基于模型预测控制的高速柔性并联机构振动控制

摘要

Considering the nonlinearity and uncertainty of a high-speed flexible parallel mechanism,a robust model predictive control strategy was presented to suppress the vibration response of the system.Piezoceramic patch actuator and strain gauge sensors were used.The finite element method and modal truncation technique were applied to obtain the dynamic model of the mechanism.The nonlinear,coupling factors and high-order modal effects existing in the dynamic model of the system were considered as disturbances.The modal force was treated as an uncertain disturbance and the measurement noise was considered.The predictive model of the system dynamic response was introduced and the output was forecasted by the model.A Kalman filter estimator was designed to estimate the state variables of the system.A standard quadratic programming optimization problem was formed where the performance index function minimizes a quadratic performance function.The constraints were the control input voltage and its change rate.The optimization problem was solved to obtain the optimal control output voltages and a rolling optimization control system was then constructed to suppress the vibration response of the system.The optimum placements of the actuators and sensors were determined by using the controllability index featured as actuating energy and the observability index featured as signal energy.Taking a novel 2-DoF parallel mechanism as an example,the experimental modal method was applied to obtain the first two natural frequencies and damping ratios.Comparing with the results obtained by the finite element method,it shows that the theoretical model is not accurate enough.Using dSPACE real-time simulation system and MATLAB/Simulink,the control system was built and the vibration control experimental study was carried out.The experimental results show the proposed controller can effectively suppress the vibration response,and the effectiveness and robustness of the controller was verified.%由于高速柔性并联机构系统的非线性和不确定性，提出一种鲁棒模型预测振动控制策略以抑制系统的振动响应。以压电陶瓷为作动器，电阻应变片为传感器，采用有限元方法和模态截断技术建立机构不精确动力学模型。机构动力学模型中的非线性因素、耦合因素及系统高阶模态影响作为扰动，将模态力视为不确定扰动，并且考虑输出噪声对系统的影响，建立系统动态响应的预测模型，以预测输出值。采用Kalman滤波估计器估计系统状态量，以控制电压及其变化率为约束条件，将系统性能指标和约束条件化为一个标准二次规划优化问题，通过求解这一优化问题来得到最优控制输出，形成滚动优化控制输出来抑制系统振动响应。采用表征作动能量的可控性指标和表征观测信号能量的可观性指标，确定作动器和传感器的最优位置。以新型2自由度并联机构为实例，采用实验模态方法得到系统的前2阶固有频率和阻尼比，与有限元方法得到的结果比较分析表明理论模型不精确。基于该模型采用dSPACE 实时仿真系统和MAT-LAB/Simulink搭建鲁棒控制系统，进行振动主动控制试验研究。试验结果表明，所设计的控制器能有效地抑制柔性构件产生的弹性振动，验证了控制器的有效性和鲁棒性。