Informatica

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.

This paper presents a direct adaptive, control algorithm, based on a σ-modification rule, which is robust respect to additive and multiplicative plant unmodelled dynamics for plants involving both internal (i.e., in the state) and external (i.e., in the output or input) known point delays. Several adaptive controller structures are given and analyzed for the case of plants with unknown parameters while being assumed that the nominal plant is of known order and relative order. The parametrized parts of two of the controller structures involve delays while those of the two remaining controllers are delay-free. However, auxiliary compensating signals which weight the plant input and output integrals are incorporated in all the controller structures for stabilization purposes. It is proved that, if the unmodelled dynamics is sufficiently small at low frequencies, then the adaptive algorithm guarantees boundedness of all the signals in the closed-loop system.