Mu Synthesis

Robust controller synthesis for uncertain systems

The technique of μ synthesis extends the methods of H_∞ synthesis to design a robust controller for a SISO or MIMO uncertain plant. You can perform μ synthesis on plants with parameter uncertainty, dynamic uncertainty, or both using the musyn command.

musyn uses an iterative process called D-K iteration to optimize the robust H_∞ performance of the system. To get started with μ synthesis, see Robust Controller Design Using Mu Synthesis.

Functions

`musyn`	Robust controller design using mu synthesis
`musynOptions`	Options for `musyn`
`musynperf`	Robust H_∞ performance optimized by `musyn`
`cmsclsyn`	Approximately solve constant-matrix, upper bound µ-synthesis problem

Topics

Robust Controller Design Using Mu Synthesis
Use μ synthesis to design an unstructured robust controller or a fixed-structure robust controller for an uncertain plant.
Improve Results of Mu Synthesis
You can sometimes improve the results of controller synthesis with musyn by changing certain computation options.
Robust Performance Measure for Mu Synthesis
The measure of robust performance calculated by musynperf and optimized by musyn is the μ upper bound.
D-K Iteration Process
The musyn command synthesizes robust controllers using an algorithm that includes iterating between optimizing robust performance (the D step) and computing an H_∞ controller (the K step).

Related Information

H-Infinity and Mu Synthesis

Featured Examples

First-Cut Robust Design

Use the Robust Control Toolbox™ commands usample, ucover and musyn to design a robust controller with standard performance objectives. It can serve as a template for more complex robust control design tasks.

Open Script

Robust Control of Active Suspension

In this example, use H_∞ synthesis to design a controller for a nominal plant model. Then, use μ synthesis to design a robust controller that accounts for uncertainty in the model.

Open Live Script

Control of a Two-Tank System

Use Robust Control Toolbox™ to design a robust controller (using D-K iteration) and to do robustness analysis on a process control problem. In our example, the plant is a simple two-tank system.

Open Script

Simultaneous Stabilization Using Robust Control

Uses the Robust Control Toolbox™ commands ucover and musyn to design a high-performance controller for a family of unstable plants.

Open Live Script

Control of Aircraft Lateral Axis Using Mu Synthesis

Use mu-analysis and synthesis tools in the Robust Control Toolbox™. It describes the design of a robust controller for the lateral-directional axis of an aircraft during powered approach to landing. The linearized model of the aircraft is obtained for an angle-of-attack of 10.5 degrees and airspeed of 140 knots.

Open Live Script

Control of a Spring-Mass-Damper System Using Mixed-Mu Synthesis

Perform mixed-mu synthesis with the musyn command in the Robust Control Toolbox™. Here musyn is used to design a robust controller for a two mass-spring-damper system with uncertainty in the spring stiffness connecting the two masses. This example is taken from the paper "Robust mixed-mu synthesis performance for mass-spring system with stiffness uncertainty," D. Barros, S. Fekri and M. Athans, 2005 Mediterranean Control Conference.

Open Script

Robust Controller for Spinning Satellite

Design a robust controller using an uncertain plant model that accounts for gain and phase variations. This example expands on the example MIMO Stability Margins for Spinning Satellite.

Open Live Script

Robust MIMO Controller for Two-Loop Autopilot

Design a controller for a two-loop autopilot that is robust against gain and phase variations in the multichannel feedback loop.

Open Script