Linear periodic controller design

在系统控制中，目标是通过使用（自动）控制器使物理系统（工厂）以期望的方式动作，例如在飞机（工厂）上使用自动驾驶仪（控制器）来保持速度，高度和方向。控制系统设计的第一步是获得被控对象的数学模型，然后设计一个控制器，该控制器由数学方程描述，通常用软件实现。由于被控对象模型的不确定性，这一过程通常很困难，目前实现的大多数控制器都是用具有固定参数的线性方程来描述的，例如众所周知的比例积分微分（PID）补偿器。随着微处理器变得更快，实现（可能复杂的）非线性和/或时变控制器变得可能。这里的目标是开发先进的线性周期控制器，提供增强的容忍植物模型的不确定性，以及良好的性能。我们正在考虑三种不同的情况：（i）自适应控制，其中对象参数是未知的，可能会迅速随时间变化，（ii）鲁棒控制，其中对象是知之甚少，但参数是固定的，（iii）控制延迟，其中对象模型是众所周知的，但在反馈回路中存在不确定的延迟，例如当通过Internet进行控制时，这项工作具有潜在的长期利益，无论控制被用于何处，从机器人到航空航天到工业自动化，我以前的研究生都在所有这些领域工作。

In systems control, the objective is to make a physical system (the plant) act in a desired manner through the use of an (automatic) controller, e.g. an autopilot (the controller) is used on an aircraft (the plant) to maintain speed, altitude and direction. The first step in control system design is to obtain a mathematical model of the plant, and then one designs a controller, described by a mathematical equation, which is typically implemented in software. This process is often difficult due to uncertainty in the plant model.Most controllers presently implemented are described by linear equations with fixed parameters, such as the well-known proportional-integral-differential (PID) compensator. As microprocessors become faster, it is becoming possible to implement (possibly complicated) nonlinear and/or time-varying controllers. The objective here is to develop advanced linear periodic controllers which provide enhanced tolerance to plant model uncertainty as well as good performance. We are considering three different contexts:(i) adaptive control, in which the plant parameters are unknown and possibly rapidly time-varying,(ii) robust control, in which the plant is poorly known, but the parameters are fixed, and(iii) control with delay, in which the plant model is well known but there is an uncertain delay in the feedback loop, such as when carrying out control over the Internet.This work has potential long-term benefits wherever control is used, from robotics to aerospace to industrial automation, and my former graduate students work in all of these areas.