Semi-symbolic operational computation for robust control system design

Semi-symbolic simulation is becoming popular for inclusion of parameter uncertainties in the system design analysis. For robust control system design optimization, computational methods enabling fast semi-symbolic simulations are necessary. We propose an operational computation method based on orthogonal signals that is faster than step integration methods and allows the direct evaluation of system robustness to parameter variations. In order to improve the simulation performance during design optimization, we derive a novel operational method to compute the multiplication of signal expansions. Thus, common nonlinear cost functions can be directly computed, using only signal coefficients. The evaluation of signals during the optimization is avoided by this method, which is a significant advantage compared to other known approaches for dynamic system simulation. We validate the capability of our design methodology for the improvement of system performance and robustness by optimizing a DC motor control. The obtained results show that affine arithmetic computations are well suited for robust control system design optimization in the time domain.