Analysis And Design Of Dynamic Matrix Control Algorithms For Time-Varying Delay Systems

In many natural science and social science phenomena, the rate of change of state variables at current time is depended on the state variables information of the past time, this character is called time delay. People noticed the time delay character in biological phenomena early and discovered time delay is widely exist in many engineering systems such as mechanical transmission system, fluid transfer system, metallurgical industry process and networked control system. Furthermore, systems with time delay character are called Time Delay Systems (TDS). Because of system structure, external disturbances and other factors, time delay may appeared as different properties such as time varying, bounded and random, which lead to the research on TDS become even more complicated and difficult. Concurrently, time delay is one of the main elements which deteriorated performance of system and even caused system instable, so delay problem is an ineluctable problem during the process of analysis and design of TDS.Dynamic Matrix Control (DMC) is a typical model predictive control algorithm. Because of simple structure, good performance and flexible application, DMC is widely used in the process control area. DMC adopts multi-step model-based prediction, moving horizon optimization with feedback correction strategy to achieve optimal control. DMC estimates a set of future control sequences at one time, then DMC algorithm is applied during the TDS analysis and design process, the control input at current time is expressed by the last time control input which included the time delay information through the form of functions, and it provides a possible implementation for time delay problem.In recent years, research on time-varying delay systems based on model predictive control method is becoming a hot research topic in control area and obtained substantial achievements. This thesis is concerned with analysis and design of time varying systems, which based on DMC algorithm and Linear Matrix Inequality (LMI) method. The main achievements of the thesis are summarized as follows:Firstly, a class of multi-input and multi-output (MIMO) system with time-varying delay is designed and analyzed based on DMC algorithm. The time-varying delay is converted to the fixed bound by the appropriate data buffer. To take one step ahead, the system is designed based on DMC algorithm. By optimizing the performance index function, the optimal control law of DMC algorithm is derived and broadened to a form of state-space model structure. On basis of the model structure, the sufficient condition for asymptotic stability of DMC algorithm with delay is given based on Lyapunov stability theory and LMI method.Secondly, the problem of robust stability for a class of multiple variables system DMC algorithm with time-varying delay is analyzed. The model mismatch between the prediction model and system model is indicated by norm squared of impulse response coefficients error matrix. On basis of the Lyapunov stability theory, the sufficient condition for robust stability of DMC algorithm with delay is gained under LMI method and the robust stability condition is determined whether a set of LMIs have feasible solutions. The simulation based on improved distillation column illustrated the proposed method is effective.Finally, design and analysis of time delay controller of grade transition in polypropylene continuous production process is studied based on DMC algorithm. To solve the optimal control problem in grade transition process, Hammerstein model description with the time-delay information for the Melt Index (MI) of grade transition process is obtained. Based on the Hammerstein model, the corresponding input-output model is gotten and the grade transition controller is derived on the basis of DMC algorithm, which aimed to accomplish the optimal control during the transition process. The sufficient condition which ensured asymptotic stability of grade transition controller is derived under LMI method. The simulation of large scale double-loop tube polypropylene grade transition process in industry demonstrated the proposed controller design is effectiveness and practicability.