MODEL-PREDICTIVE CONTROL OF LINEAR-MULTIVARIABLE SYSTEMS HAVING TIME DELAYS AND RIGHT-HALF-PLANE ZEROS

The design of high performance model-predictive controllers for multivariable systems having both time delays and right-half-plane (RHP) zeros is a challenge. For multivariable systems, G(s), having time delays in each element, time delay compensation methods are known. However, even after time delay compensation the system can still have an infinite number of RHP zeros arising from the determinant of G(s). These RHP zeros are the roots of exponential polynomials, \G\ = SIGMA(j = 1)n p(j)(s)e(-gamma-js)\q(s), where p(j)(s), q(s) are polynomials. Even more challenging problems arise when the original problem has exponential polynomials in each element of G(s) rather than a single delay term. In this paper, model-predictive controller design methods are presented for this class of problems which allow either decoupled control systems or control systems which dump all the undesirable dynamics onto a single output. Perhaps the most striking result is that the effects of RHP zeros can be removed completely if the problem is nonsquare with one more input than output. Examples are provided to illustrate the design procedures and resulting control system performance.