Robust Control Toolbox™ 3.3.1

Product Description

• Introduction and Key Features
• Working with the Robust Control Toolbox
• Modeling and Quantifying Plant Uncertainty
• Performing Robustness Analysis
• Synthesizing Robust Multivariable Controllers
• Reducing Controller and Plant Model Order

Synthesizing Robust Multivariable Controllers

The Robust Control Toolbox provides a variety of controller synthesis algorithms based on loop shaping, H or µ-synthesis, and LMI techniques. These algorithms are applicable to SISO and MIMO control systems. MIMO controller synthesis does not involve sequential loop closure, and is therefore well suited to multi-loop control systems with strong loop interaction and challenging I/O decoupling requirements.

Loop Shaping

Performance and robustness requirements can often be expressed in terms of the open-loop response gain. For example, high gain at low frequencies reduces steady-state offsets and improves disturbance rejection. Similarly, high-frequency roll-off improves stability where the plant model is poor. Loop shaping aims at designing a controller that achieves a particular loop shape.

The Robust Control Toolbox provides tools to automate computing controllers that best match user-defined loop shape. In MIMO systems, these tools operate on the singular values of the open-loop response to increase or decrease the gain in all input/output directions.


Loop shaping tools automate frequency-domain design of the open-loop response. Click on image to see enlarged view.

H and µ-Synthesis

The Robust Control Toolbox provides several algorithms for synthesizing robust MIMO controllers directly from closed-loop specifications. These specifications may include point-to-point gain limitations, frequency-dependent gain constraints, sensitivity constraints, pole placement objectives, and LQG-like cost functions. Powerful µ-synthesis algorithms can optimize controller performance in the presence of model uncertainty, ensuring effective performance under all realistic scenarios. Together, these tools provide unique insight into the performance limits of your control architecture, as well as quick first-cut compensator designs.