Offset Free Stabilization Of Switched Systems Under Model-plant Mismatch

As the 14 th Five-Year Plan proposes to promote the transformation of industry to a high-end industrial structure,low-carbon energy consumption and recycling of resources,the complexity of industrial process is increasing.The model with single characteristics can not describe the industrial processes with high complexity and high precision accurately.Therefore,switched systems have attracted extensive attention from scholars at home and abroad because they can describe complex systems with switching characteristics well.The switched system is composed of a limited number of subsystems and switching rules between subsystems.Both of them are integral parts of the switched systems.However,in the modeling process,affected by unknown disturbances or unmodeled dynamics,an accurate model of the real plant is difficult to obtain,which is the so-called model plant mismatch(MPM).The tracking problem,offset free control,optimal control,and other problems of the systems with MPM have become research hotspots.For switched systems,the MPM may exist in the subsystems or in the switching rules.When the subsystems of the switched system are mismatched,the control performance of the system will be deteriorated,the system output can not reach the expected value,and static error will occur.When the switching rules of the switched system are mismatched,the controller and the real plant may operate asynchronously.The asynchronous operation may lead to the system instability,even safety accidents may occur in some severe cases.On this basis,the stabilization problems of switched systems with MPM in subsystems and/or in switching rules are studied in this thesis,and the following new methods and ideas are proposed.(1)For the piecewise affine(PWA)systems with MPM in the subsystems,an event-triggered model predictive controller is proposed,which can render the system achieve exponentially stable and offset free control.Firstly,the MPM is introduced to the nominal model to obtain the augmented model of the switched system.Since the state variables and MPM are unmeasurable,an observer is designed to estimate them.By introducing state error and estimate error,an equivalent augmented model of the PWA system is constructed.By defining events,an event-triggered model predictive controller is designed.Then,using the mode dependent average dwell time(MDADT)method and Lyapunov stability theory,the stability conditions of the closed-loop system based on the linear matrix inequality(LMI)form can be obtained.The controller gain can be solved simultaneously.Based on some mild assumptions,the offset free control of the system can also be guaranteed.Finally,simulations have been taken to verify the proposed method can render the PWA system with MPM achieve exponential stability and offset free control.(2)A new adaptive factor-based output compensation strategy for mixed logic dynamic model-based model predictive control(MLD-MPC)with MPM in the subsystems is proposed to eliminate the static error and ensure the control performance of the system.By using the Lyapunov stability theory and the dynamic characteristics of MLD-MPC,the adaptive factor that satisfying the stability conditions can be solved by the LMI method.In addition,the output compensation strategy proposed in this thesis considered the influence of subsystem switching and is easy to carry out online.Finally,simulations have demonstrated that the proposed strategy can make the MLD-MPC with MPM realize stable and offset free control,and the control performance can be guaranteed as well.(3)For state dependent switched systems with MPM in the switching rules(switching boundaries),a control strategy based on an observation algorithm is designed to ensure the robust exponential stability of the switched system.Firstly,a switching boundary mismatch compensation term is introduced to the nominal model,and an iterative learning control law is designed based on feedback control.By constructing the state increment and error increment,the equivalent augmented model can be obtained.An observation algorithm is designed to estimate the unmeasurable switching boundary mismatch.Combining the designed observation algorithm with the iterative learning control law,the control strategy based on the observation algorithm can be derived.By using the MDADT method and Lyapunov stability theory,the robust exponential stability condition of the closed-loop system based on the LMI form can be obtained.The controller gain can be solved simultaneously.Finally,simulations have been taken to verify that the proposed strategy can ensure the robust exponential stability of the state dependent switched system with switching boundary mismatch and guarantee a better control performance.(4)For state dependent switched systems,since the state variables are unmeasurable,the switching rules may be mismatched.When the subsystems are affected by random disturbances,a controller is designed to ensure the exponential mean square stability of the switched systems and maintain better control performance.Firstly,a state observer is designed to estimate the state of the system.The estimate error is introduced as well.By augmenting the state,state estimation and the estimate error,an equivalent model can be obtained.By using the MDADT method and the Lyapunov stability theory,the exponential mean square stability condition of the equivalent model based on the LMI form can be derived.The controller gain can be solved simultaneously.Finally,simulations have been taken to verify that the method proposed in this thesis can ensure the exponential mean square stability of the state dependent switched systems with random disturbances and unmeasurable state variables.At the same time,the satisfying control performance of the switched system can be guaranteed.