Robust Control Toolbox

Design robust controllers for uncertain plants

 

Robust Control Toolbox™ provides functions and blocks for analyzing and tuning control systems for performance and robustness in the presence of plant uncertainty. You can create uncertain models by combining nominal dynamics with uncertain elements, such as uncertain parameters or unmodeled dynamics. You can analyze the impact of plant model uncertainty on control system performance and identify worst-case combinations of uncertain elements. H-infinity and mu-synthesis techniques let you design controllers that maximize robust stability and performance.

The toolbox adds robust tuning to the automated tuning capabilities of Control System Toolbox™. The tuned controllers can be decentralized with multiple tunable blocks spanning multiple feedback loops. You can optimize performance for the nominal plant while enforcing a lower, minimum performance over the entire range of uncertainty.

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Modeling and Quantifying Plant Uncertainty

Capture not only the typical, or nominal, behavior of your plant, but also the amount of uncertainty and variability.

Build detailed uncertain models by combining nominal dynamics with uncertain elements, such as uncertain parameters or neglected dynamics. Represent uncertain systems using uncertain state-space and frequency response models.

Add uncertainty when linearizing Simulink models by designating some blocks as uncertain.

Bode plot of a system with uncertain parameters.

Performing Robustness Analysis

Analyze how uncertainty affects stability and performance.

Robust Stability and Performance

Calculate the disk-based gain and phase margins of SISO and MIMO feedback loops. Quantify how uncertainty affects the stability and performance of your control system. Compute robust stability and robust performance margins for system-specific uncertainty.

Disk margins provide a fuller picture of robust stability than classical gain and phase margins.

Worst-Case Analysis

Identify worst-case combinations of uncertain element values. Compute the worst-case values of tracking error, sensitivity, and disk margins. Compare nominal and worst-case scenarios.

Nominal and worst-case rejection of a step disturbance.

Monte Carlo Analysis

Generate random samples of uncertain system within the specified uncertainty range. Visualize how uncertainty affects the system time and frequency responses. Use the Uncertain State Space block to inject uncertainty in Simulink and perform Monte Carlo simulations.

Nyquist diagram of sampled systems.

Designing and Tuning Robust Controllers

Synthesize and automatically tune centralized or distributed controllers.

H-infinity and Mu Synthesis

Synthesize robust MIMO controllers using algorithms such as H-infinity and mu-synthesis.

Optimize H-infinity performance of fixed control structures. Automate loop-shaping tasks using the mixed-sensitivity or Glover-McFarlane approaches.

Uncertain closed-loop model with H-infinity controller.

Robust Tuning of Uncertain Control Systems

Specify tuning requirements such as tracking performance, disturbance rejection, noise attenuation, closed-loop pole damping, and stability margins. Simultaneously tune for multiple plant models or control configurations. Maximize performance over the uncertainty range of plant parameters. Assess controller robustness in time and frequency response plots.

Control System Tuner with multiple parameter variations (tuned response).

Reducing Plant and Controller Order

Simplify plant or controller models while preserving essential dynamics.

Reduce model order using additive or multiplicative error methods based on Hankel singular values of the system. Reduce the order of controllers produced by H-infinity and mu-synthesis algorithms to eliminate superfluous states while preserving the essential dynamics.

Bode plots comparing the magnitude and phase of the original and reduced-order models for the rigid body motion dynamics of a multistory building.

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