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As a control system engineer you have been asked to design a controller that would improve the error and the transient response for the unity feedback system below. The proposed solution must be cost-effective, so consider a passive network-based compensator. The transient response of the closed-loop transfer function to a ramp input has a 30% overshoot (%OS = 30) and a settling time Ts= 2.73 seconds. You need to decrease the peak time by a factor of 2, decrease the percentage overshoot by a factor of 2 and improve the steady-state error by a factor of 30. a. What type of compensator should you implement in this case? b. Find the gain K for the uncompensated system. c. Find the peak time, Tp, the velocity constant, Kv, and the steady-state error, for the uncompensated system. d. Assume that the compensator zero is placed at -5 and design your compensator accordingly. R(S) + E(s) K s(s+5)(s+11)

Answer 1

Q) a. For decreasing the steady state error we need to use lag compensator for the given tranfer function system

Q) b,c ) Gain K and steady state error is calculated below step by step,i have calculated in details.
11 0.3 ( (2) s(3+5) (sell) Mp, overshoot = e As Nina? - AS/Nens = mm (0.3) - 0.2 I-2 S = 1:44 1.44fK S = 0.1273 a 0.356 1.4 lt (A) - lt = 0 s(5+5) (STU) s(s' +168+55) + K 50 33 + 108²558tk zo S

using Routh Heswita cridesian s3 - K 81 16815-K K for the stability, 16815-k so ka 240 steady stote esserar ess et SBCB) = S. (82 = 4 6.1 sto t6 (8) sto I 240 s(SP3)(sto =lt sto s(s+5) (5411 + 940) 55 stugcers) 240 0.229

Q)c .Velocity error coefficient is calculated below -
velocity essor longtone S.R(S) Css = et s → 16 (8) steady stole essor with Romp Esput is given 9 By sit - et s to 2 et sto st SG (8) a sto 3 G 8) Kv KV =lle sto SG (8) =et fik S & (345) (Stil) 240 SI- Velocity 4.36 esser Kv= 4.36 Coefficient
The peak time tp is calculated below -
A peak time to, to In vende taking Auxilary equation, P68 A K = 0 1 168 & 240 20 s²= -290 15 LB- s = vis ord/s. - 3.87 rools tp = 5 bosta 3182 vi-0.356 ک A .2 3.88% 0.87 peak tim to 0.933 sec