Question

please help answer all the question and dont skip. Thank you!

1. Sketch the pole-zero diagram for the following transfer function. Ensure you label the axes and the pole-zero locations. Assume a > b > 0. TF(s) = (s + a) s(s+b) 2. If the time constant of the lowest frequency pole in a system is 1 second, after approx- imately what period of time following turn-on could the system be considered to be in steady-state conditions? 3. The PID controller is a common controller in process control applications. What is the P, the I and the D and what do they each do? 4. Closed loop gain moves the poles. What factors external to the s-plane impact on this movement? 5. Given a system with three poles: s = –2 + j4, s = –2 – j4 and s = –10. Based on just the pole locations (you do not have to derive the time response mathematically), sketch the time response to a unit step input, clearly showing whether the response is under-damped, critically damped or over-damped and state your reasoning.

Answer 1

1:. Question solved on paper and uploaded .

2: Question solved on paper and uploaded .

3: These are actually controllers and are used to control the transient steady state responses as for the requirements.

The best system demands smallest rise time ,small settling time , smallest peak overshoot and small steady state error .To get the above requirements we add controllers to systems.

P in PID CONTROLLER stands for Proportional controler .It's purpose is to change the transient behaviour of the system by adjusting system gain.Transfer function isois written on paper .

I stands for Integral controller .it's purpose is to decrease the steady state errors inthe system.The integral controller adds 1 pole atbthe origin which increases the type of the system but the Steady state error decreases and stability is affected.. Before using Integral controller it is essential bro check the closed loop stability if the stability is affected then integral controller is not used.

D stands for derivative or Rate controller

It's purpose is to improve stability.The transfer function =sK

Example is tachometer .the derivative controller added 1 zero at the origin .Hence type decreases as type decreses the stability increses .the system becomes less stable.

4:The external parameter which impact the movement is The damping ratio (zeta) .

Zeta is the ratio of Energy lost to energy stored.

Since this is a second order system it is dependent on zeta .

As shown on paper and

5: solved on paper.

PAGE-3 Ee is blu and I Since Therefore the unit step ecesponse is ty my a these a 2 poles are these hence slower poles and determine response. 컨 Thumb up / Like

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Since ayb yo PAGE 1 T.FIS)= ZEROS POLES ZERO: stazo {s= POLES: ses+b=0 ?s=0 X = pole o = Zeko stb =0 Isa-b it has Since a pole at origin. Therefore it is marginally stable system. Also lowest frequency pole is the pole at Origin. constant (2) = we Know Time 7- Real part of Dominant Ple or lowest freqe pole z = 1 Z- a (infinite) After infinity time steady state. the system will achieve