Control theory is interested in how we can allow systems with interconnected components to function with a desired system response (often autonomously). A key element of this is feedback within systems, which protect against disturbances, noise, and uncertainties of parameters.
This study is fundamentally the study of dynamical systems: systems whose behaviour changes over time, often in response to some external stimulus.
There are broad applications of control theory in:
- Robotics
- Autonomous vehicles
- Active prosthetic devices
- Bio-molecular regulatory networks
- Multi-agent networks (i.e., a smart grid, communications)
Basics
Some components used within control systems include:
- Sensors, which provide measurements of an external signal.
- Actuators, used by the system to alter or adjust the environment. These are devices that provides motive power to the process (like a DC motor).
- Plant (or process), which is the device or system under control.
- Controllers, which are a catch-all for blocks that cause closed-loop systems to perform in a specific way, i.e., stability, transient parameters, steady-state tracking.
An open-loop control system is a connected system that gets the desired response only with actuators and controllers, without a feedback connection. Closed-loop systems have feedback, which allow it to reject external disturbances and deal with noise better. Many control systems contain more than one feedback loop.
Block diagrams are an important visual representation of control systems. They allow the system’s components to be visualised in terms of their dependencies, and also facilitates design within Simulink and other design tools. Control systems also have several mathematical representations. These allow us to analyse the behaviour of the systems:
- State-space model
- Differential equation (input-output model)
- Transfer function (s-domain)
The conversion between the frequency domain and time domain with the Laplace transform is particularly important. The poles and zeroes in the frequency response can correspond directly with the behaviour of the system’s time response.
Resources
- Modern Control Systems, by Richard C. Dorf and Robert H. Bishop
- Modern Control Engineering, by Katsuhiko Ogata
- Feedback Systems, by Karl Johan Astrom and Richard M. Murray