第9章-机器人线性控制.pptVIP

线性控制仅适用于能够用线性微分方程进行数学建模的系统. We will model a manipulator as a mechanism that is instrumented with sensors at each joint to measure the joint angle and has an actuator at each joint to apply a torque on the neighboring link. Sometimes velocity sensors (tachometers) are also present at the joints. We wish to cause the manipulator joints to follow prescribed position trajectories, but the actuators are commanded in terms of torque, so we must use some kind of control system to compute appropriate actuator commands that will realize this desired motion. 1. 开环控制 1由轨迹生成器给定关节角、关节角速度、关节角加速度 2用指定模型计算所需要的扭矩: 如果模型是完备和精确的，且没有噪声或者其它干扰存在，上式即可实现期望轨迹. Imperfection in the dynamic model and the inevitable presence of disturbances make such a scheme impractical for use in real applications. Such a control technique is termed an open-loop scheme, because there is no use made of the feedback from joint sensors. 2. 闭环系统 建立高性能的控制系统的唯一方法就是利用关节传感器的反馈. 伺服误差: The control system can then compute torque of the actuators as some function of the servo error. The basic idea is to compute actuator torques that would tend to reduce servo errors. 利用反馈的控制系统称为闭环系统. 一个好的控制系所应该具备的功能： 这个系统应该是一个稳定的系统. 保证闭环系统的性能满足要求. 1.二阶线性系统 由质量块的受力图得到运动方程: 特征方程: 方程的根: 一种描述二阶振动系统的两个参数是 阻尼比 （ damping ratio ）and 固有频率（natural frequency） : 对于有阻尼的质量-弹簧系统，阻尼比和固有频率分别为: 当无阻尼时 ( ), 阻尼比为0; 对于临界阻尼 ( ), 阻尼比是 1 . 过阻尼 (两个不等实根): 主要受摩擦影响，缓慢回到平衡位置. 欠阻尼 (复根): 弹性力影响，出现振荡. 临界阻尼 (相等实根): 此时摩擦力与弹性力平衡，系统以最短时间回到平衡位置. 时域特征指标 Rise time上升时间 Settling time 2. 二阶系统的控制 Design a controller so that the system has some desired characteristics. Typical objectives: 稳定: stabilize the sya