A delta operator approach to discrete-time H ∞ control
1999; Taylor & Francis; Volume: 72; Issue: 4 Linguagem: Inglês
10.1080/002071799221127
ISSN1366-5820
Autores Tópico(s)Real-time simulation and control systems
ResumoTo increase the performance of digitally implemented control laws, it is desirable to directly synthesize the digital control law. Hence, this paper considers the direct synthesis of discrete-time, H ∞ control laws. Previously, two approaches have been proposed to this problem. The most common method uses the bilinear transformation to convert the discrete-time problem into an equivalent continuous-time problem, allowing the controller to be synthesized with software developed for continuous-time systems. This method is often effective but requires unnecessary steps and is not applicable in all circumstances. The second approach is to synthesize the discrete-time, H ∞ control law by solving discrete-time, H ∞ Riccati equations. Due to numerical ill-conditioning, this approach can fail at sufficiently high sample rates. This numerical ill-conditioning can be eliminated by representing the discrete-time system and H ∞ controller using the delta operator. Hence, the H ∞ design equations for direct synthesis using the delta operator are developed. These equations reduce to standard continuous-time H ∞ design equations when the sample period is set to zero. The results are illustrated with a numerical example which also shows that the central continuous-time H ∞ controller of the continuous-time system obtained by a bilinear transformation of the original discrete-time system does not necessarily correspond to the central discrete-time controller.
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