Uncertain MIMO Systems Research Articles

Time-varying sliding mode control for a class of uncertain MIMO nonlinear system subject to control input constraint

To solve the regulator problem of a class of uncertain MIMO nonlinear systems subject to control input constraint, three types of time-varying sliding mode control laws are proposed. The sliding surfaces pass the initial value of the system at the initial time, and are shifted/rotated towards the predetermined ones. The controller parameters are optimized by genetic algorithm (GA). Lyapunov method is adopted to prove the stability and robustness to the parameter uncertainties and external disturbance. By mean of time-varying sliding mode control law, the reaching phase in the conventional sliding mode control is eliminated, and the system is guaranteed to have robustness from the very beginning. Taking the control of two-link manipulator and attitude tracking of rigid spacecraft as two examples, we illustrate the features of the time-varying sliding mode control. The simulation results show the validity of the control law to a class of uncertain MIMO systems. Better robustness against the uncertainties and external disturbance could be achieved by time-varying sliding mode control without violating the constraint on control input.

Approximate Adaptive Output Feedback Stabilization via Passivation of MIMO Uncertain Systems Using Neural Networks

An adaptive output feedback neural network controller is designed, which is capable of rendering affine-in-the-control uncertain multi-input-multi-output nonlinear systems strictly passive with respect to an appropriately defined set. Consequently, a simple output feedback is employed to stabilize the system. The controlled system need not be in normal form or have a well-defined relative degree. Without requiring a zero-state detectability assumption, uniform ultimate boundedness, with respect to an arbitrarily small set, of both the system's state and the output is guaranteed, along with boundedness of all other signals in the closed loop. To effectively avoid possible division by zero, the proposed adaptive controller is of switching type. However, its continuity is guaranteed, thus alleviating drawbacks connected to existence of solutions and chattering phenomena. Simulations illustrate the approach.

Chattering-free fuzzy sliding mode control in MIMO uncertain systems

Control of nonlinear multivariable systems is very challenging in the area of systems and control. This paper is concerned with a framework that unifies sliding mode control (SMC) and fuzzy logic control (FLC). Based on the combination of the SMC with fuzzy control, this paper presents a new and feasible design algorithm to synthesize a robust fuzzy sliding mode controller which can easily tackle the stabilizing and tracking problem of a class of MIMO nonlinear systems in the presence of uncertainties and external disturbance. A practical design that combines a fuzzy technique with SMC to enhance robustness and sliding performance in a class of uncertain MIMO nonlinear systems is proposed. Using a fuzzy scheme, a Fuzzy Sliding Mode Controller (FSMC) is used to approximate the hitting control in the neighborhood of the sliding manifold. The main contribution of the proposed method is that the structure of the controlled system is partially unknown and does not require the bounds of uncertainty and disturbance of the system to be known; meanwhile, the chattering phenomenon that frequently appears in the conventional variable structure systems is also eliminated without deteriorating the system robustness. A series of computer simulations are included to verify the effectiveness of the proposed design algorithm.

DESIGN MODIFICATION OF SLIDING MODE OBSERVERS FOR UNCERTAIN MIMO SYSTEMS WITHOUT AND WITH TIME-DELAY

In this paper, the sliding mode observers design techniques for MIMO and as a simple example for SISO systems are systematically advanced as a first purpose. Design parameters are selected such that on the defined switching surface always is generated asymptotically stable sliding mode. Moreover, observer state error dynamics is globally robustly asymptotically stable. Then, advanced design techniques are generalized to the design of a new modification of sliding mode observers for uncertain MIMO systems with time-delay. Robust sliding and global asymptotic stability conditions are derived by using Lyapunov-Krasovskii V-functional method. By these conditions observer parameters are designed such that an asymptotically stable sliding mode always is generated in observer and observer state error dynamics is robustly globally asymptotically stable. The main results are formulated in terms of Lyapunov matrix equations and inequalities. Design example for AV-8A Harrier VTOL aircraft with simulation results using MATLAB-Simulink show the effectiveness of proposed design approaches.

Decentralized Robust PI Controller Design For An Industrial Utility Boiler - An IMC Method

This paper presents a scheme for designing a robust decentralized PI controller for an industrial utility boiler system. First, a new method for designing robust decentralized PI controllers for uncertain LTI MIMO systems is presented. Sufficient conditions for closed-loop stability and diagonal dominance of a multivariable system are given. For each isolated subsystem a first order approximation is obtained. Then, achieving robust stability and closedloop diagonal dominance is formulated as local robust performance problems. It is shown by selecting time constants of the closed-loop isolated subsystems appropriately, these local robust performance problems are solved and the interactions between closed-loop stabilized subsystems are attenuated. The internal model control (IMC) method is used to design local PI controllers. The suggested design strategy is applicable to unstable systems as well. Thereafter, the nonlinear model of an industrial utility boiler is linearized about its operating points and the nonlinearity is modeled as uncertainty for a nominal LTI MIMO system. Using the new proposed method, a decentralized PI controller for the uncertain LTI nominal model is designed. The designed controller is applied to the real system. The simulation results show the effectiveness of the proposed methodology.

Almost disturbance decoupling control of nonlinear MIMO uncertain system and application to half-car active suspension system

This paper studies the tracking and almost disturbance decoupling problem of nonlinear multi-input multi-output uncertain systems based on the feedback linearisation approach. The main contribution of this study is to construct a controller, under appropriate conditions, such that the resulting closed-loop system is valid for any initial condition and bounded tracking signal with the following characteristics: input-to-state stability with respect to disturbance inputs and almost disturbance decoupling, i.e., the influence of disturbances on the L2 norm of the output tracking error can be arbitrarily attenuated by changing some adjustable parameters. One example, which cannot be solved by the first paper on the almost disturbance decoupling problem, is proposed in this paper to exploit the fact that the tracking and the almost disturbance decoupling performances are easily achieved by the proposed approach. In order to demonstrate the practical applicability, the paper has investigated a famous half-car active suspension system.

A risk adjusted approach to robust simultaneous fault detection and isolation

This paper addresses the problem of detecting and isolating faults in noisy MIMO uncertain-systems, subject to structured dynamic uncertainty. Its main result shows that this problem can be efficiently solved using a combination of sampling and LMI optimization tools. These results are illustrated with two examples and benchmarked against existing methods.

Robust Controllability for a Class of Uncertain Linear Time-Invariant MIMO Systems

This note studies the problem of robust controllability of linear time invariant multiple-input-multiple-output systems with A being or A and B both being sign-invariant interval matrices. For controllability, sufficient conditions as well as necessary and sufficient conditions based on interval division method are presented. The note also provides a way to handle interval systems that are not sign-invariant in the A matrix. Some examples illustrate the results.

DIRECT ADAPTIVE FEEDBACK DESIGN FOR LINEAR DISCRETE‐TIME UNCERTAIN SYSTEMS

ABSTRACTIn this paper, we develope a direct adaptive control framework for linear discrete‐time uncertain MIMO systems, based on assumptions that the system is controllable and the difference of the unknown system matrix from the stable solution is bounded by a given value. The proposed framework is Lyapunov‐based, and the controller guarantees adaptive stabilization. In addition, the adaptive laws are characterized by means of Kronecker calculus. Furthermore, the results can easily be extended to time‐varying cases, where the deviation from the stable solution is bounded, and the controllability assumption holds. The controller not only tolerates plant deviation, but also guarantees asymptotical stability of the closed‐loop system. Two numerical examples are provided to demonstrate the performance of the controller.

H∞ Tracking-based adaptive fuzzy-neural control for MIMO uncertain robotic systems with time delays

In this paper, a novel adaptive fuzzy-neural control (AFNC) scheme for multi-input multi-output uncertain robotic systems is proposed for H ∞ tracking performance and to suppress the effects caused by multiple time-delayed state uncertainties, unmodeled dynamics, and disturbances. Each delayed uncertainty is assumed to be bounded by an unknown gain. A reference model with the desired amplitude and phase properties is given to construct an error model. A fuzzy-neural (FN) system is used to approximate an unknown controlled system from the strategic manipulation of the model following tracking errors. The proposed AFNC scheme uses two on-line estimations, which allows for the inclusion of identifying the gains of the delayed state uncertainties and training the weights of the FN system, simultaneously. Stability and robustness of the AFNC scheme is analyzed in Lyapunov sense. It is shown that the proposed control scheme can guarantee parameter estimation convergence and stability robustness of the closed-loop system with H ∞ tracking performance for the overall system without a priori knowledge on the upper bounds of the delayed state uncertainties. The performance of the proposed scheme is evaluated through the simulation results. Simulations are given to show the validity and confirm the performance of the proposed scheme.

Control of Discrete MIMO Uncertain System

An algorithm for control of discrete multi-input multi-output linear uncertain systems is presented. The algorithm is based on the state and parameters observability form and a certainty equivalence controller. The algorithm provides single controller for the problem of control of uncertain MIMO system that approaches the performance of a controller designed for perfectly known parameters within the whole range of the system’s parameters uncertainty. The algorithm is globally bounded input bounded output stable and needs only the knowledge of the order of the plant. The algorithm is presented and results stating its performance are stated. The proposed control algorithm is consistent, that is when the parameters uncertainty diminishes the control algorithm converges to well known control approaches for certain systems.

Synthesis of robust nonlinear state feedback for regulation of uncertain MIMO systems

Linearization of the input-output response of a nonlinear system via state feedback has found many applications in control of nonlinear processes. However, in the presence of uncertainties, this approach leads to inexact linearization and results in loss of performance and stability. In this paper, a controller design methodology is developed based on Input/Output linearization and multi-objective H 2/ H ∞ synthesis that ensures robust stability and performance MIMO nonlinear systems.

Output Stabilizing Robust Control for Discrete Uncertain Systems

A comprehensive solution to the problem of the robust output min–max control for discrete uncertain MIMO systems with matched uncertainties is presented in this paper. In the literature, state-dependent Lyapunov and Riccati min–max controllers were treated independently and the existence problem of the output min–max controllers has not been fully resolved. In this paper, both Lyapunov- and Riccati-based min–max output control laws are treated, and a simple criterion for the existence of a min–max output controller is provided. It is shown that when the criterion is satisfied, both Riccati- and Lyapunov-based output min–max controllers exist. The first controller is applied directly to the given system, while the latter controller is applied to the given system closed with a suitable feedback. Moreover, it is shown that both overall controllers are identical. In addition, an alternative criterion for the existence of a Lyapunov-based min–max output control, in terms of discrete positive real properties of the system, is derived.

Inverse Nyquist array: a quantitative theory

Rosenbrock's inverse Nyquist array (INA) (1970, 1974) is made robust for uncertain MIMO systems by direct application of SISO quantitative feedback theory (QFT) methodology to each element of the inverse closed loop system. This enables quantitative bounds to be generated for not only the elements of the closed loop transfer function matrix but also for the overall closed loop interaction index; thereby making precise the heuristic notion of 'sufficient' diagonal dominance used in the traditional Nyquist array. This technique will be used to convert the original MIMO problem into a series of exact robust performance problems involving both parametric and unstructured uncertainty. An illustrative example is presented comparing the solution using this new technique and a mu-synthesis solution.

A Genetic Algorithm for MIMO Feedback Control System Design

This paper describes a control design method for uncertain MIMO systems which utilizes a hybrid scheme combining a genetic algorithm and sequential quadratic programming. The structured singular value is used to formulate a robust performance objective function, whose unity value becomes the constraint in the overall problem of maximizing the achievable closed loop bandwidth. For a MIMO problem, this leads to the definition of the limiting trade-off between performances of the output channels. A representative MIMO control problem is used to test the algorithm. The performances of full-block IMC controllers designed with the algorithm are compared with that of an optimally tuned decentralized PID scheme.

Robust noniterative synthesis of ill-conditioned plants

Ill-conditioned plants with delays are generally difficult to control. Skogestad, Morari and Doyle (1988) applied the mu method to achieve synthesis and analysis of such a problem. An alternative synthesis using the Horowitz method for MIMO uncertain feedback systems is applied to the same example. An economical bandwidth solution was achieved without iterations. Design details and simulations are presented. >

Discontinuous output feedback stabilizing an uncertain MIMO plant

The problem of output stabilization for uncertain MIMO systems is considered. Using structural transformations, an uncertain system is changed to a form convenient for output feedback design. Synthesis of observer-based variable structure control for asymptotical stabilization and uniform ultimate boundedness of the closed-loop system is provided. Examples are considered and simulation results are given.