Abstract of Thesis presented at COPPE/UFRJ as a partial fulfillment of the requirements for the degree of Doctor of Science (D.Sc.)

Improving Transient Behavior of Multivariable Adaptative Controllers

Marcos Ferreira Duarte Pinto

April/2009

Advisor:

Ramon Romankevicius Costa

Department:

Eletrical Engineering

      This thesis presents a new model-reference adaptive control (MRAC) algorithm for linear time invariant multi-input-multi-output (MIMO) uncertain plants with relative degree one, which is refereed to as α-MRAC MIMO. The main characteristic of this new algorithm is its improved transient behavior compared to the standard MIMO adaptive controllers. The α-MRAC MIMO is obtained by combining the structure of the recently proposed MIMO generalization of the MRAC of SISO systems, where a convenient factorization of the high frequency gain matrix of the plant was employed, with the α-MRAC algorithm developed originally to SISO plants. The key of this algorithm is the introduction of an estimate of the error derivative, obtained via lead filters, in the update law of the parameters. The closed loop system is shown to be at least uniformly asymptotically stable, irrespectively of the time constants chosen for the filters. By singular perturbation method, it is shown that for a sufficiently high adaptation gain and a sufficiently small time constant of the filters, both the tracking error and the control mismatch converge exponentially to zero. To tackle the problem of uncertain plants with small unmodeled dynamics, a modification of the algorithm is proposed by including normalization and a switching term in the update law.