000028385 001__ 28385 000028385 005__ 20190812204622.0 000028385 02470 $$2ISI$$a000178974700831 000028385 037__ $$aCONF 000028385 245__ $$aPredictive Control of Fast Unstable and Nonminimum-phase Nonlinear Systems 000028385 269__ $$a2002 000028385 260__ $$c2002 000028385 336__ $$aConference Papers 000028385 520__ $$aPredictive Control of Unstable Nonminimum-phase Systems K. Guemghar, B. Srinivasan, Ph. Mullhaupt, D. Bonvin ´ Institut d’Automatique, Ecole Polytechnique F´d´rale de Lausanne, ee CH-1015 Lausanne, Switzerland. Predictive control is a very eﬀective approach for tackling problems with constraints and nonlinear dynamics, especially when the analytical computation of the control law is diﬃcult. Standard predictive control involves predicting the system behavior over a prediction horizon and calculating the input that minimizes a criterion expressing the system behavior in the future. Only the ﬁrst part of the computed input is applied to the system, and this procedure is repeated with the advent of each new measurement. This methodology is widely used in the process industry where system dynamics are sufﬁciently slow to permit its implementation. In contrast, applications of predictive control to fast unstable dynamic systems are rather limited. Apart from computational considerations, a fundamental limitation arises from the accuracy of that prediction, which can be quite poor due to accumulation of numerical errors if the prediction horizon is large. In this paper, an upper bound on the prediction horizon based on the location of the unstable pole(s) of the linearized system will be provided. The problem becomes more acute when nonminimum-phase systems are considered. Nonminimum phase implies that the system starts in a direction opposite to its reference (inverse response). To control such systems, it is reasonable to predict the maneuvers, thus making predictive control a natural strategy. However, a large prediction horizon is required since it is necessary to look beyond the inverse response. In this context, a lower bound on the prediction horizon based on the location of the unstable zero(s) of the linearized system will be provided. The two bounds mentioned above may lead to the situation where there exist no value of the prediction horizon that can stabilize a given unstable nonmiminum-phase system. For such a case, a combination of tools from diﬀerential geometry and predictive control is proposed in this paper. The envisaged procedure has a cascade structure and is outlined below: 1. Using the input-output linearization technique, the nonlinear system is transformed into a linear subsystem and internal dynamics. However, since the original nonlinear system is nonminimum-phase, the internal dynamics are unstable. 2. The linear subsystem is made arbitrarily fast by using a stabilizing high-gain linear feedback (inner-loop). 3. A predictive control scheme is then used to stabilize the slow internal dynamics (outerloop) by manipulating the reference of the inner loop. The stability of the proposed procedure is analyzed using a singular perturbation approach. The results will be illustrated in simulation on a system consisting of an inverted pendulum on a cart. 1 000028385 700__ $$aGuemghar, K. 000028385 700__ $$0240471$$g106464$$aSrinivasan, B. 000028385 700__ $$0241652$$g105941$$aMullhaupt, Ph. 000028385 700__ $$0240449$$g104596$$aBonvin, D. 000028385 773__ $$tAmerican Control Conference$$q4764-4769 000028385 8564_ $$zn/a$$yn/a$$uhttps://infoscience.epfl.ch/record/28385/files/fulltext.pdf$$s145915 000028385 909C0 $$pLA$$0252053 000028385 909CO $$pSTI$$ooai:infoscience.tind.io:28385$$qGLOBAL_SET$$pconf 000028385 917Z8 $$x104596 000028385 937__ $$aLA-CONF-2002-010 000028385 970__ $$a537/LA 000028385 973__ $$rREVIEWED$$sPUBLISHED$$aEPFL 000028385 980__ $$aCONF