RobustControlToolbox：鲁棒控制工具箱

Robust Control Toolbox

Design robust controllers for plants with uncertain parameters and unmodeled dynamics

Overview

Robust Control Toolbox™provides tools for analyzing and automatically tuning control systems for performance

and robustness. You can create uncertain models by combining nominal dynamics with uncertain elements, such

as an uncertain parameter or unmodeled dynamics. You can analyze the impact of plant model uncertainty on

control system performance and identify worst-ca combinations of uncertain elements. Using H-infinity or

mu-synthesis techniques, you can design controllers that maximize robust stability and performance. The toolbox

can automatically tune both SISO and MIMO robust controllers, including decentralized control architectures

modeled inSimulink. You can validate your design by calculating worst-ca gain and pha margins and

worst-ca nsitivity to disturbances.

Key Features

▪Modeling of systems with uncertain parameters or neglected dynamics

▪Worst-ca stability and performance analysis of uncertain systems

▪Automatic tuning of centralized and decentralized control systems

▪Robustness analysis and controller tuning in Simulink

▪H-infinity and mu-synthesis algorithms

▪General-purpo LMI solvers for feasibility, minimization of linear objectives, and generalized eigenvalue

minimization

▪Model reduction algorithms bad on Hankel singular values

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Model of an aircraft autopilot system (top), the algorithm ud to tune it (middle), and a plot of the clod-loop

respon to a step tpoint and a step disturbance before and after tuning (bottom). You can u Robust Control

Toolbox to automatically tune complex multivariable controllers consisting of basic Simulink blocks and then evaluate

the improvement in the clod-loop respon.

Modeling and Quantifying Plant Uncertainty

With Robust Control Toolbox, you can capture not only the typical, or nominal, behavior of your plant, but also

the amount of uncertainty and variability. Plant model uncertainty can result from:

▪Model parameters with approximately known or varying values

▪Neglected or poorly known dynamics, such as high-frequency dynamics

▪Changes in operating conditions

▪Linear approximations of nonlinear behaviors

▪Estimation errors in a model identified from measured data

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Plot, created by the accompanying MATLABcode, of the worst-ca gain of a system with an uncertain parameter.

Robust Control Toolbox lets you create an uncertain model by adding uncertain elements to nominal plant models and

then analyze the effect of uncertainty by calculating the worst-ca system performance.

The toolbox lets you build detailed uncertain models by combining nominal dynamics with uncertain elements,

such as uncertain parameters or neglected dynamics. By quantifying the level of uncertainty in each element, you

can capture the overall fidelity and variability of your plant model. You can then analyze how each uncertain

element affects performance and identify worst-ca combinations of uncertain element values.

Building and Manipulating Uncertain Models

Build uncertain state-space models and analyze the robustness of

feedback control systems that have uncertain elements.

Performing Robustness Analysis

Using Robust Control Toolbox, you can analyze the effect of plant model uncertainty on the clod-loop stability

and performance of the control system. In particular, you can determine whether your control system will

perform adequately over its entire operating range, and what source of uncertainty is most likely to jeopardize

performance.

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Robustness of Servo Controller for DC Motor

Model uncertainty in DC motor para墨家机关城 meters and analyze the effect of this

uncertainty on motor controller performance.

You can randomize the model uncertainty to perform Monte Carlo analysis. Alternatively, you can u more

direct tool形容动物的词语 s bad on mu-analysis and linear matrix inequality (LMI) optimization; the tools identify worst-ca

scenarios without exhaustive simulation.

Robust Control Toolbox provides functions to asss worst-ca values for:

▪Gain and pha margins, one loop at a time

▪Stability margins that take loop interactions into account

▪Gain between any two points in a clod-loop system

▪S沃尔森法则 ensitivity to external disturbances

The functions also provide nsitivity information to help you identify the uncertain elements that contribute

most to performance degradation. With this informa自评材料 tion, you can determine whether a more accurate model,

tighter manufacturing tolerances, or a more accurate nsor would most improve control system robustness.

Nominal and worst-ca rejection of a step disturbance (top) and Bode diagram of a nsitivity function (bottom).

Robust Control Toolbox lets you analyze the effect of plant model uncertainty on clod-loop stability and control

system performance.

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Synthesizing Robust Controllers

Robust Control Toolbox lets you automatically tune centralized and decentralized MIMO control systems. The

controller synthesis algorithms are bad on H-infinity or mu-synthesis techniques combined with nonsmooth

and LMI optimization. The algorithms are applicable to SISO and MIMO control systems. MIMO controller

synthesis does not require quential loop closure, and is therefore well suited for multiloop control systems with

significant loop interaction and cross-coupling.

Automatic Tuning of Fixed-Structure Control Systems

Most embedded control systems have a fixed, decentralized architecture with simple tunable elements such as

gains, PID controllers, or low-order filters. Such architectures are easier to understand, implement, schedule, and

retune than complex centralized controllers. Robust Control Toolbox provides tools for modeling and tuning

the decentralized control architectures. You can:

▪Specify tunable elements such as gains, PID controllers, fixed-order transfer functions, and fixed-order

state-space models

▪Combine tunable elements with ordinary linear time-invariant (LTI) models to create a tunable model of your

control architecture

▪Specify requirements on bandwidth, loop shape, tracking performance, and disturbance rejection

▪Automatically tune the controller parameters to meet requirements

▪Validate controller performance in the time and狠狠打屁股 frequency domains

Tuning of a Two-Loop Autopilot

Tune a two-loop autopilot to control the pitch rate and vertical

acceleration of an airframe.

H-Infinity and Mu-Synthesis Techniques

Robust Control Toolbox provides veral algorithms for synthesizing robust MIMO controllers directly from

frequency-domain specifications of the clod-loop respons. For example, you can limit the peak gain of a

nsitivity function to improve stability and reduce overshoot, or limit the gain from input disturbance to

measured output to improve disturbance rejection. Using mu-synthesis algorithms, you can optimize controller

performance in the prence of model uncertainty, ensuring effective performance under all realistic scenarios.

H-infinity and mu-synthesis techniques provide unique insight into the performance limits of your control

architecture, and let you quickly develop first-cut compensator designs.

Analyzing and Tuning Controllers in Simulink

Robust Control Toolbox provides tools for performing robustness analysis and tuning of controllers modeled in

Simulink.

Uncertainty Modeling and Robustness Analysis

The toolbox lets you model and analyze uncertainty in Simulink models. You can:

▪Introduce uncertainty into a Simulink model by using an Uncertain State Space block or by specifying block

linearization for any Simulink block

▪Linearize a Simulink model to create an uncertain system that reprents the whole Simulink model

▪Analyze the resulting uncertain system for stability and performance

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Linearization of Simulink Models with Uncertainty

Compute uncertain linearizations of a Simulink model.

Automatic Controller Tuning

Robust Control Toolbox lets you aut燃烧的英文 omatically tune decentralized controllers modeled in Simulink. You can:

▪Specify Simulink model blocks that should be tuned

▪Specify requirements on bandwidth, stability margins, tracking performance, and disturbance rejection

▪Automatically tune specified blocks to meet requirements

▪Validate your design by running nonlinear simulations

Using this approach you can automatically tune complex multivariable controllers that are modeled using

Simulink blocks. For example, you can automatically tune inner-loop and outer-loop PID controllers in a

multiloop control system without changing the control system architecture.

Tuning a Decentralized Control System for a Helicopter

5:45

Tune a complex flight control system fo朴叔俊 r a helicopter.

Reducing Plant and Controller Order

Detailed first-principles or finite-element plant models often have a large number of states. Similarly, H-infinity or

mu-synthesis algorithms tend to produce high-order controllers 评价同学的评语 with superfluous states. Robust Control Toolbox

provides algorithms that let you reduce the order (number of states) of a plant or controller model while

prerving its esntial dynamics. As you extract lower-order models, which are more cost effective to implement,

you can control the approximation error.

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Bode plots comparing magnitude and pha of the original and reduced-order models for the rigid body motion

dynamics of a multistory building.

The model reduction algorithms are bad on Hankel singular values of the system, which measure the energy of

the states. By retaining high-energy states and ignoring low-energy states, the reduced model prerves the

esntial features of the original model. You can u the absolute or relative approximation error to lect the

order, and u frequency-dependent weights to focus the model reduction algorithms on specific frequency

ranges.

Simplifying Higher-Order Plant Models

Approximate high-order plant models with simpler, lower-order models.

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