Trajectory Planning And Optimal Control Of Coupled Water Tank System Based On Differential Flatness

The process control technology of multi tank liquid level system is widely used in chemical production,petroleum,beverage processing and other fields.In this paper,the experimental device of double tank produced by Quanser company of Canada is taken as the research object,based on the theory of differential flattening,the liquid level control of double tank system is studied by using state feedback control method.The main work of this paper is as follows:(1)A constrained robust H_? control method for dual tank is studied.Firstly,the equivalent linear system is obtained by linearizing the nonlinear system model of the water tank at the working point.The nonlinear characteristics of the fluctuation at the working point can be regarded as the uncertainty of the linear system.Then the physical constraints in the system,such as the upper limit of pump supply flow and the size limit of water tank,are described as control quantity constraints and state constraints.Finally,considering the possibility of liquid leakage,the level control problem of double tank can be described as an interference suppression problem of uncertain linear system with actuator saturation constraints and state constraints.In this paper,the constrained robust H_? state feedback control scheme is studied,the corresponding LMI conditions are derived,and the LMI optimization problem is solved.The experimental results show that the constraint robust H_? state feedback controller has good disturbance rejection ability.(2)In order to solve the overshoot caused by the sudden change of the reference signal in the system,the differential flattening method is used to study the liquid level trajectory planning method of the double tank by arranging the reasonable transition process.Firstly,the differential flatness of the dual tank is verified.Then,within the feasible range of the actuator,the control law to achieve the desired"s"type trajectory is derived and used as the feedforward control law of the closed-loop system.Finally,the particle swarm optimization algorithm is given to optimize the relevant parameters in the desired trajectory.The experimental results show that this method can solve the contradiction between overshoot and rapidity.(3)Aiming at the problem that the designed fixed controller may be conservative to the system and can not solve the contradiction between the performance index and the state constraint in real time,the rolling optimization control strategy in predictive control is introduced to linearize the dual tank system in real time on the planned trajectory at each sampling time.Then,considering the system constraints,the linearized system is used to solve the state feedback control law at the current time,which is applied to the controlled system and kept until the next time.Finally,the rolling optimization control strategy is realized.The simulation results show that the proposed control strategy is better than the offline optimization strategy.