Draw the root locus of the following open loop transfer function, with the assumption that a constant gain K is multiplied by the open loop transfer function G(s) and it varies from 0 to ∞. 1. G(s) = s+4 s(s²+2s+5)

Problem #2 A system is represented by the block diagram shown below. C(s) (a) Calculate the transfer function using block diagram reduction techniques. You must R(S) show the reduction process step by step (b) Draw the signal flow graph (SFG) for the block diagram and calculate the transfer function using Mason's formula (show all the various components of the formula) C(s) R(S) R(s) + G₁ H₁ G4 H₂ H₁ G₂ G3

Vout (s) of the circuit shown in figure Q4 Vin (s) Derive the transfer function · R4 R1 RS R2 C2 Vin(t) Vout (1) RS C1

R(s) + E(s) Σ V(s) N(s) K P(s) We want to design a speed control for a DC motor. The transfer function form voltage V(s) to DC motor speed Q(s) is: N(s) 100 P(s) = V (8) 50s² + 600s + 1000 We want to design a compensator K so that the response of the feedback system to a reference step of 1-rad/sec satisfies the following requirement settling time 2/3 sec and percent overshoot 2%.

Problem 4. Consider the following so-called lead-lag transfer function (s+3) (s+0.05) Y(s) G(s) = (s+18)(s+0.005) U(s) Lead Lag Find a state space representation using phase variables for the lead-lag transfer function Draw a simulation diagram by hand or in Simulink. a) b)

S:53) Using G and H notation reduction rules, reduce the following closed loop transfer function to a single transfer function block diagram.

Reduce the diagram into a single transfer function Fill in the blanks the numerical coefficients (in integers) to the transfer function shown below that corresponds to A B D & F C(s) As+Bs+C R(s) Ds2+Es+F

The block diagram of a feedback system is shown in the figure. Input +Output s(s+3) G>0 0.1 Step response (a) Find the closed loop transfer function.

Find the closed-loop transfer function, T(s) C(s)/R(s) for the system shown in the following figure using Mason rule/ G1(s) C(s) R(s) G2(s) G5(s) (s)99 G3(s) GA(S) G7(s)

Apply the Routh-Hurwitz Criterion to find the range of gain, K, to ensure stability in the following feedback systems. System 1: R(s) + E(s) (s + 6) C(s) K s² (s+20)