Ramon R. Costa

Variable structure model reference adaptive control using only input and output measurements

Abstract A variable structure model reference adaptive controller (VS-MRAC) using only the input and output measurements of the plant is proposed. Stability and transient properties are analysed and discussed. Remarkable transient behaviour is revealed, in particular, model following can be perfectly achieved in a finite time. The effect of plant input disturbance is investigated and the performance of the VS controller is also shown to be qualitatively superior to that obtained with (conventional) integral adaptation algorithms. A link between the VS-MRAC and the conventional MRAC is suggested. Simulations are presented to highlight the theoretical results.

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 adaptive control using high-frequency gain matrix factorization

In this note, we extend the application of a less restrictive condition about the high-frequency gain matrix to design stable direct model reference adaptive control for a class of multivariable plants with relative degree greater than one. The new approach is based on a control parametrization derived from a factorization of the high-frequency gain matrix K/sub p/ in the form of a product of three matrices, one of them being diagonal. Three possible factorizations are presented. Only the signs of the diagonal factor or, equivalently, the signs of the leading principal minors of K/sub p/, are assumed known.

Design of a high performance variable structure position control of ROVs

An adaptive control scheme for dynamic positioning (DP) of remotely operated underwater vehicles (ROV) is proposed based on a recently developed output feedback variable structure control (VSC) algorithm named VS-MRAC. Only position measurement is required. Precise modeling of the ROV is not needed and unmodeled perturbations can be effectively rejected. A simple method for discretizing the original continuous-time VS-MRAC is proposed based on dead-beat response. Other important practical implementation issues are considered. The performance is evaluated by simulation with a realistic ROV model and by full-scale experimental pool tests with an actual ROV. >

Dynamic positioning of remotely operated underwater vehicles

The paper describes an automatic dynamic positioning system for remotely operated underwater vehicles (ROVs) using a mechanical passive arm for position measurement that is suitable for inspection and intervention tasks requiring precise positioning. Good dynamic performance in tracking was also attained, particularly with the variable structure model reference adaptive control strategy.

A variable structure model reference robust control without a prior knowledge of high frequency gain sign

The design of a variable structure model reference robust control without a prior knowledge of high frequency gain sign is presented. Based on an appropriate monitoring function, a switching scheme for some control signals is proposed. It is shown that after a finite number of switching, the tracking error converges to zero at least exponentially for plants with relative degree one or converges exponentially to a small residual set for plants with higher relative degree, and the input disturbance can be completely rejected without affecting the tracking performance.

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).

Lyapunov/Passivity-Based Adaptive Control of Relative Degree Two MIMO Systems With an Application to Visual Servoing

This note presents a Lyapunov-based design of model-reference adaptive control (MRAC) for multiple-input-multiple-output (MIMO) systems of uniform relative degree two. It consists of an extension of a well known MRAC Lyapunov-based scheme for single-input-single-output (SISO) plants with relative degree one or two. The case of relative degree one, was completely extended to the MIMO case only recently. The corresponding extension of the relative degree two case remained hitherto unpublished. While MIMO MRAC schemes exist which can deal with arbitrary relative degree, the one presented here has the significant advantage of possessing an explicit Lyapunov function which easily leads to a stability and error convergence proof. It can also be regarded as a passivity-based approach. As a result, it becomes easier to guarantee stability when connecting such adaptive system to other adaptive control systems with similar passivity properties, e.g., in adaptive visual servoing of robot manipulators

MIMO direct adaptive control with reduced prior knowledge of the high frequency gain

This paper addresses the problem of designing model-reference adaptive control for linear MIMO systems with unknown high-frequency gain matrix (HFGM). The concept of hierarchy of control is introduced leading to a new control parametrization and an error equation with triangular HFGM, which allows a sequential design of the adaptation scheme. Significant reduction of the prior knowledge about the HFGM is achieved, overcoming the limitations of the known methods. A complete stability and convergence analysis is developed based on a new class of signals and their properties. Exponential stability is guaranteed under explicit persistency of excitation conditions.

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.