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7/30/2019 SN 3 What is Robust Control
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Dr. S. UshakumariAssociate Professor
Department of Electrical EngineeringCollege of Engineering Trivandrum
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It is the analysis and design of
control systems in the presence of
uncertainty.
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1. Obtain a mathematical model of the system
2. Use a control design method together withthe system model to come up with acontroller with certain parameters and
structure.3. Simulate the closed loop system to verify
that specifications are met.
4. Implement the controller in the real system
and tweak the controller parameters if necessary.
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Signal uncertainty.
Eg. Unknown disturbances, measurementnoise.
Model uncertainty.Eg. Unknown parameters, unmodelled high
frequency dynamics, ignorednonlinearities.
Uncert ain t y cann ot b e avoided, bu t i t can b emanaged.
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1. Identify and quantify uncertainty
2. Analyse the impact of uncertainty on controlsystem performance (Analyse the robustnessof the control system)
3. Design control systems that provide goodperformance in the presence of uncertainty(Design robust control systems)
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One degree of freedom controller
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Upto page 8 of what I robust
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The term complementary followsfrom the identity S +T = I
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Stability is one of the main issues in controldesign.
Two methods commonly used to determineclosed loop stability are:
Evaluate the poles of the closed loop system
(1+L(s) = 0). Plot the frequency response of L(s) in the
complex plane and use Nyquist's stabilitycriterion.
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Time domain performance (step response)
Rise time
Settling time
Overshoot
Steady stateoffset
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Gain and phase margins
Typically, we require GM > 2 and PM > 300
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The concept of bandwidth is important inunderstanding the benefits and trade-offsinvolved with feedback.
The closed loop bandwidth, B, is the
frequency where first crosses
from below.
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)3(707.02/1 dB)( jS
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Loop shaping
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e = y - r = -Sr +SGdd - Tn
where S = 1/(1+L) and T = L/(1+L).
The following trade-offs exist:
Good command following L large.
Good disturbance rejection L large
Good noise attenuation L small. Small input u K,L small.
Nominal stability (stable plant) L small
Robust stability (stable plant) L small
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