MATLAB Examples

You can create and analyze uncertain state-space models made up of uncertain state-space matrices. In this example, create a MIMO system with parametric uncertainty and analyze it for

Use Robust Control Toolbox™ to build uncertain state-space models and analyze the robustness of feedback control systems with uncertain elements.

Design a feedback controller for a plant with uncertain parameters and uncertain model dynamics. The goals of the controller design are good steady-state tracking and

Consider a stable transfer function,

Suppose that the variables of the problem include a 3-by-3 symmetric matrix X and a 3-by-3 symmetric Toeplitz matrix, Y , given by:

Consider three matrix variables, X , Y , and Z , with the following structure.

In many cases, a model's j\omega -axis poles are important to keep after model reduction, e.g., rigid body dynamics of a flexible structure plant or integrators of a controller. A unique

Given a system G in LTI form, the following commands reduce the system to any desired order you specify. The judgment call is based on its Hankel singular values.

Use Robust Control Toolbox™ to approximate high-order plant models by simpler, low-order models.

In most cases, the multiplicative error model reduction method bstmr tends to bound the relative error between the original and reduced-order models across the frequency range of

Construct a generalized state-space ( genss ) model of a control system that has both tunable and uncertain parameters. You can use systune to tune the tunable parameters of such a model to

Tune a fixed-structure controller for multiple operating modes of the plant.

Perform mixed mu-synthesis with the dksyn command in the Robust Control Toolbox™. Here dksyn is used to design a robust controller for a two mass-spring-damper system with uncertainty in

Use Robust Control Toolbox™ to design a multi-input, multi-output controller by shaping the gain of an open-loop response across frequency. This technique is applied to controlling the

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

Use Robust Control Toolbox™ function ncfsyn to improve the stability robustness of a closed-loop system while approximately maintaining the high-gain and low-gain characteristics of

Robustly tune a controller for reducing vibrations in a flexible beam. This example is adapted from "Control System Design" by G. Goodwin, S. Graebe, and M. Salgado.

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

Robustly tune a PID controller for a DC motor with imperfectly known parameters.

Take into account model uncertainty when tuning a motion control system.

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

Robustly tune a PID controller for an uncertain mass-spring-damper system modeled in Simulink.

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

Use Robust Control Toolbox™ to design a robust controller for an active suspension system.

One of the most powerful yet simple controller synthesis tools is loopsyn. Given an LTI plant, you specify the shape of the open-loop systems frequency response plot that you want. Then

Use Robust Control Toolbox™ to analyze and quantify the robustness of feedback control systems. It also provides insight into the connection with mu analysis and the mussv function.

Illustrates the pitfalls of using frequency gridding to compute robustness margins for systems with only real uncertain parameters. It presents a safer approach along with ways to

Use uncertain objects in Robust Control Toolbox™ to model uncertain systems and to automate robustness calculations using the robustness analysis tools.

Calculate the robust stability and examine the worst-case gain of the closed-loop system described in System with Uncertain Parameters . The following commands construct that system.

You can make substitutions for uncertain elements in uncertain matrices and models using usubs . Doing so is useful for evaluating uncertain objects at particular values of the uncertain

Use Robust Control Toolbox™ to analyze the robustness of an uncertain system with only real parametric uncertainty. You compute the stability margins for a rigid body transport aircraft

When sampling an ultidyn element or an uncertain object that contains a ultidyn element, the result is always a state-space ( ss ) object. The property SampleStateDimension of the ultidyn

The command usample randomly samples the uncertain system at a specified number of points. Randomly sample an uncertain system at 20 points in its modeled uncertainty range. This gives a

You can generate an array from an uncertain object by replacing the uncertain elements with specified values. There are several ways to do this using usubs .

A common way to generate an array is to sample the uncertain elements of an uncertain object. This example shows how to generate arrays by taking random samples of a umat uncertain matrix that

Varying the eccentricity parameter E amounts to changing the shape of the uncertainty disk \left(1+\delta \right)\; from which the gain and phase margins are derived. Disks of different

If an uncertain matrix or model object ( umat , uss , ufrd ) has many uncertain parameters, it is often useful to freeze some, but not all, of the uncertain parameters to specific values for

Illustrates how to compute classical and disk-based gain and phase margins of a control loop modeled in Simulink®. To compute stability margins, linearize the model to extract the

Use Simulink® blocks and helper functions provided by Robust Control Toolbox™ to specify and analyze uncertain systems in Simulink and how to use these tools to perform Monte Carlo

Use the Robust Control Toolbox™ command ucover to model a family of LTI responses as an uncertain system. This command is useful to fit an uncertain model to a set of frequency responses

Compute uncertain linearizations using Robust Control Toolbox™ and Simulink® Control Design™. There are two convenient workflows offered depending on how Simulink is used. The

Make a Simulink® block linearize to an uncertain variable at the command line. To learn how to specify an uncertain block linearization using the Simulink model editor, see

You create uncertain matrices ( umat objects) by creating uncertain parameters and using them to build matrices. You can then use uncertain matrices to build uncertain state-space models.

You decompose an uncertain model into a fixed certain part and normalized uncertain part using the lftdata command. To see how this command works, create a 2-by-2 uncertain matrix ( umat )

Create uncertain real parameters, modify properties such as range of uncertainty, and sample uncertain parameters.

You can create a 1-by-1 (scalar) positive-real uncertain linear dynamics element, whose frequency response always has real part greater than -0.5. Set the SampleStateDimension property

Create a 4-by-3 uncertain complex matrix ( ucomplexm ), and view its properties. The simplest construction requires only a name and nominal value.

It is possible to form interconnections of uss objects. A common example is to form the feedback interconnection of a given controller with an uncertain plant.

An uncertain parameter has a name (used to identify it within an uncertain system with many uncertain parameters) and a nominal value. Being uncertain, it also has variability, described in

Uncertain frequency responses ( ufrd ) arise naturally when computing the frequency response of an uncertain state-space model ( uss ). They also arise when frequency response data in an frd

Uses the hinfstruct command to tune a fixed-structure controller subject to H_\infty constraints.

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