Predictive Control of Nonlinear Nonminimum-Phase Systems

Srinivasan B., P. Huguenin, K. Guemghar and D. Bonvin. A Global Stabilization Strategy for an Inverted Pendulum. IFAC World Congress 2002, Barcelona, Spain (July 2002), 1224

Guemghar K., B. Srinivasan , Ph. Mullhaupt and D. Bonvin. Predictive Control of Fast Unstable and Nonminimum-phase Nonlinear Systems. American Control Conference, Anchorage, Alaska (May 2002), 4764-4769 GUEMGHAR Kahina, BONVIN Dominique, MUELLHAUPT Philippe, SRINIVASAN Bala

Recently, a strong research effort has been done for the analysis and control of nonlinear systems. With the use of differential geometry tools, a class of nonlinear systems can be ransformed into a linear subsystem and internal dynamics. When the system is minimum phase, the internal dynamics are stable which considerably simplifies the control design. However, this is not the case for nonlinear nonminimum-phase systems, because the internal dynamics are unstable.

An alternative for controlling nonlinear systems is the use of a predictive control scheme. Nevertheless, fast unstable nonminimum phase systems are difficult to control using such a strategy. There exists indeed a conflict between the need to have a sufficiently large optimizing horizon (so as to handle the nonminimum phase effect properly) and the need to ensure a high bandwidth by repeating the optimizing phases frequently (so as to stabilize the system). The limited computing power may therefore prevent a direct application of standard predictive control schemes.

As a result, a systematic approach for state space stabilisation of nonlinear nonminimum phase systems does not exist.

In this project, a new strategy for the control of nonlinear nonminimum-phase systems is pursued. A cascade scheme that uses both differential geometry tools and predictive control is proposed. The idea is to separate the system into two parts by using differential geometry tools:

– A fast part consisting of both the output dynamics and the fast internal dynamics that are approximated by simple integration.

– A slow part consisting of the internal dynamics of the system.

Then, predictive control is applied for stabilizing the slow internal dynamics, and a fast linear controller is applied on the output dynamics.