Multirate predictive control and performance assessment

The objectives of this thesis are to develop data-driven approaches for control performance assessment and predictive control design for multirate systems. Some related outstanding problems for univariate systems are also addressed. The benchmark is chosen as minimum variance control (MVC) to assess multirate control loop performance because MVC provides us a theoretical lower bound of the output variance under linear feedback control, and it provides useful information such as how well the current controller is performing and how much "potential" there is to improve the control performance.; Generally speaking, a multirate controller performs better than a slow-single rate (SSR) controller but worse than a fast single-rate (FSR) controller in the sense of minimum variance control. This conjecture is theoretically proved in Chapter 2 for a continuous linear time-invariant (LTI) single-input and single-output (SISO) system. The optimal FSR multirate and SSR controllers are designed under the same performance criterion: variance of the fast sampled output. Basic statistical properties of the discretization of continuous stochastic disturbance models are investigated. A linear matrix inequality (LMI) approach is developed to derive the optimal controllers for dual-rate (DR) and SSR loops.; Chapter 3 discusses data-driven MVC design and control performance assessment based on the MVC-benchmark for multirate systems. A lifted model is used to analyze the multirate system in a state-space framework and the lifting technique is applied to derive a subspace equation for multirate systems. From the subspace equation the multirate MVC law and the algorithm to estimate the multirate MVC-benchmark variance or performance index are developed. The multirate optimal controller is derived from a set of input-output open-loop experimental data and thus this approach is data-driven since it does not involve an explicit model. The presented MVC-benchmark algorithm requires a set of open-loop experimental data and closed-loop routine operating data. In contrast to traditional control performance assessment algorithms, no explicit models or model parameters, namely, transfer function matrices, Markov parameters or interactor matrices, are needed in the data driven approach.; Besides the data-driven MVC control, predictive control laws are also designed in Chapter 3 and 4 for both single-rate and multirate systems via system open-loop input-output data. Comparing with the previous data-driven predictive control approach, the developed predictive controllers can handle systems where only partial on-line outputs measurements are available and multirate systems. This is to circumvent the problems that in reality, some outputs may not be measured in real-time, or are too costly to measure at fast sampling rate.