Stability Analysis And Performance Optimization Of Multi-dimensional Taylor Network Control For Nonlinear Systems

Nonlinear is the most common phenomenon in nature and the engineering that the direct design method of the controller for nonlinear systems is desired eagerly in the automatic control field.So,a good performance controller for nonlinear systems is of great significance in theory and practice.Based on this problem,this thesis aims to provide a basis for the application of the multi-dimensional Taylor network(MTN)controller in nonlinear systems theoretically.MTN controller,a new fixed structured controller based on linear controller,is extended with controller inputs for high power similar as Taylor series which does well in approximation.In this way,the controller has the advantages of good real-time,easy to implement with a simple structure and the strong ability to improve the transient response.Due to the fixed structure of controller,the dependence of controller design on system model information can be weakened.In response to this situation,this thesis focuses on the application of MTN controller in nonlinear systems.It mainly studies the application of the MTN controller in nonlinear systems from four aspects:What assumptions are necessary for the system?What information of the system is needed for the controller?What is the relationship between system performance and the controller parameters?What kind of the method can be used for the controller design?The research of this thesis is oriented to above four problems of nonlinear systems with three types which described by different mathematical tools and some constraints in practice.The main contributions of this thesis can be summarized as follows:1.For tracking control and performance optimization of single-input single-out(SISO)sampled-data nonlinear systems with zero-order holder(ZOH),a new control method based on the discrete MTN controller is proposed.Through the feedback linearization and Delta operator,the SISO nonlinear systems can track the reference by the discrete MTN controller.And the performance of the closed-loop system can be improved through dynamic regulation without of the online optimization.Assumptions for asymptotic tracking and dynamic regulation of discrete MTN controller for SISO nonlinear systems are obtained by the above proof.The relationship between system response and controller parameters is also demonstrated by the above proof.And a convenient design procedure of the discrete MTN controller is given.In addition,asymptotic tracking and performance optimization of SISO nonlinear systems are illustrated by an example.2.Target of asymptotic stabilization and performance optimization of SISO nonlinear systems with state time-varying delay,a novel approach based on the MTN controller is proposed.By using the augmented feedback linearization,Lyapunov-Razumikhin theorem and polynomial approximation theorem,it is proved that the MTN controller can stabilize the SISO nonlinear time-varying delay systems.And the system transient is improved according to an index through dynamic regulation without of the online optimization.Assumptions for asymptotic stability and dynamic regulation of the MTN controller for SISO nonlinear systems are obtained by the above proof.The relationship between system response and controller parameters is also demonstrated by the above proof.And a convenient design procedure of the MTN controller is given.Through a continuous stirred tank reactor(CSTR)and a numerical example,the MTN controller for SISO nonlinear time-varying delay systems cannot only asymptotically stabilize the system can also optimize the performance of the system is verified.3.Considering actuator saturation and implicit form of system input,the problem of asymptotic tracking and performance optimization of multi-input multi-output(MIMO)nonaffine nonlinear systems with the MTN controller is studied.Therefore,a new control scheme based on the MTN controller is proposed.By constructing the filter variable and its estimation,it is proved that asymptotically tracking for MIMO nonaffine nonlinear systems can be achieved by the MTN controller.Through the polynomial approximation theorem,the transient response can be enhanced by dynamic regulation without online optimization.Assumptions for asymptotic tracking and dynamic regulation of the MTN controller for MIMO nonlinear nonaffine systems with two degrees-freedom design method are obtained by the above proof.The relationship between system response and controller parameters is also demonstrated by the above proof.And a convenient design procedure of the MTN controller is given.Through a two-stage manipulator,asymptotic tracking and dynamic regulation of the MTN controller for MIMO nonlinear affine systems are showed.4.Based on above two contents,a novel control scheme,that based on the MTN controller,is proposed to deal with the tracking control and performance optimization for nonlinear time-varying delay systems which influenced by time-varying delay and nonlinearity.By using the augmented feedback linearization and Lyapunov-Razumikhin theorem,tracking control for nonlinear time-varying systems with the MTN controller is proved through constructing the filter variable and its estimation.By the polynomial approximation theorem,the transient response can be improved by dynamic regulation without online optimization.Assumptions for tracking control and dynamic regulation of the MTN controller for nonlinear time-varying delay systems with two degrees-freedom design methods are obtained by the above proof.The relationship between system response and controller parameters is also demonstrated by the above proof.And a convenient design procedure of the MTN controller is given.Tracking control and dynamic regulation for nonlinear time-varying delay systems by a CSTR and a numerical example are illustrated.Based on above numerical example,the problem of tracking control and dynamic regulation of MIMO nonlinear time-varying delay systems by the MTN controller also has been briefly discussed.