Feedback error learning (FEL) control is a kind of adaptive control. Different from some conventional adaptive control schemes, FEL adjusts the feedforward block instead of the feedback. FEL includes two blocks, the feedback stabilizes the closed-loop system and the feedforward achieves a tracking performance. Characteristics of FEL control mainly depend on the adjustment method (tuning laws) of the feedforward. In this research we concentrate on FEL control under a strictly positive real (SPR) condition. For simplicity, we call this scheme the SPR method.
In this thesis, we first make a brief introduction about FEL control and the SPR method. After that we show some simulations. For comparison we also conduct simulations on a conventional FEL control using recursive least squares. By these simulations we reveal advantages of the SPR method. On the other hand, there exist some tough examples for the SPR method. We show one of the tough examples and provide some measures for it.
Then we discuss problems and restrictions of the SPR method. This is because the SPR condition is fairly strict. Many practical control objectives do not meet the condition. We focus on two kinds of non-SPR problems, one is caused by a design parameter in the feedforward, which is called the filter problem; the other one is caused by relative degree, which is called the relative degree problem. To extend the practical application, we give solutions for these two kinds of problems, to make it easier to establish the SPR condition.
With respect to the filter problem, we analyze the control objective with state space model. And we propose a method using Kalman-Yakubovich-Popov lemma, to construct a mathematic relationship between the SPR condition and the design parameter. This method is systematic and reliable, its effectiveness is demonstrated by numerical simulation.
As for the relative degree problem, inspired by the backstepping method we introduce a virtual plant. The virtual plant meets an SPR condition so we can apply the SPR method. Then we modify the current tuning law, in order to control the true plant indirectly. This method is also verified by numerical simulation.