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（设备）以期望的方式运行，例如，在飞机（设备）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，然后设计一个由数学方程描述的控制器，该控制器通常在软件中实现。由于植物模型的不确定性，这一过程往往很困难。

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.