Cascade Auto-disturbance-rejection Control For A Class Of High Order Nonlinear Systems With Model Uncertainty

In the nonlinear systems, with the order of the systems increasing, the difficultiesof analysis and control are increasing ceaselessly.The research with modeluncertainty, coupling, complex systems become more difficult. Nonlinear cascadesystems are representative high order nonlinear systems, the mathematical model ofthese systems usually have a high order. The whole system can be divided intomultiple subsystems, superior subsystems associate with subordinate subsystemthrough a certain state variable.Through many of theoretical studies, it was found thata lot of high order nonlinear systems can be converted into cascade systems throughstate feedback, coordinate transformation method. Cascade systems also exist widelyin engineering application of complex systems such as electric power, metallurgy,machinery and other systems. Because of the special structure and existing widely, thestudy of the control strategy of the nonlinear cascade systems has more importanttheoretical value and engineering application significance.According to the high order nonlinear cascade systems, a lot of study works havebeen done in this paper. Especially for the systems with model uncertainty, the studyof control strategy is done through theoretical analysis and experiment research. A setof effective control theories and controller designs are put forward in this paper. Inaddition, multi-input high order nonlinear ball and plate system is studied. Thecontroller design and experiment research of ball and plate system are completed. Theexperimental results show that the proposed control strategy is effective and feasible.The specific research contents are as follows:1. The theory of dynamic compensation linearization using nonlinear stateobserver is analysis. The stability and error convergence domain are studied and asteady-state error analysis with the extended state observer (ESO) is also given. Inaddition, an improved ESO structure design method is put forward toward modelpartial unknown system. This design method can reduce the ESO observation burdenand improve the observation accuracy. In addition, aiming at measured noise pollutionof the system output variable, a variety of design methods of ESO which havefiltering functions are given. Finally, the problem of nonlinear multivariable decoupling is studied using more than one active disturbance rejection controller(ADRC).Analysis and simulation results show that the above mentioned methods areeffective.2. According to the model uncertainty nonlinear cascade systems which havestrict feedback form, the backstepping recursive design theory is studied. On the basisof this study, the cascade auto disturbance rejection control strategy independent onsystem model, having features of recursive design is proposed. The control strategydoes not rely on system model and is easy to satisfy the constraint conditions for thecontrolled plant. It does not require the give track high order differentiable in thetrajectory tracking system and the controller has advantages of simple structure design,easy to realize. In addition, the structure classification of model uncertainty nonlinearcascade system is study and the cascade auto disturbance rejection control strategy isextended to the cascade systems which are defined as generalized feedforwardcascade systems, generalized nontriangular cascade systems. The defining of the autodisturbance rejection control standard structure is also given. So much simulationexperiments have been done aiming at typical third-order cascade system which iscomposed of three first-order subsystem and forth-order cascade system which iscomposed of two second-order subsystem. At last, the simulation experiments ofcontrolling a typical feedforward cascade system, cart pendulum system has done. Allthe simulation experiments achieve satisfactory control effects.3. The controller parameter setting rules for ADRC is analyzed and a basicparameter setting rules is also given. It is found that the parameters of trackingdifferentiator (TD) and ESO do not need to change when the controlled plant andtrajectory are determined. The controller parameter setting rules for ADRC areanalyzed and a basic parameter setting rules are also given. In order to improve theadaptability of controller, some parameters optimization methods can be used tooptimize the parameters in nonlinear state error feedback control law (NLSEF) ofADRC. The parameters optimization method of using neural network technology isproposed based on the study. In order to meet the on-line fast control, the radial basisfunction neural network which has simple structure, good approximation results isused. The algorithm of momentum factor gradient descent method is used to adjustthe main effects of the approximation capability and improve the operation speed. Inaddition, the controller structure design and parameters selecting are discussed, thesimulation experiments of the ADRC based on RBF validate the control effect and meet the design requirement.4. The feasibility and practicability of the proposed theory are validated throughthe ball and plate system. The full mathematical model of ball and plate systemconsidering the friction, disturbances and uncertainties and coupled problem ofmultiple input systems is established. The cascade auto disturbance rejection controlscheme is used to the tracking and pointing control of the ball and plate system. Thecontroller structure designs based on ADRC are completed both with the simplesecond-order and the forth-order ball and plate system. Much simulation experimentsfor different conditions and practical experiments on BPVS-JLU-II experimentalplatform are completed. The results of experiments show that ADRC has goodtracking control ability and better robustness and achieves high-precision trajectorytracking task. The results also make a beneficial attempt for the engineeringapplication of proposed control strategy.To sum up, further theoretical and experimental studies are done based oncascade auto disturbance rejection control strategy for a class of uncertain, high ordernonlinear systems. The results show that the proposed control strategy is effective,feasible. The applied study on ball and plate system with proposed control strategyalso obtains the satisfactory control effect and provides a reference basis forexperimental study.