Theoretical Studies On Virtual Reference Feedback Tuning

Since the middle of last century,the modern control theory has been developed and perfected,and has been formed with many branches and fields.The traditional control theory based on precisely modeling is overdenpendent on the system model credibility.The data driven control theory and the traditional control theory are complementary,which makes the development of the data driven control theory an inevitable requirement for the development and application of control theory.Virtual reference feedback tuning(VRFT)as a kind of data driven control theory,with important significance in researching,dose not need modeling,the structure of controller is simple and the controller designing is transformed into a parameter identification processing,Compared to other data-driven control methods,VRFT is efficient for saving the time consuming process of collecting experimental data repeatedly and deal with it iteratively,instead,the parameters are needed to be tuned only once.on the other hand,virtual reference feedback theory is still one of the offline tuning methods,which for the complex nonlinear system controller design are especially troublesome and difficult to be combined with other control methods to achieve better control effects.In view of these shortcomings,this paper makes a deep research on that method.1.In this paper,the design of a controller for a non minimum phase linear system is presented.Because of the instability of the system or the controller may be caused by the zero pole cancellation,a design method of the virtual reference feedback tuning controller for a non minimum phase system is proposed.By defining a flexibility criterion,it is proved that without the full order model system identification,minimizing that criterion function will give the same non minimum phase zeros of the adjustable reference model as those of the actual object system;then with the identification results of non minimum phase zeros,design the ideal closed loop system transfer function,and make use of the conventional virtual reference feedback tuning method to get the controller parameters.Simulation results show that the method is effective in the non minimum phase system controller design.2.In the design of two degrees of freedom controllers for linear systems,unknown parameters are presented nonlinearly.In order to solve that problem,a Prediction error identification method is presented to identify controller parameters.The controller design is transformed into the identification of the controller parameters by using the virtual reference tuning method.A standard form of the prediction error identification is obtained by reparameterizing of the original input-output relation.The nonlinear least squares identification method is used to determine two kinds of controllers' parameters.Theoretical analysis of the convergence of the Algorithm and simulation is given.3.Considering the complex dynamic characteristics of the nonlinear system,a design of the two degrees of freedom controller is proposed.Designing the nonlinear feedforward part of the two degrees of freedom controller is transformed into a series expansion of nonlinear functions with basis functions multiplied by parameters and parameter identification using the design of virtual reference signal.Then add a linear controller part in a feedback loop to enhance the tracking performance of the system,and use the recursive least squares identification method to identify the parameters of the linear controller.The stability of the closed-loop system are theoretically analyzed,and derive that to ensure the IO finite gain stability of the nonlinear system the Lipschitz coefficient must satisfy some conditions,and the value of the upper bound of the tracking error is given.Finally,simulation results are shown.4.As the traditional theory of virtual reference feedback tuning mainly make use of off-line data,which can no longer be used in the situation of time varying system controling.For linear time varying systems,an adaptive virtual reference feedback controller design is proposed.With the use of off-line virtual reference feedback correction method to initialize the controller parameters,the observation data is real-time collected at both ends of controlled object to construct virtual reference signal and the controller parameter is identified and updated via filter data.The convergence of the proposed algorithm is theoretically analyzed,and simulation results verify the adaptability of the proposed method in condition of changes of control object properties.In view of the complex properties of nonlinear time varying systems,a nonlinear VRFT controller design method based on Volterra series is proposed.Construct virtual instruction and performance index,and prove the equivalence of that performance index and the global performance index;then design the nonlinear controller and determine the initial network structure and initial weights of the network of Volterra series,make use of improved nonlinear mean square error to on-line update weights to treat the change of the controlled system.Theoretical analysis of the convergence of the closed-loop system,and the simulation is conducted.5.Designing traditional internal model controller is excessively dependent on the information of real objects and the internal model,and mainly relies on filter coefficients to adjust controller parameters,so it will certainly sacrifice the rapidity of the system.To avoid the real object modeling,the controlled object modeling and internal model controller design can be synchronized based on the virtual reference feedback correction method,and solved by transforming into the parameter identification process.Establish the equivalence of VRFT and internal model control,derive the filters' specific expressions,and make use of filtered data to identify the parameters.The asymptotic theory is used to derive those two kinds of unknown parameters' asymptotic variance matrix,witch is used to measure the identification accuracy.And the effectiveness of the proposed method is verified by simulation.