Problem #1 (35 pts) Looking to implement an inexpensive PID controller, you find online references that suggest five or more op-amps are needed to implement PID control. A colleague, however, quickly draws out a schematic (shown below) and says you can implement PID control with only two op-amps. You decide to investigate further by analyzing the circuit. 10 k2 e(t) v(t) u(t) a) Using the "golden rules" for negative feedback op-amps, determine the transfer function between input e(t) and intermediate voltage v(t) b) Using the "golden rules" for negative feedback op-amps, determine the transfer function between intermediate voltage v(t) and output u(t), in terms of R1,R2, C1, and C2 c) What is the transfer function between input E(s) and output U (s)? (Factor your answer so that the TF denominator is D(s) - s.) d) You would like to implement an "ideal" PID controller of the form K] Express Kp, KD, and Kj in terms of R1, R2, C1, and C2. Problem #1 (35 pts) Looking to implement an inexpensive PID controller, you find online references that suggest five or more op-amps are needed to implement PID control. A colleague, however, quickly draws out a schematic (shown below) and says you can implement PID control with only two op-amps. You decide to investigate further by analyzing the circuit. 10 k2 e(t) v(t) u(t) a) Using the "golden rules" for negative feedback op-amps, determine the transfer function between input e(t) and intermediate voltage v(t) b) Using the "golden rules" for negative feedback op-amps, determine the transfer function between intermediate voltage v(t) and output u(t), in terms of R1,R2, C1, and C2 c) What is the transfer function between input E(s) and output U (s)? (Factor your answer so that the TF denominator is D(s) - s.) d) You would like to implement an "ideal" PID controller of the form K] Express Kp, KD, and Kj in terms of R1, R2, C1, and C2