两种带增益预补偿的四级倒立摆线性控制器的设计与比较
Design and comparison of two linear controllers with precompensation gain for the Quadruple inverted pendulum
摘要：
在这项工作中，我们提出了一个工作流程，设计两个线性控制技术应用于动态系统四重倒立摆安装在车上（QIP）的车位置上的稳态误差是通过预补偿增益消除。设计的第一控制律基于LQR，基于系统状态的总能量的最小化来稳定系统状态的技术，并且第二控制技术是通过二阶系统近似的极点配置，该方法允许定义设备的期望响应的稳定时间和超调，对于该控制，系统被认为是SISO，作为设备的唯一输出，小车的水平位置。为了消除由两个线性控制器产生的稳态误差，在拉普拉斯域中对受控系统的稳态响应进行了分析。仿真环境是Matlab的Simscape，它是一个可以模拟非线性机械系统动态特性的仿真环境。所获得的结果表明，这两个控制器都能够稳定的植物和移动车的位置所需的设定点。最后，我们讨论了这两种线性控制技术的性能。
英文摘要：
In this work we present a workflow for designing two linear control techniques applied to the dynamic system quadruple inverted pendulum mounted on a cart (QIP) where the steady state error on cart position is eliminated through a precompensation gain. The first control law designed was based on LQR, technique that stabilizes the system states based on a minimization of the total energy of the system states and the second control technique was pole placement by 2nd order system approximation, this method allowed to define a settling time and overshoot of the desired response of the plant, for this control the system was considered SISO, being the only output of the plant the horizontal position of the cart. To eliminate the steady-state error generated by both linear controllers, an analysis of the stationary response of the system under control in the Laplace Domain was performed. The simulation environment used to validate the results presented in this paper was Simscape of Matlab, it is a simulation environment that allowed to simulate the dynamic of nonlinear mechanical systems. The results obtained indicate that both controllers are able to stabilize the plant and move the cart position to the desired setpoint. Finally, we discuss about the performances of both linear control techniques.
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