The controller synthesis is probably the most difficult and time consuming stage of embedded control system design. In this chapter, we present the design and analysis of five different discrete-time controllers which may be implemented successfully in embedded systems. To compare the controller properties, they are applied in single precision to steer one and the same system, namely, the cart-pendulum system presented in Chapter 2. This system has some peculiarities which lead to difficulties in the implementation of design methods. One of our primary goals is to investigate the behavior of the corresponding closed-loop systems in presence of plant uncertainty.

Chapter Contents:

• 4.1 PID controller
• 4.2 LQG controller with integral action
• 4.2.1 Discrete-time LQG controller
• 4.2.2 Colored measurement noise
• 4.2.3 LQG controller with bias compensation
• 4.3 LQ regulator with H∞ filter
• 4.3.1 Discrete-time H∞ filter
• 4.3.2 H∞ Filter with bias compensation
• 4.4 H∞ Design
• 4.4.1 The H∞ design problem
• 4.4.2 Mixed-sensitivity H∞ control
• 4.4.3 Two degrees-of-freedom controllers
• 4.4.4 Numerical issues in H∞ design
• 4.5 Synthesis
• 4.5.1 The synthesis problem
• 4.5.2 Replacing with its upper bound
• 4.5.3 DK iteration
• 4.5.3.1 First step of DK iteration: holding D fixed
• 4.5.3.2 Second step of DK iteration: holding K fixed
• 4.5.4 Numerical issues in synthesis
• 4.6 Controller comparison
• 4.7 HIL simulation
• 4.8 Notes and references

Inspec keywords: control system synthesis; closed loop systems; embedded systems; discrete time systems; pendulums

Other keywords: plant uncertainty; cart-pendulum system; discrete-time controllers; controller synthesis; closed-loop systems; embedded control system design; design methods; controller design

Subjects: Control system analysis and synthesis methods; Discrete control systems