Research On Optimal Design For Multivariable Systems Based On Internal Model Control Theory

The research on advanced process control for multivariable system is on of the hot issues that attract the domestic and foreign scholars, and optiaml design is an important branch of advanced process control. Although a lot of achievements in the development of the optiaml control design for multivariable system have been obtained, the research on optiaml control design for multivariable system is still not perfect. Multivariable processes, especially those with multiple time delays, contain the coupling elements and time delays, which makes the control methods developed for single-input single-output(SISO) processes can not be directly apllied to multivariable processes with multiple time delays. It has significant theory and practical value to develop analytical control design method for multivariable system with multiple time delays based on optimal control theory, which not only can provide excellent closed-loop performances but also can be conveniently applied in practice.Based on frequency-domain multivariable control techonology, this dissertation studied the analytical control design problem for multivariable processes using multivariable control theory and optimal control theory. By analyzing the inverse or the Moore-Penrose Pseudo-inverse of the given multivariable process, the given multivariable process was factorized into an all-pass function and a minimum phase(MP) portion analytically. Subsequently, based on the analytical factorization, several advance analytical control design methods are developed through rigorous theoretical derivation. The proposed methods have three primary merits. Firstly, the design procedure is simple, no weighting functions need to be chosen. Secondly, the designed controller can optimize the defined performance index, and given in an analytical form. It can be used in practice easily. Thirdly, the performance and robustness of the closed-loop system can be quantatitively tuned by adjusting the parameters in the designed controller. This is very useful in practice engineering.The main contributions can be concluded as follows:1) For the non-identical singular multivariable square process, a new analytical extended inner-outer factorization alogithm based on the expansion of the inverse of the multivariable system is developed. Using the zeros and zero directions of the square multivariable sytem, the structure expansion of the inverse of the square multivariable system is derived. Based on the structure expansion of the inverse of the square multivariable system, the inner of the square multivariable system is obtained in an analytical form. Finnaly, the outer of the square multivariable system is derived. The proposed extended inner-outer factorization algorithm is an exact solution without numerical error. And the proposed extended inner-outer factorization can be applied to the controller design for both stable and unstable multivariable systems.2) For stable square multivariable processes, a new analytical optimal input load disturbance rejection control method is proposed. Based on the analytical extended inner-outer factorization algorithm mentioned above, the given stable square multivariable process is factorized into an all-pass function and a stable MP portion firstly. Consequently, all of the controllers that can stabilize the stable square multivariable process and have a zero steady-state error for a step input are parameterized. Finally, the detailed analytical design formula of the optimal input load disturbance rejection controller is derived from the point of view of optimizing the system performance index. The proposed design method can optimize the performance index from the input load disturbance to the system output.3) For the ill-conditioned distillation plant with gain and time delay uncertainties given by the 1991 Confernce of Decision and Control(CDC91), a two-degree-of-freedom(TDOF) controller is designed for the given ill-conditioned process based on the H2 decoupling control method. Firstly, the unity feedback controller was designed by the H2 decoupling control method. The designed controller can make the closed-loop system be decoupled and the performance and rpbustness of the closed-loop system can be tuned easily by adjust the parameters in the designed controller. Then, the designed closed-loop system was regarded as a new plant, and a TDOF control scheme based on the obtained closed-loop system is proposed. For one thing, the proposed TDOF control design method is suitable for CDC91 benchmark problem. All the design specifications are satisfied by the designed two controllers. For another, the orders of the designed two controllers are 2 and 1 in element respectively, which are much lower than the previously developed methods. Therefore, the proposed method can reduce the complexity of the controller dramatically.4) The autopilot of a high-angle-of-attack missile is designed using the H2 optimal decoupling control method proposed by our group. Fisrt of all, the aerodynamic model of the high-angle-of-attack missile is linearized according to linearization method under small perturbation and the transfer function model of the high-angle-of-attack missile is derived subsequently. Then, the H2 optimal decoupling method is applied to design the autopilot of the high-angle-of-attack missile based on the derived transfer function of the high-angle-of-attack missile. The developed autopilot design method for high-angle-of-attack missile using H2 optimal decoupling control can make the closed-loop system be decoupled. Moreover, the response of the designed closed-loop system is fast and the deisgned controller has good robustness. Therefore, the proposed method can solve the problems of high-angle-of-attcak missile well, such as serious couplings and model uncertainties. The developed method provides an effective and simple approach for the autopilot design of high-angle-of-attack missile.5) A new H2 optimal analytical control method based on the internal model control(IMC) for non-square multivariable systems is developed. Firstly, the pole of the Moore-Penrose Pseudo-inverse of non-square multivariable palnts is analyzed based on basic results of the polynomial theory and the Binet-Cauchy theorem. The necessary and sufficient condition to judge whether the Moore-Penrose Pseudo-inverse of a non-square multivariable palnt is stable is given. Then, the definition of the minimum phase(MP) non-square system is redefined and the given non-suqare multivariable plant is factorized as the product of an all-pass function and a MP part of the non-square plant. Finally, the detailed analytical design formula of the controller is derived systematically from the point of view of optimizing the system performance. The design procedure of the proposed method is simple and the designed controller is given in analytical form. The designed controller can not only quantitatively tune the performance of the closed-loop system, but also conveniently adjust the robustness of the the closed-loop system.