CONTROL SYSTEMS(EC 205, 3L + 1T)

Force (Torque)-voltage(Current) analogyMechanicalElectrical

Force (Torque)-voltage(Current) analogy

Find the electrical equivalent of the system

Time Domain Specifications (Design Specifications)

Time Domain Specifications (Design Specifications)TF may be of any order. However, it can be reduced to 1st and 2nd order for easy analysis

Test Signals1. Step Input2. Ramp Input

Test Signals3. Parabolic Input

Time Domain Response of 1st Order Systems

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.

General form:

Roots of denominator:Where,: Damping ration: Undamped natural frequencyTime Domain Response of 2nd Order Systems

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

- 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

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

Time domain Response Specifications

Time domain Specifications

Time domain Specifications

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.

Settling Time tsThe time required for the transients damped oscillation to reach and staywithin 2% of the steady-state value.

Design a controller (as) so that overshoot is 4.6 %Requirement

Without controller

With controllerRequirement