Design And Applications Of Quasi-linear Systems Based On Fully Actuated System Approaches

The fully actuated system approaches is a new approach proposed in recent years for the control system design problem.Many fully actuated systems exist in nature,and currently available control methods may destroy the full-actuation of the system.The full-actuation eliminates all dynamic characteristics of the open-loop system(whether linear or nonlinear)and subsequently allows the desired linear constant closed-loop system to be built.The fully actuated system approaches takes advantage of this property to greatly simplify the difficulty of control system design,and this approaches has received a lot of attention from scholars at home and abroad.Quasi-linear systems are widely used in practical engineering applications,and they are a special class of nonlinear systems that have a linear form but retain nonlinear characteristics,which are a bridge for extending the study of linear systems to nonlinear systems and have certain research value.Therefore it is necessary to use this approach to study quasi-linear systems.In this paper,the controller design problems of quasi-linear systems,quasi-linear time-delay systems,and cascade quasi-linear systems are investigated respectively based on the fully actuated system approaches.In the framework of the fully actuated system model,the form of the control law is proposed using the full-actuation,and the parametric form of the control law is finally obtained by establishing the Sylvester matrix equation and solving it.This paper mainly includes the following aspects of research:(1)For the controller design problem of quasi-linear systems,a controller with a parametric form is proposed based on the fully actuated system approaches.First,a class of affine nonlinear systems is written in the form of quasi-linear systems.Based on the rank condition,the quasilinear system is quasi-similarly transformed to obtain the controllable standard type of the system,and the fully actuated system model is obtained by the transformation.Secondly,the form of the control law can be given directly under the fully actuated system approaches to obtain a linear constant closed-loop system with the desired eigenstructure.Further,the parametric form of the control law is obtained by establishing a class of generalized Sylvester matrix equations and solving them.Finally,the effectiveness of the proposed method is verified by the simulation results of a numerical example.(2)For the design of controllers for high-order quasi-linear systems with time-varying time delay,a controller with a parametric form is proposed based on the fully actuated systems approaches,taking into account the effects of the time delay link.First,a class of higher-order quasi-linear time delay systems is introduced,where the effects of the time delay link can be eliminated due to the presence of the full-actuation,and the form of the control law is given to obtain a linear constant closed-loop system with the desired eigenstructure.Secondly,the Sylvester matrix equation is developed and solved to obtain the parametric form of the controller,and the performance of the system is further optimized due to the presence of free parameters.Finally,the feasibility of the proposed method is illustrated by the simulation results of the numerical algorithm.(3)A controller with parametric form is proposed based on the fully actuated system approaches for the controller design of a cascade quasi-linear system.First,the subsystems are connected in series to form a new system model.The discriminative condition of controllability is proposed for this cascade system.Secondly,the system is transformed into controllable standard type,and the fully actuated system model is obtained after another transformation.Further,the form of the control law is given using the fully actuated system method.The parameterized form of the controller is obtained by solving a class of Sylvester matrix equations.Using the freedom provided by the free parameters,the appropriate performance index is selected to optimize the performance.Finally,the feasibility of the proposed method is illustrated by the simulation results of the numerical algorithm.(4)For the controller design of the permanent magnet synchronous motor system,a completely parametric form of the controller is proposed based on the fully actuated system approaches,and the practical engineering application background of the fully actuated system approaches is explored.First,a mathematical model of the permanent magnet synchronous motor system is established,and the mathematical model is represented in the form of a quasi-linear system.Subsequently,the fully actuated system model is obtained by transformation,and the design method obtained in the first part is used to derive its control law,and the general parametric form of the controller is obtained based on the solution of the Sylvester equation.Finally,the simulation results verify the effectiveness and feasibility of the method,which has some guiding significance for the application in practical engineering.