Study On Generalized Predictive Control For Non-single-rate Sampled-data Systems

Non-single-rate sampled-data systems, namely non-single-rate systems, arise sometimes in wide applications. Studying non-single-rate systems and control approaches for them is required in engineering and theory. In this thesis, we study lifting modeling and generalized predictive control (GPC) algorithm for non-single-rate systems. Some innovative fruits are mainly received as follows:First, it is demonstrated that lifting technical is a map transform; it is shown that a shift-invariant operator exists for a shift-varying operator via lifting technical; and a history, current features of GPC are summarized.Second, we derive and prove lifted models in the state-space domain for single-input, single-output non-uniformly sampled systems. A sufficient condition to preserve controllability and observability of original continuous-time model is given for the lifted model. Based on the lifted model, an absolute GPC algorithm is proposed.Third, we derive iteratively predictive expression for output directly from the lifted input-output model for SISO non-uniformly sampled system and then propose a novel GPC algorithm. In the novel algorithm, not only causality constraint on the lifted controllers is explicitly dealt with, but also the computational overhead is reduced because of solving free Diophantine equations. In addition, the form of the novel algorithm, which is similar with that of PID controller, is simple.Forth, we define the sampling and updating scheme for MIMO multi-rate system in detail, and then give a lifted model for the system and derive a causal GPC algorithm via constructing a chain of new lifted output signals and new models and applying conventional GPC design approach for each new model.The proofs and simulation show that the approaches proposed in this thesis are effective.