control 4_5
DESCRIPTION
paady notes iiit jabalpur eceTRANSCRIPT
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CONTROL SYSTEMS(EC 205, 3L + 1T)
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Force (Torque)-voltage(Current) analogyMechanicalElectrical
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Force (Torque)-voltage(Current) analogy
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Find the electrical equivalent of the system
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Time Domain Specifications (Design Specifications)
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Time Domain Specifications (Design Specifications)TF may be of any order. However, it can be reduced to 1st and 2nd order for easy analysis
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Test Signals1. Step Input2. Ramp Input
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Test Signals3. Parabolic Input
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Time Domain Response of 1st Order Systems
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Design SpecificationsTime constant, The time for e-at to decay 37% of itsinitial value.
Rise time, trThe time required to gofrom 10 to 90 % or 0 to 100 % of its final value.
Settling time, tsThe time for the response to reach,and stay within 2-5% of its final value.
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General form:
Roots of denominator:Where,: Damping ration: Undamped natural frequencyTime Domain Response of 2nd Order Systems
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Damping of System- According the value of , a second-order system can be set into one of the four categories:Overdamped - when the system has two real distinct poles ( >1).
Underdamped - when the system has two complex conjugate poles (0
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- Given a step input, i.e., R(s) =1/s, then the system output (or step response) is;- Taking inverse Laplace transform, we have the step response;Where;or
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Rise time, trThe time for the waveform to go from 10 to 90 or 0 to 100 % of its final value.
Peak time, tpThe time required to reach the first or maximum peak.
Settling time, tsThe time required for the transients damped oscillation to reach and staywithin 2% of the steady-state value.
Time domain Response Specifications
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Time domain Response Specifications
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Time domain Specifications
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Time domain Specifications
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Percent overshoot, %OSThe amount that the waveform overshoots the steady-state, or final value at peak time, expressed as a percentage of the steady-state value.
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Settling Time tsThe time required for the transients damped oscillation to reach and staywithin 2% of the steady-state value.
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Design a controller (as) so that overshoot is 4.6 %Requirement
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Without controller
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With controllerRequirement