Sensitivity-Based Approaches for an Efficient Design of Feedforward Controllers and Parameter Estimators for a Distributed Heating System

A combination of feedforward and feedback control is typically employed to guarantee accurate tracking of desired trajectories. These two degrees of freedom are usually exploited in such a way that the feedback control part guarantees asymptotic stability of the closed-loop system dynamics. The feedforward control part depends on the desired reference trajectory and guarantees, in the ideal case, perfect tracking properties. For that purpose, feedforward control signals are computed in many cases by means of an analytic inversion of the system dynamics. This is, however, only possible in symbolic form if a relation between the flat outputs of a dynamic system and the desired outputs can be established. Note that in many practical scenarios either the considered system is not differentially flat or the system inversion becomes prohibitively complex in symbolic form. If the latter case is true, still numerical solvers for differential-algebraic systems can be employed. However, in the first case - if a system inversion is not exactly possible - numerical approaches can be used to solve the task approximately. In this paper, sensitivity-based approaches are presented for such kinds of scenarios. The focus is on a numerically efficient implementation for the feedforward control design of high-dimensional system models, and (after slight modifications) for a learning-type control as well as for the estimation of parameters. Besides piecewise constant control inputs, also piecewise smooth input representations are considered for the control of multi-input multi-output systems.