具有自适应非线性增益的开环PD型迭代学习控制

针对同时存在周期性干扰和随机测量噪声的一类非线性系统,提出一种基于误差幅值和误差变化率的开环PD型迭代学习非线性增益自适应算法,分别给出了比例和微分的增益调整规则,并对所提算法进行了严格的理论分析,同时推导出收敛条件。结果表明,与传统学习增益固定的开环PD型迭代学习律相比,当非线性系统同时存在周期性扰动和幅值较大测量噪声时,自适应非线性增益学习律能根据误差幅值和误差变化率在线调整比例和微分学习增益,抑制扰动和噪声,使得在学习收敛速度和收敛精度之间在某种程度上得以折中,在学习初始阶段高增益下保证了迭代学习的收敛速度,学习末了阶段小增益下具有较强的鲁棒性和收敛精度,得到的误差跟踪曲线更加平滑。

Open-loop PD-type iterative learning control with adaptive nonlinear gain

An open-loop PD-type iterative learning nonlinear gain adaptive algorithm based on the error amplitude and error rate of change is proposed for a class of nonlinear systems with both periodic disturbance and random measurement noise. The adjustment rules of the proportional and differential nonlinear gain are given respectively, and the proposed algorithm is analyzed theoretically and the convergence conditions are given. The results show that compared with the traditional open-loop PD-type iterative learning law with the fixed learning gain, when the nonlinear system has both periodic disturbance and measurement noise with large amplitude, the adaptive learning law of the nonlinear gain can regulate the proportional and differential learning gain online according to the error amplitude and error change rate, and suppress the disturbance and noise. Using this algorithm, the convergence speed of iterative learning is guaranteed under the high gain in the initial stage of learning, and the convergence precision and robustness are stronger under the small gain in the final stage of learning, and the error tracking curve obtained is smoother.