A new indirect adaptive pole placer for possibly non-minimum phase mimo linear systems

The use of generalized sampled-data hold functions, in order to synthesize adaptive pole placers for linear multiple-input, multiple-output systems wi th unknown parameters, is investigated in this paper, for the first time. S uch a control scheme relies on a periodically varying controller, which sui tably modulates the sampled outputs of the controlled plant. The proposed c ontrol strategy allows us to assign the poles of the sampled closed-loop sy stem arbitrarily in desired locations, and does not make assumptions on the plant other than controllability and observability of the continuous and t he sampled system, and the knowledge of a set of structural indices, namely the locally minimum controllability indices of the continuous-time plant. The indirect adaptive control scheme presented here, estimates the unknown plant parameters land hence the parameters of the desired modulating matrix function) on line, from sequential data of the inputs and the outputs of t he plant, which are recursively updated within the time limit imposed by a fundamental sampling period To The controller determination is based on the transformation of the discrete analogue of the system under control to a p hase-variable canonical form, prior to the application of the control desig n procedure. The solution of the problem can, then, be obtained by a quite simple utilization of the concept of state similarity transformation, where as known indirect adaptive pole placement techniques require the solution o f matrix polynomial Diophantine equations. Moreover, in many cases, the sol ution of the Diophantine equation for a desired set of closed-loop eigenval ues might yield an unstable controller, and the overall adaptive pole place ment scheme is then unstable with unstable compensators because their outpu ts are unbounded. The proposed strategy avoids these problems; since here g ain controllers are essentially needed to be designed. Moreover, persistenc y of excitation and, therefore, parameter convergence, of the continuous-ti me plant is provided without making assumptions either on the existence of specific convex sets in which the estimated parameters belong or on the cop rimeness of the polynomials describing the ARMA model, pr finally on the ri chness of the reference signals, as compared to known adaptive pole placeme nt schemes.