## Control System Design

The field of control system design covers a broad spectrum of topics and methodologies. These include:

- System Identification, either from first principles or measured data.
- Modeling, using physical knowledge or dynamic equations.
- Optimization.
- Classical PID design.
- H-infinity loop shaping.
- Kalman filtering and state observers.
- Fixed-point arithmetic implementations.
- Simulation and real-time implementations

Tutorials and articles discussing many of the fundamentals of these topics in control system design are available on this website. These tutorials and articles discuss the mathematical foundations; practical considerations that must often be addressed when implementing real-time controllers; and how-to's for using leading model-based controller design software.

### PID Controller Tuning Using Loop Shaping Design

Loop shaping is one of the primary methodologies used for designing classical controllers such as PID controllers. In loop-shaping, the controller structure and gains are selected such that the magnitude of the frequency response of the open loop transfer function has particular characteristics -- or a particular shape.

This Loop Shaping Design tutorial is the first in a series of tutorials discussing the control design process. It discusses how the open-loop shape directly influences the performance of the closed loop. Specifically it shows how to select the P, I and D terms of a PID controller to achieve desirable open and closed loop responses. The frequency response of the transfer functions is viewed using a Bode diagram. Read Tutorial...

### Kalman Filters - Theory and Implementation

Kalman Filters are a form of predictor-corrector used extensively in control system design for estimating the unmeasured states of a process. The estimated states may then be used as part of a strategy for control law design.

The Kalman Filter tutorial discusses the original Kalman Filter formulation which was developed for linear discrete-time processes (or at least processes that may be modeled with sufficient accuracy as a linear discrete-time process). Other tutorials discuss non-linear forms of the Kalman Filter -- the Extended Kalman Filter and a continuous time formulation -- the Kalman-Bucy Filter.

In addition, the following implementation examples are provided:

- Kalman Filtering in Simulink
- Kalman-Bucy Filtering in Simulink
- Object Tracking using an Extended Kalman Filter
- Using an Extended Kalman Filter for Estimating Vehicle Dynamics and Mass

If you are unfamiliar with the mathematics behind the Kalman Filter, Extended Kalman Filter or the Kalman-Bucy Filter, then start with the Kalman Filter, Extended Kalman Filter and Kalman-Bucy Filter tutorials.