On the Stabilizability of the Delayed Inverted Pendulum Controlled by Finite Spectrum Assignment in Case of Parameter Uncertainties

An application of the Finite Spectrum Assignment (FSA) control technique is presented for an inverted pendulum with feedback delay. The FSA controller predicts the actual state of the system over the delay period using an internal model of the real system. If the internal model is perfectly accurate then the feedback delay can be compensated. However, slight parameter mismatch of the internal model may result in an unstable control process. In this paper, stabilizability of the inverted pendulum for different system and delay parameter mismatches are analyzed. It is shown that, for the same parameter uncertainties, the FSA controller allows stabilization for significantly larger feedback delays than a conventional delayed proportional-derivative controller does. In the analysis, it is assumed that the controller input is piecewise constant (sampled), this way the destabilizing effect of the difference part of the governing neutral functional differential equation is eliminated. The relation of the FSA controller to the Smith predictor is also described in time domain.