Research On Model-free Backstepping Control Strategy And Dynamic Analysis For Underactuated System

An underactuated system is a nonlinear system in which the degree of freedom is greater than the independent control input dimension.Underactuated systems are widely used in transportation,metallurgy,defense and equipment manufacturing because of their advantages of light weight,low energy consumption,low cost and simple structure.In addition,when a drive of the full-drive system fails,it can be designed as an underactuated system to ensure the normal operation of the entire system.Underactuated systems usually have complex dynamic structures and strong coupling or nonholonomic constraints between system states,which increase the difficulty of system control.Especially for non-minimum phase underactuated systems,the tracking control must consider both output tracking and internal dynamic stability.What's more,uncertainties such as unmodeled dynamics and external disturbances also bring challenges to its control design.The existing control theories and methods of nonlinear systems usually have their own limitations,such as dependence on system model,difficulty in ensuring stability and poor robustness.Therefore,a robust and universal model-free control method for underactuated mechanical systems is of great theoretical significance and practical value.In this paper,for underactuated mechanical system with model uncertainty,a data-driven model-free approach is adopted to estimate the system model online,combined with the backstepping control algorithm,to ensure the Lyapunov stability of the closed-loop control system.On this basis,the dynamic analysis of the underactuated closed-loop control system based on model-free backstepping control is performed,and the analysis results can be used to improve the control design.The main contents of this paper are as follows:1.Model-free backstepping control(MFBSC)strategy for underactuated systemsUnderactuated mechanical systems have many characteristics,such as complex internal dynamics,lack of partial actuation,strong coupling between system states and non-integrity constraints.There are many problems in the control design,such as system-underactuation,state coupling,dependent system model,poor algorithm robustness,complex control design process,and difficult to prove the system stability.In this paper,the standard cascade form of model-free backstepping control design for underactuated mechanical system is obtained by using coordinate transformation and adding pseudo-control coefficient.Based on this,the backstepping control algorithm is used to inversely design each Lyapunov function to obtain the intermediate virtual controller and the actual control rate,which solves the problem of lacking partial actuation in the underactuated system.Among them,the required model for backstepping control is obtained by online estimation of the input and output data of the measurement system.The decoupling problem of the underactuated controller is transformed into the model estimation problem under the series structure.At the same time,the online estimation solves the problem of model unknown caused by the unmodeled dynamic and unknown disturbance.In this paper,numerical simulation and physical experiments are carried out with the flexible ruler as the research object,and the feasibility and effectiveness of the model-free backstepping control algorithm are verified by a comparative study with the LQR control algorithm.2.Research on model-free backstepping control strategy for non-minimum phase underactuated systemsNon-minimum phase underactuated system refers to the underactuated system with unstable zero dynamics,that is,the internal dynamics in the system are unstable.When designing controller for such a system,it is necessary to consider both the output tracking and internal dynamic stability of the system.In this paper,for the non-minimum phase underactuated mechanical system,the output tracking error of the system is combined with the internal dynamic stabilization error in the system to form the system Lyapunov function.On the premise of ensuring system output tracking convergence and internal dynamic stability at the same time,the virtual controller and control rate are designed.The simulation and experiment of single-stage rotary inverted pendulum and linear two-stage inverted pendulum are carried out respectively.And a comparative study was conducted with LQR control method to further verify the robust control effect and model-free and nonlinear advantages of the proposed algorithm.3.Dynamic analysis of underactuated closed-loop control system based on model-free backstepping controlUnderactuated mechanical systems have complex dynamic characteristics due to the lack of partial actuation.At present,the commonly used dynamic analysis method is usually based on the physical model of the system.Once the system has unmodeled dynamics and inaccurate modeling,it is usually difficult to conduct a complete dynamic analysis.The use of model-free backstepping control methods provides the possibility for dynamic analysis of such systems.Based on the model-free backstepping control strategy,the dynamics of the underactuated closed-loop control system with uncertain model is analyzed in this paper.By drawing the bifurcation diagram and the state diagram of the closed-loop control system,the influence of the control parameters and the initial value of the system on the dynamic behavior of the underactuated system is studied.Moreover,the stability range of the system and the selection range of controller parameters are determined,which provides an important basis for the optimal design of the controller.