Tube-Based Internal Model Control of Differentially Flat Input-Affine SISO Systems under Input Constraints

In this paper an optimal control approach based on a combination of the flatness theory and the internal model control (IMC) concept is designed to keep the controlled state within a predefined tube while respecting input constraints. This contribution uses ideas developed in the design of flatness-based feedforward IMC controllers for setpoint tracking and extends them to ‘tube tracking’. It shows the interesting result that for flat input-affine systems the control task of remaining within a tube while minimizing energy consumption and respecting input constraints can be expressed by a convex quadratic optimization problem. The computational feasibility of the developed control strategy is ensured by a purely analytical solution for the quadratic optimization problem derived based on the Karush-Kuhn-Tucker (KKT) optimality conditions. The control approach is illustrated by a simulation example.