A Design Methodology for Uncertain, Unstable Plants with Hard Actuator Saturation

本研究项目的主要目标是开发一套透明和实用的设计工具，用于合成控制器，以保证在硬执行器饱和的不确定，不稳定设备中可接受的性能；开发一种方法，消除对整体控制的需要，更一般地说，不需要在控制回路中嵌入一个内部模型来解决大类问题；并演示了所开发的方法在两个实验室系统中的适用性；一种是附着在刚性轮毂上的单一柔性连杆，另一种是由蜗轮传动驱动的柔性连杆。为了达到建立设计方法的目的，首先考虑饱和控制下的稳定、不确定单输入单输出（SISO）对象。接下来，对SISO、线性、不确定植物，其极点在封闭的左半平面上，受致动器饱和；最后，对线性、不确定植物，其极点在封闭的右半平面上，受致动器饱和进行研究。初步结果表明，在饱和非线性周围使用局部反馈，使闭环系统具有一个符号的脉冲响应，使系统能够优雅地脱离饱和状态，从而使反馈在大部分情况下保持活跃。时域和频域方法都被考虑。为了证明所提出的设计方法的可行性，使用了目前在德克萨斯a&m大学PI实验室中可用的两个实验室规模系统。两个系统都配备了仪器，可由PC机控制。其中一个系统有一个线性化的模型，其轨迹以虚轴上的极点为特征，另一个系统有一个线性化的模型，其特征是在右半平面上的极点。演示的关键目标是让驱动直流电机饱和，并将其性能与未明确考虑硬饱和的控制器设计进行比较。

The major objectives of this research project are to develop a transparent and practical set of design tools for synthesizing controllers for guaranteeing acceptable performance in uncertain, unstable plants under hard actuator saturation; to develop a methodology that removes the need for integral control and more generically the need for imbedding an internal model inside a control loop for a large class of problems; and to demonstrate the applicability of the developed methodologies on two laboratory systems; one a single flexible link attached to a rigid hub and the other a flexible link driven by a worm gear transmission. In order to achieve the objective of developing a design methodology, first stable, uncertain singleinput single- output (SISO) plants under saturating control is considered. Next, SISO, linear, uncertain plants with poles in the closed left half plane subjected to actuator saturation are enclosed and finally linear, uncertain plants with poles in the right half plane subjected to actuator saturation are investigated. Preliminary results indicate that using local feedback around the saturation nonlinearity such that the closed loop system has an impulse response of one sign allows the system to gracefully come out of a saturation state so that feedback remains active for the most part. Both time domain and frequency domain methods are considered. To demonstrate the feasibility of the proposed design methodology two laboratory scale systems currently available in the PI's lab at Texas A&M University are used. Both systems are fully instrumented to be controlled by a PC. One of the systems has a model linearized about a trajectory characterized by poles on the imaginary axis and the other has a linearized model characterized by poles in the right half plane. The key goal of the demonstration are to let the driving d.c. motors saturate and to compare the performance with a controller design that does not explicitly consider hard saturation.