Copyright @ IFAC Adaptive Systems in Control and Signal Processing, Glasgow, Scotland, UK, 1998 TWO-DEGREE-OF-FREEDOM STABLE GPC DESIGN Zdzislaw Kowalczuk and Piotr Suchomski Technical University ofGdGllsk, Department of Automatic Control (W.E. T.l.), Narutowicza 11/ 12, P.G.Box 612, 80-952 Gdansk, Poland; e-mail kova@pg. gda . pl Abstract: The problem of discrete-time generalised predictive control of plants described by discrete-time polynomial models, which can have either minimal or non- minimal characteristics, is deliberated. Design specifications for robust GPC control are presented and a stable two-degree-of-freedom formulation of the GPC control strategy is proposed in which nominal stability, nominal performance and robust stability properties are obtained by properly choosing the control and observation horizons and the observer polynomial. Copyright © 19981FAC Keywords: system design, polynomials, predictive control, adaptive and robust control. l. INTRODUCTION The Generalised Predictive Control approach of Clarke et aJ. (1987) has attracted a considerable attention in the control literature. In that methodology the controlled plant is described by the following discrete-time model of the CARIMA type (1) where {u(t)} and {y(t)} are the input and output signals, {v(t)} is a zero-mean white-noise, q -I is the backward shift operator, and 6. = 1- q -I. The polynomials A(q-I), B(q-I) and C(q-I) are of degree N A ' NB and N c N A + I, respectively. In the above model an incremental-control channel and a disturbance channel can be distinguished (2) where A(q-I) = M(q-I). Let nb indicate a pure transportation delay in the control channel, and let nB = nb + I . It is also assumed that NB N A + I that confines the dimension of the minimal state space representation of this channel to N A + I . 207 1.1 Basic GPC control/er design Future controls 6.u(t) = [6.u(t)... 6.u(t + Nu-I) r ' where Nu denotes the control horizon, is sought after via minimisation of the quadratic cost function J(6.u(t)) = N2 Nu = +i) -8y(t +i)f +A.L 6.u(t +i _1)2, (3) ;=1 where, for i = I, ... , N 2 , e(t + i) = e(t + ilt) = lie(t) is a sequence scaled by the control error e(t) = wet) - yet) (within Nu a constant set point w(t +i) = wet) is assumed), the 'i 's are coefficients of the step response of anticipation filter (AF), and 8y(t + i) = y(t + i) - y(t) denotes a trajectory of the predicted incremental plant output, while y(t +i) stands for the minimum-variance i-step ahead predictor of the plant output. For the model (1) the predictor can be represented in the following form .v(t +i) = H,(q - I)6.u(t+i -1)+ y(t+ilt), (4) where, for i=I , ... ,N 2 , H,(q -I) =ho+· ·-+h;_lq-(i-I) , and y(t + il t) denotes the free component that can be obtained by employing the following formula