José Paulo V. S. Cunha

Output-feedback model-reference sliding mode control of uncertain multivariable systems

This note considers the robust output tracking problem using a model-reference sliding mode controller for linear multivariable systems of relative degree one. It is shown that the closed loop system is globally exponentially stable and the performance is insensitive to bounded input disturbances and parameter uncertainties. The strategy is based on output-feedback unit vector control to generate sliding mode. The only required a priori information about the plant high frequency gain matrix K/sub p/ is the knowledge of a matrix S/sub p/ such that -K/sub p/S/sub p/ is Hurwitz which relaxes the positive definiteness requirement usually needed by other methods.

Multivariable Output-Feedback Sliding Mode Control

This chapter addresses the problem of model-reference sliding mode control of uncertain linear multi-input-multi-output systems by output-feedback. After a brief revision of the main approaches and results available in the literature, a new method to solve the problem is presented using unit vectors as switching functions to induce sliding modes. It is named Unit Vector Model-Reference Adaptive Control (UV-MRAC).

Peaking free variable structure control of uncertain linear systems based on a high-gain observer

An output-feedback model-reference variable structure controller based on a high-gain observer (HGO) is proposed and analyzed. For single-input-single-output (SISO) linear plants with relative degree greater than one, the control law is generated using the HGO signals only to drive the sign function of the variable structure control component while the sign function gain, also called modulation, as well as the other components of the control signal are generated using signals from state variable filters which do not require high gain and are free of peaking. This scheme achieves global exponential stability with respect to a small residual set and does not generate peaking in the control signal.

Design of First-Order Approximation Filters for Sliding-Mode Control of Uncertain Systems

The focus of this paper is on the synthesis of first-order filters which generate approximations for upper bounds of some signals needed in sliding mode control laws. The approximation is based on optimization methods which are applied to reduce the amplitude of the control signal. This paper also considers the application of these filters in output-feedback sliding mode controllers of linear systems in regular form with uncertain parameters and uncertain order. An experimental setup where the filters are applied to the model-reference control of an electromechanical system is presented to illustrate the design method.

Wave-to-Wire Model and Energy Storage Analysis of an Ocean Wave Energy Hyperbaric Converter

This paper addresses the dynamic modeling and the energy storage analysis of a wave energy hyperbaric converter, which consists of a set of oscillating bodies (named as pumping modules) linked to hydropneumatic accumulators and an electric generating unit. A mathematical model of the accumulator is presented and a model for the generating unit is proposed, including a nonlinear model of a Pelton turbine. Then, the hydrodynamic, mechanical, and electrical characteristics of the subsystems that compose the converter are discussed. With the proposed model, it is possible to evaluate the dynamic behavior of the entire system. That is, for a given incident ocean wave, it is possible to evaluate all the system state variables and the generated electric power, including the quality (fluctuation, for example) of the generated voltage and frequency for islanded or power-grid-connected operation. Simulation results considering the proposed wave-to-wire model under the action of regular and irregular incident waves are presented to illustrate the performance of the system.

Efficiency optimization in a wave energy hyperbaric converter

This paper considers the problem of optimizing the efficiency of the primary conversion on an ocean wave energy hyperbaric converter. This wave energy converter (WEC) is an oscillating-body linked to a hyperbaric chamber. By solving the equation of motion of the power take-off mechanism, it is shown that optimal conditions for improving the absorbed power relate the buoy parameters and the chamber pressure with the incident waves. This work also proposes an algorithm for finding the best time interval that the body remains locked when latching control strategy is used to enhance the efficiency of the WEC. Numerical simulations are presented in order to evaluate the optimum conditions of the hyperbaric WEC and the performance of the proposed algorithm.

Controle de sistemas lineares incertos por modos deslizantes e observador de alto ganho sem peaking

A model-reference variable structure controller based on a high gain observer (HGO) is proposed and analyzed. For single-input-single-output plants with relative degree larger than one, the switching law is generated using the observed state while the modulation function in the control law is generated using signals from state variable filters. With this scheme, global exponential stability with respect to an arbitrarily small residual set is achieved. Moreover, the closed loop system shows no peaking phenomena which could degrade the performance. Experimental results illustrate the good performance obtained with the algorithm in actual conditions.

Adaptive sliding mode control for disturbances with unknown bounds

In this paper, we propose an adaptive sliding mode approach based on average control to deal with disturbances of unknown bounds in nonlinear plants. Some advantages with respect to earlier results in the literature are its simplicity and the possibility of including non smooth disturbances. Differently from other adaptive algorithms, no overestimation for the controller gain neither the loss of the sliding motion are observed. The developed method allows for ideal sliding modes and reduces the chattering phenomena. In theory, the sliding variable which drives the relay function becomes identically zero after some finite time. Global stabilization is demonstrated and numerical simulations illustrate the potential of the new adaptation scheme.

Extremum seeking control via monitoring function and time-scaling for plants of arbitrary relative degree

An output-feedback variable-structure based extremum seeking controller was recently introduced for nonlinear uncertain systems by using a monitoring function. The class of systems considered was restricted to the relative degree one case. In this paper, generalization is achieved to include more general dynamics with arbitrary relative degree, uncertain parameters and order. Global stability properties of the closed-loop system and exponential convergence to a neighborhood of the desired extremum are proved. The main contribution of this paper is to develop a time-scaling procedure to essentially reduce the analysis and control design to that of a relative degree one case. Simulation results illustrate the performance of the proposed extremum seeking control algorithm in different time scales.

Output-feedback sliding-mode control via cascade observers for global stabilisation of a class of nonlinear systems with output time delay

This article proposes a sliding-mode control scheme for a class of triangular nonlinear systems with arbitrarily long and known time delay in the output signal. The proposed control strategy guarantees global asymptotic stability of the closed-loop system using only output feedback, without using any kind of approximations. The state of the system is estimated by asymptotic observers connected in cascade. The analysis of such observers in closed-loop feedback is also a contribution of the present manuscript as well as the theoretical demonstration of the chattering elimination even in the presence of delays. Simulation results and a physically motivated example with a full-bridge power converter illustrate the effectiveness of the proposed approach.