Review questions

EXPERIMENT 5 TRANSIENT RESPONSE ANALYSIS Purpuse :The main purpose of software experiments is to introduce the computer-aided control system analysis and design. In this experiment, you will practice about transient response analysis by using MATLAB. İntroduction Rise Time : This time is represented by tr. We define rise time in case of under damped systems where the value of ζ is less than one, in this case rise time is defined as the time required by the response to reach from zero value to hundred percent value of final value. Peak Time : On differentiating the expression of c(t) we can obtain the expression for peak time. dc(t)/ dt = 0 we have expression for peak time Maximum overshoot : Now it is clear from the figure that the maximum overshoot will occur at peak time tp hence on putting the valye of peak time we will get maximum overshoot as Settling Time : Settling time is given by the expression Under damped system : A system is said to be under damped system when the value of ζ is less than one. In this case roots are complex in nature and the real parts are always negative. System is asymptotically stable. Rise time is lesser than the other system with the presence of finite overshoot. Critically damped system : A system is said to be critically damped system when the value of ζ is one. In this case roots are real in nature and the real parts are always repetitive in nature. System is asymptotically stable. Rise time is less in this system and there is no presence of finite overshoot. Over damped system : A system is said to be over damped system when the value of ζ is greater than one. In this case roots are real and distinct in nature and the real parts are always negative. System is asymptotically stable. Rise time is greater than the other system and there is no presence of finite overshoot. Results (Part 1) Specify the nature of the system response 1) 0 < ζ <1 underdamped 2) ζ >1 overdamped 3) ζ=1 crtically damped 4) ζ=0 zerodamped PART 1- 2 damping ratio ζ and natural frequency Wn Part 2 (rise time , peak time , settling time , and maximum overshoot values.) Part 2 (Specify the nature of the system.) **Transfer function= K/(s^2+8s+K) K=12 Overdamped K=16 Critacallydamped K=20 Underdamped K=50 Underdamped Comments : for k=12 (POLES and FREQUENCY) Results of the poles and frequency would have come out exactly the same but different output. In this case roots are real and distinct in nature and the real parts are always negative. System is asymptotically stable. Rise time is greater than the other system and there is no presence of finite overshoot. An overdamped response is the response that does not oscillate about the steady-state value but takes longer to reach than the critically damped case. Here damping ratio is >1 it is the response of a system with respect to the input as a function of time Plot the step responses C) EFFECT OF ADDITIONAL POLES Discuss the effect of third pole location on the step responses. For which values of , the systems can be modeled as a second order system? If the system has a cluster of poles and zeros that are much closer (5 times or more) to the origin than the other poles and zeros, the system can be approximated by a lower order system with only those dominant poles and zeros. (2 kutupla simetrik elde edilir reel kızma sonradan eklediğimiz 3.kutup 5 kat fazla akarsa ignore edilir.) D) EFFECT OF ADDITIONAL ZEROS Discuss the effect of zero locations on the step responses.? Effect of addition of zero to closed loop transfer function Makes the system overall response faster. Rise time, peak time, decreases but overshoot increases. Addition of right half zeros means system response slower and system exhibits inverse response. Such systems are said to be non-minimum phase systems.

A frequency response is the steady state response of a system when the input to the system is a sinusoidal signal.

IEEE Instrumentation & Measurement Magazine, 2000

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Jafar AL-Jassim, 2020