Research On Tracking Control Of Rotary Double Inverted Pendulum Based On Servo Compensation

As a kind of natural unstable system with multivariable,nonlinear,strongly coupling characteristics,inverted pendulum system is a typical experimental device to verify the effectiveness of control algorithms in the field of control science.Compared with a linear inverted pendulum,a rotary inverted pendulum has no restrictions on the length of the guide rail,and the device occupies a small space,but the mathematical model is more complicated,so it is a more effective algorithm experimental device.In this context,this thesis made an in-depth discussion on the tracking control problem of the rotary double inverted pendulum,in other words,whether the rotation angle of the pendulum can accurately track the given signal.The main work completed in this thesis is as follows:Firstly,the research background and significance,development process and research status at home and abroad of inverted pendulum system are summarized,and some basic theoretical concepts,important theorems and mathematical tools used in the research process are studied to provide theoretical basis for the subsequent controller design.Secondly,the structural characteristics and working principle of the rotary double inverted pendulum system are analyzed.The nonlinear mathematical model is established by using the Lagrange equation,and then the linear approximation is performed in the neighborhood of the vertical upward working point to obtain the state space equation.It is also verified that the linearization model of the system is completely controllable and observable near the equilibrium point,but is naturally unstable.Then,the design method of the controller based on servo compensation was studied,and the block diagram of the control system is given.Based on the unstable mode in the reference input signal,a servo compensator is designed,and the zero-static error adjustment of different reference inputs is realized under the linearization model.The servo compensator and the controlled object are combined to the augmented controlled objected,and the state feedback control law is designed.A reduced-order state observer is established to reconstruct some unknown state variables in the system,and the LQR(Linear Quadratic Regulator)optimal control is used to optimize the control parameters and transient performance of the control system.Finally,the tracking control problem of the angle of rotary arm and the upper pendulum angle is studied,and the simulation curve is obtained by using the designed controller.It can be seen from the simulation results that the designed controller can make the angle track the given sinusoidal signal no matter the angle of rotary arm or the upper pendulum angle.The innovation of this thesis is reflected in the following three aspects.First,the given signal is not limited to a constant value,so it is a program control system;second,the controlled object has three degrees of freedom,but only detects the angle of the rotary arm,which simplifies detection;third,a reduced-order state observer is used to simplify the correction.