On The Hierarchical Supervisory Intelligent Adaptive Control Algorithm For Nonlinear Ball And Plate System

The ball and plate system is a typical multivariable, uncertain and nonlinear controlobject. It has become a typical benchmark experimental research platform of control theory.In order to consider nonlinear characteristics such as underactuation and coupling, modeluncertainty, much attention have been paid to design control strategies based on a simplifiedmodel of the non-linear ball and plate system. In addition, intelligent control algorithmsbased on a large number of trial and error and language experiential knowledge can beapplied to uncertain systems such as the ball and plate system, therefore the combination ofintelligent control and nonlinear control approaches is extremely effective for the uncertainnonlinear systems.In general, the main factors which affect the control performance of the BPS includetwo aspects: environment and task constraint, and the movement speed of the ball. Whenmotion trajectory of the ball which is determined by environment and task requirements hasa frequent curvature change or a big curvature, and a high movement speed of the ball isrequired, it has put forward higher demands for control system.In this paper, the specific research content is as follows:1. In the condition of the nonlinear ball and plate system to ignore the shaft coupling oftwo direction and the friction of small ball plate, the controller of two layers is proposed. Thebasic controller is composed of the ratio, differential and integral controller (PID) based onneural network as the underlayer controller. The complement controller is designed by thecontroller using the particle swarm-differential evolution (PSO-DE) algorithm as theupperlayer controller that is the adaptive controller for online learning structure of theweighted factor of PID neural network controller using the PSO-DE algorithm. From thebasic rules of PID controller and human experience, gave out the layer number of PID neuralnetwork, the number of neurons in each layer and the connection methods between eachneuron. Thus the PID neural network has the ability of online learning, remembering andapproximation for any function. Moreover, for closed-loop system of the nonlinear ball andplate, each connecting weighted value of PID neural network (PIDNN) controller is adjustedby the PSO-DE optimization process of the upperlayer controller, therefore the stability andconvergence of the ball and plate system was assured. The proposed approach overcame thepropagation algorithm (BP) disadvantage easy falling in local optimum, at the same time,make the controller has the advantages of PID controller: the simplification mechanism,good dynamic characteristics and stability.2. The design method of the hierarchical supervisory direct adaptive fuzzy slidingmode controller based on the stability supervision is proposed for the uncertainty andinterference of the nonlinear ball and plate system when the small ball is moved with the high speed. Based on the Lyapunov stability theory and supervision of state variables, theupper supervision-complement controller was researched, and the underlying controlleralgorithm is proposed as a direct sliding mode controller. The external interference based onthe coupling between the two axis direction and the friction term etc is behaved as sum h(t)of a variety of disturbance terms, and ball movement of two axes is respectively studied. Andthe ball and plate system is decomposed into four subsystems, each subsystem definesrespectively the sliding surface, two sliding surfaces is combined to one sliding surface bythe coupling coefficient, thereby a direct fuzzy sliding mode controller is constituted. Thefuzzy adaptive rule was constructed by the fuzzy input variables: the sliding surface anddifferential function of the sliding mode surface. Based on Lyapunov stability theory and thesuroervition of state variables, the adaptive rule of the coupling coefficient of sliding modesurface is designed, so the stability control of the ball and plate system is achieved, and thecomplex calculation was avoided. The experiment result shows that this proposed controlmethod can realize better the stabilization control and trajectory tracking problems ofnonlinear uncertain systems.3. For the strong coupling and the uncertain friction of the multivariable nonlinearsystem-ball and plate system, the hierarchical supervisory fuzzy adaptive indirect controlalgorithm which has the supervisory control and adaptive compensation function has beenproposed. In fact, in recent decades, the fuzzy adaptive control method is proposed for theuncertain SISO nonlinear system. But, in the practical engineering, a kind of commonsystems are all the multivariable nonlinear system are easy to encounter. Also, in manypractical engineering, control gain matrix is irreversible nonlinear. When the ball is movedon the laboratory plate, the moment that the control gain matrix determinant equal to zero isexist, exactly is appear the moment which the control matrix is irreversible, this time the balleasily exist in the out of control state. Therefore, for the multivariable uncertain systemswhich the control gain matrix is irreversible, the fuzzy adaptive controller design ismeaningful. In this paper, the method that can overcome the above problems is researched.Through as same design algorithm of previous chapter, the upperlayer controller is designedas the hierarchical supervisory fuzzy adaptive controller and the error adaptive compensationcontroller based on tracking function error and state variable error, and that the underlyingcontroller is composed of the indirect type fuzzy control law. This method does not requirethe invertibility of the control gain matrix of the objects. In this paper, for the typicaluncertain nonlinear MIMO system-uncertain nonlinear ball and plate control system, underthe condition that does not require the reversible control gain matrix, a kind of indirect fuzzyadaptive control method with the supervisory control term is proposed. The Adaptive controlrule and the adaptive compensation control law parameters is induced by Lyapunov stabilitytheory, so can guarantee the stability of the closed-loop system and the convergence of thetracking error to zero within a small territory.On the ball and plate experimental platform BPVS-JLU-II, With the proposed controlalgorithm, completed stable simulation experiment of a wide change of variables and various trajectory tracking control simulation experiment (circular, square and curve eight, etc.) withthe proposed control algorithm.In conclusion, in this paper, the hierarchical supervisory intelligent adaptive controllerfor the uncertain nonlinear ball and plate systems is designed, had in-depth theoretical andexperimental research. Through the simulation experiment research of the uncertainnonlinear ball and plate system BPVS JLU–II, the research results clearly show that theeffectiveness of the proposed control scheme, feasibility, stable and convergence.