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
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:
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.
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
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
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
Uses the Robust Control Toolbox™ commands ucover and dksyn to design a high-performance controller for a family of unstable plants.
Uses the hinfstruct command to tune a fixed-structure controller subject to constraints.
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.
Robustly tune a PID controller for a DC motor with imperfectly known parameters.
Take into account model uncertainty when tuning a motion control system.
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
Calculate the robust stability and examine the worst-case gain of the closed-loop system described in docid:robust_gs.f3-11915. The following commands construct that system.
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
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 .
You can make substitutions for uncertain elements in uncertain matrices and models using docid:robust_ref.f10-90905 . Doing so is useful for evaluating uncertain objects at particular
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
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 (docid:robust_ref.f10-328118 objects) by creating uncertain parameters and using them to build matrices. You can then use uncertain matrices to build
You decompose an uncertain model into a fixed certain part and normalized uncertain part using the docid:robust_ref.f10-120643 command. To see how this command works, create a 2-by-2
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
To create an uncertain state-space model, you first use control design blocks to create uncertain elements. Then, use the elements to specify the state-space matrices of the system.
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.
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 loopmargin to analyze the closed-loop robustness of Simulink models with specified loop-breaking points.
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.
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
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.
Use Robust Control Toolbox™ to build uncertain state-space models and analyze the robustness of feedback control systems with uncertain elements.