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Robust, Fragile, or Optimal? by Keel and Bhattacharya in IEEE database

Take into account that tobustness evaluation depends on the design (mathematical) tool ... Robust, fragile and Optimal is linear systems oriented ...

for electrical machines i use always ajdustement of gain used in the control,or if you want more robustness you can use GA or Neural networks,ils gives good results.

It depends on whether you are working with a deterministic or stochastic control systems. But you can check the robustness by changing parameters of the control system and evaluating how they influence some measure of performance e.g amount of actuation, tracking error, disturbance rejection etc.

Mohohlo, what if deterministic and what if stochastic? Could you elaborate more..

deterministic cases are much nicer since by changing a parameter of the system you can solve the resulting differential equations (or transfer functions in the linear case) to see the effects on the performance variables (or cost functions thereof). In the stochastic case the probabilistic nature of the cause-effect makes it a bit tricky. Which are you working with?

the robustness problem is always resolved face to the parameters that influence on the system. Generaly the robustness test can be verified by sensitivity calculation.

You can show some of my papers. Is talk about motor control robustness

A system is robust if despite the change of initial conditions and the change of environment will remain stable, so apply the controller on the system in order, after changing the initial settings or add a noise and see the result, if the system will remain stable it means that your controller is robust.

well robutness is the ability to with stand with characteristics

For stochastic case try using Linear Parameter Varying system depending of the parameter variations. Then having some polytopic approximation will solve the problem.

There are many approaches to solving robustness problems. In general, the most frequently used method is applying "small-gain theorem". This is a powerful tool for solving the LTI system's robustness issue. A detailed discussion can be found in many literature and books.

Generally, there are two mainstreams the control community - 1) use the (feedback) controller to get a desired closed-loop performance, and 2) to stabilize the closed-loop system in presence of disturbances and/or unmodeled system dynamics. The people from the first group call a controller 'robust' if it can deliver the required closed-loop performance in presence of disturbances and/or unmodeled system dynamics. In any case, a measure of the robustness is the tolerated uncertainty before the closed-loop system becomes unstable. Traditionally, the gain and phase margins, GM and PM, are such figures of merit, when one looks at the frequency response, and keeps in mind that the close-loop stability is determined by the open-loop 'loop transmission'. The sensitivity function, or complementary sensitivity function are a natural extension of the GM/PM that limit the H_inf (!) peak.

The system robust stability and the system robust performance are the two things that a robust controller must offer. There are two approches to design a robust controller; the first is to use special theories which are developed to give robust controller like H-infinity loop shapping, Khartinove theorem, small-gain theorem, mu synthesis, etc. The second approch is to design on the basis of known structures, which have some robustness features, like the PID, nueral networks, etc. Only with the second approach a test of robustness has to performed.

Generally robustness of a controller is not directly measured. What is measured is the robustness of the closed loop system with controller. There are four things in it: 1. Nominal stability, 2. Nominal performance, 3. Robust stability and 4. Robust performance. Usually the complexity of achieving a controller performance increases in the ascending order of the performance indicated. There is an usual assumption on the perturbation like infinite norm of the perturbation does not increase more than 1 in magnitude and is the only assumption. Then controller design proceeds. Nominal stability and performance is what a controller achieves usually. Then you consider perturbation in the model and design a controller. There are various methods available then to design the controller. Simplest ones are loop shaping approaches to computationally intensive H-infinity methods. Hope this helps.

Anybody can offer any insights from a chemical engineering perspective?

How the the control is still stable when the plant is subject to uncertainties (parametric /non parametric ). The uncertainties can appear in many forms (additive, multiplicative,etc). There is a good book about robust control, Robust Control Design with MATLAB® by Da-W Gu, P. Hr. Petkov, M. M. Konstantinov. It covers about four things like Seshadhri mentioned. The good thing is it comes with numerical examples for many different plants.

There are some procedures for synthesis of controllers, that operate by specifying the desired robustness margins. Quantitative Feedback Theory , QFT for short, is one of them.