Robust Adaptive Tracking with Pole Placement of First-Order Potentially Inversely Unstable Continuous-Time Systems

Article type: Research Article

Authors: Alonso Quesada, Santiago | De la Sen, Manuel

Affiliations: Escuela Universitaria de Ingeniería Técnica Industrial de Bilbao, Plaza de la Casilla 3, 48012 Bilbao, Spain. E-mail: santi@we.lc.ehu.es

Abstract: This note presents an indirect adaptive control scheme applicable to nominally controllable non-necessarily inversely stable first-order continuous linear time-invariant systems with unmodelled dynamics. The control objective is to achieve a bounded tracking-error between the system output and a reference signal. A least-squares algorithm with normalization is used to estimate the plant parameters by using two additional design tools, namely: 1) a modification of the parameter estimates and 2) a relative adaptation dead-zone. The modification is based on the properties of the inverse of the least-squares covariance matrix and it uses an hysteresis switching function. In this way, the non-singularity of the controllability matrix of the estimated model of the plant is ensured. The relative dead-zone is used to turn off the adaptation process when an absolute augmented error is smaller than the value of an available overbounding function of the unmodelled dynamics contribution plus, eventually, bounded noise.

Keywords: Robust control, hysteresis, inversely unstable, controllability, dead-zone

DOI: 10.3233/INF-1998-9301

Journal: Informatica, vol. 9, no. 3, pp. 259-278, 1998