Research On Non-Minimum Phase System Tracking Control Based On Stable Inversion

The trajectory tracking control theory has been quite mature,but the trajectory tracking control for non-minimum phase system is still a difficult problem in the control theory.The problem of trajectory tracking control for non-minimum phase systems is widespread in practical industrial applications.Especially,as the requirement of trajectory tracking control accuracy becomes more and more strict,the research of accurate tracking control for the system is becoming more and more valuable in engineering application.The inversion technique is a kind of accurate tracking control algorithm with application value.However,the classical inversion technique algorithm can only achieve the accurate tracking control of the minimum phase system.The stable inversion algorithm can achieve the accurate tracking control of the non-minimum phase system.However,it also has other limitations,such as relying on the high precision model and requiring complex calculations.It is very difficult to describe the dynamic characteristics of process objects and establish accurate models because of the inherent complexity and disturbance in modern industrial process systems.Therefore,in the practical application of industrial processes,the stable inversion algorithm may face the challenges of model error and disturbance,as well as the computational complexity caused by strong nonlinearity.To overcome these challenges,the algorithm needs to be improved and optimized.This paper aims to further study and expand related theories based on traditional stable inversion theory.This includes overcoming model errors and disturbance,as well as optimizing algorithm calculation.The specific contents include:(1)Aiming at the accurate tracking control problem of non-minimum phase system with model error or output disturbance,an iterative learning control algorithm based on stable inversion is proposed.The principle of stable inversion algorithm is to obtain the corresponding model input trajectory according to the output trajectory of the dynamic model.However,this algorithm is only applicable to control systems with accurate model.For the control system with repeated operation,the idea of iterative learning can be introduced,and the compensation control quantity of iterative error can be calculated by the stable inversion algorithm and superimposed on the original control action.This can not only improve the robustness of the algorithm to the model mismatch,but also overcome the output disturbance in the iterative process,so as to achieve accurate tracking control of the controlled object.Finally,a chemical batch process simulation example is used to verify the effectiveness of the proposed algorithm.(2)Aiming at the tracking control problem of nonlinear non-minimum phase system in industrial processes,a stable inversion feedforward and feedback compound control based on T-S fuzzy model is proposed.By introducing the concept of T-S fuzzy model,the nonlinear object can be transformed into a fuzzy system,which is modeled by the weighted combination of several locally linearized models.Based on this,the new stable inversion output is the weighted sum of the stable inversion output of each locally linearized model,which not only improves the accuracy of the linear stable inversion algorithm,but also expands the application range of the linear stable inversion algorithm.In practice,it is necessary to realize the accurate tracking control of non-minimum phase system by stable inversion feedforward and feedback compound control strategy.Finally,a simulation example of chemical reaction process is used to verify the effectiveness of the proposed algorithm.(3)Aiming at the tracking control problem of non-minimum phase chemical reactor,a nonlinear stable inversion approximate solution algorithm is proposed.By discretizing the internal dynamics in the principle of stable inversion,the original problem of solving the internal dynamic analytical solution using nonlinear internal dynamic equations is transformed into a problem of solving the internal dynamic discrete numerical solution using recursive formula.This transformation can solve the problem of excessive computation when Picard iteration method is used to solve internal dynamics.In addition,for complex tracking trajectories and tracking objects,the proposed algorithm is more robust than the analytical solution method.Finally,simulation is used to verify the effectiveness of the proposed algorithm.