PI Control Method Based On Virtua Un-modeled Dynamics Compensation For A Class Of Time-Delay High-Order Linear Systems

In the industrial process control systems, due to the impact of variables measurement, transmission of substance and signals and other factors, the phenomenon of time delay is ubiquitous, which deteriorates system’s control performances, even making it unstable. In the meantime, because process industry’s production technique is complex, so usually the system is high-order, making the low-order PI or PID controller can’t gain satisfactory control results. As a result, for a class of time-delay high-order SISO LTI systems, the issue of low-order PI or PID controller stabilizing and improvement of traditional PI or PID control systems have great research significance in both theory and practical fields.With the support of State Key Laboratory of Synthetical Automation for Process Industries (Northeastern University), aiming at a class of time-delay high-order SISO LTI systems,this paper proposes a PI control method based on compensations of virtual un-modeled dvnamics. The main research work is concluded as following:1. For a class of time-delay high-order SISO LIT systems, the control difficulties are analyzed, and the corresponding control objectives are set. Then, according to Shannon Sampling Theory, we establish the low-order controller design model in discrete domain aiming at continuous high-order time-delay systems, and the rationality of discretization process is validated.2. Combining PI control and data-driven control method, firstly we design the PI controller using pole assignment method, then the virtual un-modeled dynamics are estimated by utilizing system’s previous input and output datas, the corresponding compensator is designed. Based on this, we propose a PI control method based on compensations of virtual un-modeled dynamics, establish the stability and convergence analysis of proposed method, and demonstrate that the proposed virtual un-modeled dynamics compensation method can effectively improve the tracking performance of stable PI control system in stabilizing set theoretically.3. For a class of time-delay high-order linear systems, the stabilizing set of PI controller is calculated according to existing analytical algorighm, then we perform PI control simulations based on compensations of un-modeled dynamics in and out of stabilizing set respectively on MATLAB/Simulink platform, by comparing the simulation results with traditional linear PI control method and 3 representative modified PID control methods, the effectiveness of the proposed control method is validated and the realizability of control objectives is verified.4. Physical experiments of water tank level system are performed on multi-function process control platform, we perform PI control experiments based on compensations of un-modeled dynamics in and out of water tank’s stabilizing set respectively, by comparing the simulation results with tradition linear PI control method, the effectiveness and practical values of the proposed control method is validated.