Ex. 812. A PID controller has an integral gain of 48 and a derivative gain equal to 1. What is the proportional gain if one zero is placed at s=-24? Where is the other zero and the pole? ans:3

Figure QI shows the circuit diagram of a "Logarithmic Amplifier". In this circuit the feedback resistor of a normal inverting amplifier is replaced by a silicon diode. Since the current flowing through the diode increases exponentially with the voltage across the diode, the voltage across the diode will be proportional to the logarithm current flowing through it. Hence the output of the circuit is proportional to the logarithm of the input voltage. QI DI RIN Al Figure QI The current flowing through a diode is given by the Shock' y Diode Equat n: 1,=1, (e" =1) where , is the current flowing through the diode g is the charge on the electron (given at the back of the examination sheet) V, is the voltage across the diode K, is Boltzmann's constant (given at the back of the examination sheet) Tis room temperature (given at the back of the examination sheet) Given that /,> 1, an approximate expression for V, as a function of I, is Continued overleaf Page 2 of 9 QI (a) 0) Neglecting any input…

An operational-amplifier circuit that may be used as a controller is shown in Figure Qla. (a) R4 ww R1 R3 e Co Figure Qla R1, R2, R3 and R4 are resistors and C1 and C2 are capacitors. Assume both op-amps are ideal and their input/output voltages are ei, e and eo, as shown in the Figure. Using the impedance approach: (i) obtain the transfer function for each op-amp, i.e. E(s)/E:(s) and Eo(s)/E(s). (ii) hence obtain the complete transfer function for the system, i.e. Eo(s)/Ei(s). (iii) Determine D(s) = Eo(s)/E:(s) when R1 = R2 = R3 = R4 = 1 N and C1=1 F, C2= 2 F. %3D (b) Consider the closed-loop control system shown in Figure Qlb. 1 Σ K.D(s) (s +2) Figure Qlb K is the gain and D(s) is the transfer function obtained in part (a)-iii. (i) Plot open loop zeros and poles for the above system in the s-plane. [. Determine whether the point (-1+j) is a closed loop pole for any value of K, by considering the angle criterion at this point. (ii) (c) Briefly summarise the steps, which need to be…

What is the DC gain of the given circuit above?