Modeling And Controller Design Of Multivariable Process With Multiple Time Delays

With the introduction of various kinds of complicated techniques, more and moreindustry process systems are built as multivariable process systems with multiple time delays.These processes are often formulated in continuous-time settings and can be represented bycontinuous-time transfer function matrix plus various time delays. The existence of thesemultiple time delays in control systems is frequently a source of instability and poorperformance. For the transfer function matrix models with multiple time delays in inputs,outputs and states in the frequency domain, few control strategies, except some specialsystems, have been developed due to the difficulty in dealing with the state delay terms in thetransfer function models. Hence, the approximated modeling of this multivariable processwith multiple time delays is of great meaning both in practice and theory.In the thesis, a research of an approximated modeling method for multivariable processwith multiple time delays represented by transfer function matrix with multiple time delays ininput, output and states is conducted based upon Observer/Kalman Filter Identification(OKID) algorithm. The method utilizes white noise as input data of the sampled-system ofmultivariable process with multiple time delays. When the output data of the sampled-systemis acquired, the simplified state-space model, as well as the corresponding pulse transferfunction matrix, of multivariable process with multiple time delays is constructed byprocessing the input and output data sets. The simplified model eliminates the states delays inthe transfer function matrix, and only contains input and output delays. This simplified modelis utilized for discrete-time PID controllers design, modified internal model controller (MIMC)design as well as linear quadratic regulator (LQR) optimal controller design.The main work of this thesis is described as follows:(1) Regarding a kind of transfer function with input, output and states delays, it isdifficult to design close-loop controller due to the existence of the states delays. To tackle theproblem, an approximated modeling method is designed for the above transfer function. Theproposed method extends the afore-mentioned OKID algorithm to transfer function withtime-delays. And this approximated modeling method is further implemented on the transferfunction matrix by a steady value scalar factor.(2) Regarding a kind of transfer function matrix with multiple time delays, acontinuous-time decouple controller is used to achieve the decomposition of input, outputcoupling. However, the decoupled subsystem contains combination of different time delays,which is hard for controller design. After that the afore-mentioned approximated method isused to construct models for the decoupled subsystems. With the approximated model, adiscrete-time PID controller as well as a modified inner model controller is designed toformulate the close-loop control.(3) Considering a general transfer function matrix with time delays in inputs, outputs andstates, the above-mentioned model approximation method is used to construct a discrete-timestate-space model to eliminate the states time delay and make the system as an output time-delay model. Then a LQR optimal controller is designed according the simplified modelto achieve optimal control of the original multivariable process with multiple time delays.