Research On Quantitative Control Method Of Spherical Inverted Pendulum System

As a very representative class of control systems in the research of control theory,inverted pendulum system has the characteristics of multivariable,nonlinear and strong coupling,and is a kind of unstable complex nonlinear system.At the same time,the simple physical properties determine that it is very suitable to test the effectiveness of various new control theories and methods.In this paper,the spherical inverted pendulum is taken as the research object,and a variety of control methods are adopted to realize the stability control of the spherical inverted pendulum.the main research contents are as follows:(1)Firstly,the research situation and related control methods of the inverted pendulum system are introduced.starting from the most primary inverted pendulum model,the mathematical model is established by using the simple Newton law analysis method,and its transfer function and state space equation are obtained.Aiming at the single input problem of the primary inverted pendulum system,the spherical inverted pendulum system in this paper is introduced.(2)Under the condition of actuator saturation and data quantization,the spherical inverted pendulum system has a partial unstabilizable subsystems.It is assumed that the switching is slow enough in the sense of combined residence time and average residence time.Under the premise of the declaration,the saturation controller can be described as a linear combination of sampling quantization feedback controllers.On this basis,four cases are discussed to obtain the increase and decrease rate of multi-time-varying Lyapunov function.If the average residence time and activation time of the stable subsystem satisfy some constraints,it is deduced that each trajectory of the initial state in a given region will fall into a small ellipsoid and stay in a slightly larger ellipsoid.An example is used to verify the effectiveness of the theoretical analysis,and finally into the spherical inverted pendulum system to get the results of stability control.(3)In order to solve the problem of a large amount of data transmission in the control process of spherical inverted pendulum system,an event-driven transmission mechanism is proposed,and the exponential stability of switched systems with partially unstabilizable subsystems under the influence of actuator saturation is also discussed.By designing appropriate event-triggered mechanism and preset propositions,the model transformation of closed-loop switched systems under input saturation constraints is realized.According to the two cases,the increasing / decreasing rate of Lyapunov function is calculated,and the sufficient condition to ensure the exponential stability of the closed-loop system is obtained,and the rationality of the preset proposition is verified.Under the premise of the stability of the switched systems,the resource occupation in the communication process can be effectively reduced.The design method of feedback matrix is given based on linear matrix inequality(LMI).The correctness of the theoretical analysis is verified by a numerical example,and the result of stability control is obtained by introducing it into the spherical inverted pendulum system.