Multi-Object Optimal Control Of Double-Wheeled Balancing Cars

Double-wheeled balancing car is supported by two wheels.By controlling the speed of two wheels,double-wheeled balancing car realize static,linear motion and turning function.And it has the characteristics of small size,light weight and flexible cornering.When the double-wheeled balancing car works,the movement process should be stable,fast and energy-saving,therefore,the double-wheeled balancing car requires good control system.In recent years.although many scholars have proposed a lot of control algorithms,but its static performance and dynamic performance could not meet the actual demand completely.This thesis focuses on the problems encountered in the control process of the double-wheeled balancing car,designs a new control algorithm,and completed the following work.Firstly,the research background and significance of the double-wheeled balancing car are summarized、development process and research status at home and abroad,some basic theoretical concepts,important theorems and LMI solvers used in the research process are also explained.It provides the basis for the design of the following controller.Secondly,according to the structure and movement of the double-wheeled balancing car,the dynamic model is established by Lagrange equation,and linearized in the vicinity of the equilibrium point of the system,and the linearized model is obtained.Thirdly,the design method of controller for double-wheeled balancing car is studied.The overall scheme and block diagram of the control system are given;by introducing servo compensator,the steady-state error of the system can be eliminated;with dynamic output feedback method,the system poles are assigned to the given area by the method of regional pole assignment.The structure of dynamic compensator is obtained by combining the linear two order performance and the controller parameters are obtained by linear matrix inequality.Finally,the control algorithm is simulated.In order to verify the performance of the controller,a comparative test is added in this paper.The system controller is solved by the method of state feedback,and the self-balancing,straight forward and backward simulation test of the dual wheel balance car is carried out.Then the controller is designed in this thesis,and the simulation test of the system’s static,linear motion and turning performance is carried out.At the same time,the anti-interference ability and robustness of the system are also tested,and the control energy is optimized.The simulation results show that the controller designed in this paper has better performance than the state feedback in less than two sensors,and achieves the desired goal.Combining the advantages of several kinds of control theory,including servo compensation,dynamic output feedback and linear quadratic regulator(LQR),this control system can realize the following functions:1)zero error output regulation for a variety of external signals.2)Rapid and stable response to the control instruction.3)Certain robustness.