摘要
机电运动系统是工业生产中最常见和应用最广泛的一种系统。随着社会生产的发展,机电运动控制系统变得越来越复杂,表现出非常复杂的非线性特性,如死区、粘滑以及速度依赖等,同时会随着外界条件诸如机械磨损、惯量变化、温度和润滑等因素而变化,具有时变特性。因此,通常难以用一般数学方法精确描述其数学模型和未建模不确定性。然而,实际工程中的超精密机床、工业机器人、半导体制造等设备对运动控制部件的运动速度和精度要求却越来越高。要获得高速高精度的运动系统,不仅需要进行精巧的机构设计,也需要设计高性能的运动控制器。
自适应技术就是针对实际工程应用而发展起来的一门具有自动学习系统不确定性的控制技术,在新的应用需求的推动下,新一轮的自适应控制得到了空前的发展。但是针对时变不确定机电运动系统的自适应控制理论仍然还有许多问题需要解决,还需要控制相关领域的研究者继续付出艰辛的努力。因此,本论文针对典型的时变不确定机电运动系统的自适应控制器设计展开研究工作,并将所得到的控制器应用到实际的机电运动系统的控制中。主要工作包括以下四个方面:
1)综合PID的简单结构和良好性能优势以及神经网络的自调节和自适应的特长,针对单输入的非线性多变量系统,提出了一种具有PID结构的多变量自适应的PID型神经网络控制器PIDNNC。通过定义误差函数作为设计目标,采用带有弹性算法的梯度下降法,并用变化率以及弹性算法中的符号法来处理某些求导关系,获得适用于实时在线调整网络权值的修正公式,并根据李亚普诺夫直接方法推导出确保闭环控制系统稳定的学习速率的取值范围。最后,在实际的二级直线倒立摆装置上使用PIDNNC实现倒立摆的镇定控制,并在相同条件下与LQR的控制结果进行对比分析。在进行实际实验之前,还详细研究了采用LQR获取最优的PIDNNC初始权值的问题。
2)将PIDNNC扩展为非线性的具有PID特性的神经网络自适应控制器NLPIDC。首先给出了控制器的结构和网络权值调整算法,然后应用离散形式的李亚普诺夫直接方法对闭环控制系统进行稳定性分析,获得了确保闭环控制系统稳定的学习速率取值范围;最后通过虚拟样机软件(ADAMS)和MATLAB联合搭建非线性动力学系统仿真平台,并在该仿真平台上应用所提出的控制器对三级倒立摆系统进行镇定控制仿真实验。
3)针对具有非线性时变不确定性的上三角系统,基于函数逼近技术和滑模控制基本原理提出了一种新的自适应控制器FASMAC。FASMAC不需要预知非线性不确定性的上界,只需要通过傅立叶级数技术将系统的不确定性转化为未知时不变的系数向量与已知的时变函数级数的乘积,再应用李亚普诺夫直接方法得到未知的非线性时变不确定项的在线逼近和逼近误差的自适应补偿,最终获得实时的滑模自适应控制律。最后将所提出的FASMAC应用到直流电机的位置跟踪控制中。
4)通过引入额外的关于误差平方和的性能函数,将时变不确定上三角系统的滑模自适应控制器扩展为一般单输入多输出系统的自适应控制器SIMOAC。然后将所得到的SIMOAC应用到实际直流电机装置的位置跟踪控制以及三级倒立摆的仿真镇定控制中,并把实际实验和仿真结果与其他方法进行对比分析。
Electro-mechanical motion system is one of the industrial systems most frequently used. As the development of social production, electro-mechanical motion system is becoming more and more complex and appers complicated nonlinear phenomenon such as dead-zone, stick-slip and velocity dependecne, it is also time varying because of the mechanical wear, inertia variation and temperature and humid changing in the environment during the operating. Therefore, it is difficult to describe the precise model and unmodeling uncertainty by common mathematical modeling methods. However, super precise machine tools, industrial robots and semiconductor equipments demand for higher velocity and precision in practical industrial production. It is demonstrated that motion system with high velocity and high precision needs not only ingenious mechanical design but also high performance motion controller.
Adaptive technology is a unique control method arising from the practical engineering application, which can learn the system uncertainty automatically, and new application demands promote a new round of development of this technology. But, there are still a lot of unsolved problems in adaptive control theory for time varying electro-mechanical motion system, and continue hard work is needed. Therefore, this dissertation studied the design of adaptive controller for time varying uncertain electro-mechanical motion system, and then applied the proposed controller to the practical electro-mechanical motion control systems. The main contents include the following four parts.
1) Based on advantages of simple structure and good property in PID and self-regulation and adaptive of neural networks, a multivariable adaptive PID-like neural network controller (PIDNNC) was proposed for single input multi output nonlinear uncertain system. By means of defining error function as the design objective, using resilient back-propagation algorithm with sign instead of the gradient to deal with some differential relations, the correcting formation of on-line updating network was obtained. Lyapunov stability theorem was used to derive the values of learning rate to insure close-loop control system stability. Finally, the proposed PIDNNC was applied to the stabilizing of actual inverted pendulum, and then the experimental result was compared with that of LQR. Besides, problem of how to obtain the optimal initial weights of PIDNNC with LQR was also discussed in detail.
2) The PIDNNC was extended to a neural network nonlinear adaptive controller with PID property (NLPIDC). Firstly, structure of the controller and on-line update law of weights was introduced, and then stability of the close-loop control system was analyzed with discrete Lyapunov direct method, and the range of learning rate was obtained which guaranteed the stability of the close-loop control system. Finally, the proposed NLPIDC was used to control the triple inverted pendulum in the nonlinear dynamic simulation software system constructed by virtual prototype software ADAMS and MATLAB.
3) Based on function approximation technique and sliding mode control principle, a novel adaptive controller for nonlinear time varying uncertain upper triangular system (FASMAC) was proposed. The bound unknown nonlinear uncertainty was transformed into the product of an unknown time invariant coefficient vector and a known time varying series vector, and then on-line approximation of the uncertainty and adaptive compensation of the approximation error were derived by Lyapunov direct method. Finally, actual experiment on the direct current motor position tracking was conduced with the proposed FASMAC.
4) Introducing an additional performance about square sum of error into the controller design, the FASMAC for the time varying uncertain upper triangular system was extended to an adaptive controller SIMOAC for general single input multi output system. Finally, the proposed SIMOAC was applied to the position tracking control on actual direct current motor system and the stabilizing of triple inverted pendulum, the experimental result and simulation result were also compared with other methods.
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