Abstracts Computer Science

Managing uncertainty in robust controller implementation

by Vahid Raissi Dehkordi

For a linear time-invariant (LTI) plant, a robust controller is often designed in order to maintain robust stability and performance of the system. In robust controller implementation, two problems might arise. First, it is interesting to know whether it is possible to simplify the controller and to what degree before its implementation while still maintaining system robust performance. The second concern arises in real-time applications where the controller may have to be retuned or redesigned several times after the initial implementation stage. In both problems, it is important to know how much a modified controller can deviate from the originally designed one in the frequency domain. The robust controller deviation is modeled as the controller uncertainty just like any other uncertainty with its own unique weighting function. A necessary and sufficient condition for robust performance as well as a sufficient condition is derived in the form of bounds on the magnitude of maximum deviation of the robust controller over a grid of frequency samples for a single-input single-output (SISO) structure. The multi-input multi-output (MIMO) case is also addressed by providing an upper bound on the maximum singular value of the system's frequency response derived at individual frequency samples, leading to a sufficient condition for robust performance. The above bounds are used in conjunction with the balanced truncation technique in order to determine how much the order of a robust controller can be reduced without losing robust performance. The order reduction limit is expressed as the maximum number of states that can be removed in a state-space realization of the robust controller for both SISO and MIMO system structures, without actually having to reduce the order. Finally, a practical approach is proposed in order to derive a robust internal model (IMC) controller for an SISO system structure. The ideal robust IMC controller is already provided as a function of the frequency response of all system components at every frequency sample. It is then approximated with a stable and preferably low order system while maintaining robust performance in three steps - the inverse fast Fourier transform (IFFT), the finite impulse response (FIR) approximation, and the FIR-to-IIR (infinite impulse response) conversion. Un contrôleur robuste est souvent conçu afin de maintenir la stabilité et la performance robuste d'un système linéaire invariant dans le temps. Durant l'implantation d'un tel contrôleur, deux problèmes se présentent. Premièrement, il est intéressant de savoir s'il est possible de simplifier le contrôleur robuste et si oui, jusqu'à quel point avant de l'implanter, tout en garantissant la performance robuste. Le deuxième problème se pose dans les applications à temps réel où le contrôleur devrait être refait ou ajusté plusieurs fois après la mise en service initiale. Il est important de savoir, concernant les deux problèmes ci-dessus, jusqu'à quel point le contrôleur modifié peut s'éloigner de l'original dans le…