Robust Inverse Control of a Class of Nonlinear Systems
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This thesis considers the output tracking problem for a class of nonlinear and non input affine systems characterized by a static, state and input dependent nonlinear map and a general smooth nonlinear system. It is shown that this system class – which is called Extended Hammerstein Systems for obvious reasons - is a sensible choice as it captures the essential characteristics of many real systems and well approximates many others.
The problem of output tracking is solved in two steps. First, three inversion techniques, namely the cancellation of the internal dynamics, the stable inversion approach and output tracking of exogenous signals, are adapted to the tracking problem assuming an exact knowledge of the model. Each of these techniques requires an inversion of a mostly imprecise known static nonlinear map so that the nonlinear static map cannot be fully compensated. The resulting compensation error is treated as an input disturbance for the following second step of the problem solution.
In this second step a state feedback compensator for robustification of the feedforward control law in case of input disturbances is introduced. To solve this feedback compensation problem a sufficient condition is given. If this condition is satisfied the feedback compensation problem can be solved by a simple extension of a stabilizing controller, which may be designed as an optimal or a robust controller and it is further possible to compute the guaranteed robustness bound a priori.
The main theoretical results are confirmed by practical experiments on an engine test bench control.