other algorithms eliminating this problem the proposed method results in faster convergence and more transparent and interpretable design of self-tuning mechanism. Moreover, the proposed method guaranteing the asymptotic reference signal tracking with bounded system signals can be easily implemented to high order systems. The performance of the presented control design is demonstrated on control of a nonlinear electro-hydraulic servo mechanism.

Fuzzy model reference control with adaptation of input fuzzy sets

An improved adaptation mechanism to fuzzy model reference learning control (FMRLC) will be introduced in this paper. The main idea of the presented approach consists in including the controller input fuzzy sets into the adaptation process. In comparison with other FMRLC modifications the proposed method can be started with smaller number of input membership functions resulting in better reference signal tracking. Performance of the proposed procedure is demonstrated on control of a nonlinear laboratory system.

Generalized Tsypkin-Polyak Locus

Abstract In this paper the problem of determining stability radius of a ball of continuous-time polynomials specified by a weighted lp norm in the coefficient space is considered. The graphical solution for equal weights considered for coefficients being above and below their nominal values was given by Tsypkin and Polyak. Based on that the solution of the same problem for the case of different weights taken for coefficient being above and below its nominal value is presented. The necessary and sufficient condition for robust stability of those systems is given.

Adaptive sliding mode control with moving sliding surface

Graphical abstractDisplay Omitted HighlightsThe paper presents an improvement of control performance of sliding mode control.The proposed method reduces duration of the undesirable approaching phase.The control parameters are tuned by fuzzy logic rules.The performance improvement was confirmed by simulation study. A continuous sliding mode control with moving sliding surface for nonlinear systems of arbitrary order is presented in this paper. The sliding surface is moved repetitively toward the target sliding surface in order to ensure that the system trajectory is close to the actual surface during the whole control process. The parameters of sliding mode control are tuned by a fuzzy logic. The proposed procedure reduces the time when the system operates in the approaching phase during which the control performance is deteriorated since the system is more susceptible to external disturbances and model uncertainties. The effectiveness of the presented approach is demonstrated on a control of a flexible robot manipulator arm.

Robust PI controller design with respect to fuzzy sensitivity margins

The paper deals with PI controller design for linear systems with parametric uncertainty with respect to sensitivity margin. The plant is considered as possibility distribution on a plant space and the closed loop specifications are given in terms of the peak of sensitivity function described by fuzzy numbers. The controller design is understood as the inclusion of respective @a-cuts. Such consideration makes it possible to degrade the closed loop specifications towards the uncertainty that occurs very rarely. The proposed procedure is applied on the speed control of a hydraulic turbine - a non-minimum phase system.

Comments on computing extreme values in 'stability issues on Takagi-Sugeno fuzzy model-parametric approach" [with reply]

The commenters analyze the results published in the above paper by Lo and Chen (ibid. vol.17 (1999)) which concern a new method of stability analysis of Takagi-Sugeno fuzzy systems, and amend the comments given by Johansen et al. (ibid. vol.8 (2000)). It is shown that the computational procedure presented by Lo-Chen is not valid for fuzzy systems where the number of rules is greater than three. In reply, Lo-Chen have modified the original claim and patched up the error to generate a sufficient effect provided that an appropriate switching is taken into account; the switching criterion is not overly restrictive and the nature of fuzzy systems permits such practices. They also point out that a computational procedure for multidimensional cases and a routine construction is readily available in the Matlab package.

Fuzzy Control of a Helio-Crane

In this paper we present a comparison of two fuzzy-control approaches that were developed for use on a non-linear single-input single-output (SISO) system. The first method is Fuzzy Model Reference Learning Control (FMRLC) with a modified adaptation mechanism that tunes the fuzzy inverse model. The basic idea of this method is based on shifting the output membership functions in the fuzzy controller and in the fuzzy inverse model. The second approach is a 2 degrees-of-freedom (2 DOF) control that is based on the Takagi-Sugeno fuzzy model. The T-S fuzzy model is obtained by identification of evolving fuzzy model and then used in the feed-forward and feedback parts of the controller. An error-model predictive-control approach is used for the design of the feedback loop. The controllers were compared on a non-linear second-order SISO system named the helio-crane. We compared the performance of the reference tracking in a simulation environment and on a real system. Both methods provided acceptable tracking performance during the simulation, but on the real system the 2 DOF FMPC gave better results than the FMRLC.

Fuzzy Model Reference Learning Control with Convergent Rule Base

Abstract New approach to adaptation ensuring convergence of the controller rule base in fuzzy model reference learning control (FMRLC) method will be introduced in this paper. The proposed method guarantees for a time-invariant plant that after few steps of adaptation the controller becomes fixed and needs not to be further tuned that results in faster response in comparison to the original FMRLC method. The main idea consists in using an additional information about the controlled system. The advantages of the proposed modification are presented on control of magnetic suspension system.

CONTROLLER SYNTHESIS WITH INPUT AND OUTPUT CONSTRAINTS FOR FUZZY SYSTEMS

Abstract This work extends the synthesis of controllers for Takagi-Sugeno fuzzy systems based on a piecewise Lyapunov function to include constraints on the input or the output. Extension follows naturally from the existing results based on a common Lyapunov function and can be implemented via linear matrix inequalities, which are numerically solvable with commercial available software. An illustrative example is provided.

On Monotonicity of Takagi–Sugeno Fuzzy Systems With Ellipsoidal Regions

This paper presents sufficient conditions on monotonicity of a Takagi-Sugeno (T-S) fuzzy system with linear submodels in the consequents of the rules where the input space is considered to be partitioned to ellipsoidal regions. Such regions commonly arise in practice if clustering algorithms are used to identify a fuzzy model from measured data. By the monotonicity, it is meant that the partial derivatives of the output of the mapping represented by the fuzzy model with respect to all inputs are nonnegative on a given universe of discourse. The conditions are given in the form of linear matrix inequalities with respect to the parameters of the submodels that may be useful in solving associated optimization problems via efficient semidefinite programming techniques. The proposed conditions reduce conservatism of the existing ones from two reasons. First, the conservatism is introduced only once, since the conditions are not separated between antecedent and consequent parts of fuzzy rules. Second, the domain of interest where monotonicity is enforced may be restricted. The proposed algorithm is illustrated on least-squares approximation of a multivariate function by a monotonic T-S fuzzy system.