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)以期望的方式运行，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对象的数学模型，然后设计由数学方程描述的控制器，该控制器通常用软件实现。由于工厂模型的不确定性，这一过程通常是困难的。 目前实现的大多数控制器都是用固定参数的线性方程来描述的，如著名的比例-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，以增强对被控对象模型不确定性的容忍度和良好的性能。 在本提案中，我们考虑了两种不同的情况： (I)自适应控制，其中对象参数未知并且可能快速时变，以及 (2)分散控制，即信息流受到限制，这可能是由于传感器和执行器在地理上的分离，例如在控制大型电网时。 这项工作是基础性的，但无论在哪里使用控制，从机器人到航空航天再到化学加工行业，都有潜在的长期好处。

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. In this proposal we consider two different contexts: (i) adaptive control, in which the plant parameters are unknown and possibly rapidly time-varying, and (ii) decentralized control, in which there is a constraint on information flow, perhaps arising from a geographical separation of sensors and actuators, such as in the control of a large power grid. This work is of a fundamental nature but has potential long-term benefits wherever control is used, from robotics to aerospace to the chemical processing industry.