![2. Consider the unity-feedback control system shown in Figure 6 with 1 G(s) = , where n is the last digit of your student ID (s+n)(s+2)(s+90) number and C(s) = K. R(s) C ( s ) G(s) Figure 6 a) Sketch the root locus of the system as K var es from 0 to . [9 marks] b) Determine the range of K such that the closed-loop system is stable and the frequency of the oscillation when the system is marginally stable. [2 marks] c) Determine the range of K such that the closed-loop poles are all real numbers. [3 marks] d) Find the appropriate second order approximation of G(s) [2 marks] e) Using the approximated G(s) in part d), design a PI or PD controller (whichever appropriate), C(s), so that the response of the system to a unit step input has: • a settling time of 1 second and percent of overshoot of 2%. (if the last digit of your student ID number is an odd number) • a settling time of 2 seconds and percent of overshoot of 1 %.(if the last digit of your student ID number is an even number) [10 marks] f) Design the analog realization of the obtained controller in part e) using op-amp circuit. [4 marks]](https://i0.wp.com/electricalstudent.com/wp-content/uploads/2022/04/15..png?w=1170&ssl=1 "2. Consider the unity-feedback control system shown in Figure 6 with 1 G(s) = , where n is the last digit of your student ID (s+n)(s+2)(s+90) number and C(s) = K. R(s) C ( s ) G(s) Figure 6 a) Sketch the root locus of the system as K var es from 0 to . [9 marks] b) Determine the range of K such that the closed-loop system is stable and the frequency of the oscillation when the system is marginally stable. [2 marks] c) Determine the range of K such that the closed-loop poles are all real numbers. [3 marks] d) Find the appropriate second order approximation of G(s) [2 marks] e) Using the approximated G(s) in part d), design a PI or PD controller (whichever appropriate), C(s), so that the response of the system to a unit step input has: • a settling time of 1 second and percent of overshoot of 2%. (if the last digit of your student ID number is an odd number) • a settling time of 2 seconds and percent of overshoot of 1 %.(if the last digit of your student ID number is an even number) [10 marks] f) Design the analog realization of the obtained controller in part e) using op-amp circuit. [4 marks]")
![2. Consider the unity-feedback control system shown in Figure 6 with 1 G(s) = , where n is the last digit of your student ID (s+n)(s+2)(s+90) number and C(s) = K. R(s) C ( s ) G(s) Figure 6 a) Sketch the root locus of the system as K var es from 0 to . [9 marks] b) Determine the range of K such that the closed-loop system is stable and the frequency of the oscillation when the system is marginally stable. [2 marks] c) Determine the range of K such that the closed-loop poles are all real numbers. [3 marks] d) Find the appropriate second order approximation of G(s) [2 marks] e) Using the approximated G(s) in part d), design a PI or PD controller (whichever appropriate), C(s), so that the response of the system to a unit step input has: • a settling time of 1 second and percent of overshoot of 2%. (if the last digit of your student ID number is an odd number) • a settling time of 2 seconds and percent of overshoot of 1 %.(if the last digit of your student ID number is an even number) [10 marks] f) Design the analog realization of the obtained controller in part e) using op-amp circuit. [4 marks]](https://i0.wp.com/electricalstudent.com/wp-content/uploads/2022/04/15-3.png?w=1170&ssl=1 "2. Consider the unity-feedback control system shown in Figure 6 with 1 G(s) = , where n is the last digit of your student ID (s+n)(s+2)(s+90) number and C(s) = K. R(s) C ( s ) G(s) Figure 6 a) Sketch the root locus of the system as K var es from 0 to . [9 marks] b) Determine the range of K such that the closed-loop system is stable and the frequency of the oscillation when the system is marginally stable. [2 marks] c) Determine the range of K such that the closed-loop poles are all real numbers. [3 marks] d) Find the appropriate second order approximation of G(s) [2 marks] e) Using the approximated G(s) in part d), design a PI or PD controller (whichever appropriate), C(s), so that the response of the system to a unit step input has: • a settling time of 1 second and percent of overshoot of 2%. (if the last digit of your student ID number is an odd number) • a settling time of 2 seconds and percent of overshoot of 1 %.(if the last digit of your student ID number is an even number) [10 marks] f) Design the analog realization of the obtained controller in part e) using op-amp circuit. [4 marks]")
2. Consider the unity-feedback control system shown in Figure 6 with 1 G(s) = , where n is the last digit of your student ID (s+n)(s+2)(s+90) number and C(s) = K. R(s) C ( s ) G(s) Figure 6 a) Sketch the root locus of the system as K var es from 0 to . [9 marks] b) Determine the range of K such that the closed-loop system is stable and the frequency of the oscillation when the system is marginally stable. [2 marks] c) Determine the range of K such that the closed-loop poles are all real numbers. [3 marks] d) Find the appropriate second order approximation of G(s) [2 marks] e) Using the approximated G(s) in part d), design a PI or PD controller (whichever appropriate), C(s), so that the response of the system to a unit step input has: • a settling time of 1 second and percent of overshoot of 2%. (if the last digit of your student ID number is an odd number) • a settling time of 2 seconds and percent of overshoot of 1 %.(if the last digit of your student ID number is an even number) [10 marks] f) Design the analog realization of the obtained controller in part e) using op-amp circuit. [4 marks]
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