3. The following closed-loop systems in Fig. 1 and Fig. 2 operate with a damping ratio of 0.707 (=0.707). The system in Fig. 1 does not have a PI controller, while the one in Fig. 2 does. R(s): S Gain Plant R(s) + E(s) 1 C(s) K (s+1)(s+2)(s+10) Fig. 1: Closed-loop system without PI controller Compensator Plant R(s) + E(s) K(s+0.1) S 1 (s+1)(s+2)(s+10) C(s) Fig. 2: Closed-loop system with a practical PI controller a. Please use Matlab to find the intersection point between line and the root locus of the system in Fig. 1. Then find the K value and one complex closed-loop pole corresponding to the intersection point. Calculate the steady-state error. Show the Matlab code in your answer sheet. b. Please use Matlab to find the intersection point between § line and the root locus of the system in Fig. 2. Then find the K value and one complex closed-loop pole associated with the intersection point. Compare the complex closed-loop pole with the one you just found in task a. Are they very different from each other? Calculate the steady-state error. Show the Matlab codes in your answer sheet. c. Use Matlab/Simulink to plot the step responses of two systems in Fig. 1 and Fig. 2, respectively.

en the following circuit below, at t = 0 the switch closes: R₁ m R3 m + Vs Vs = 18V X t=0 m R₂ R₁ = 3kn R4 = 6kN 6ΚΩ C = R₂ 6ΚΩ C = 100µF R3 = vo(t) + M 12ΚΩ RA Use the differential equation method to determine the output voltage

Are the following statements true or false? T or F A) Any graph with an Euler trail that is not an Euler circuit can be made into a graph with an Euler circuit by adding a single edge.  T or F B) If a graph has an Euler trail but not an Euler circuit, then every Euler trail must start at a vertex of odd degree.  T or F C) If a complte graph has an Euler circuit, then the graph has an odd number of vertices.  T or F D) Every graph in which every vertex has even degree has an Euler circuit.  T or F E) Every graph with an Euler trail is connected.

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do block diagram reduction

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Consider the RLC circuit shown below; 1- write the state space description only. 2- Classify the RLC circuit according to Model. İL2 12 A 4 Ohm İL1 ic L1 1 H L2 2H Vo 1 F X₁=Vc X₂=İLL X3=iL2

Thevenin's theorem states that a complex linear network with a pair of output terminals can be represented by this: a) A voltage source of value Vth (Thevenin equivalent voltage) in series with Rth (Thevenin equivalent resistance). b) A voltage source of value Vth (Thevenin equivalent voltage) in parallel with Rth (Thevenin equivalent resistance). c) A series RLC circuit d) Two fireflies O a O c d b

Analyze a series RLC circuit like the figure given below and find the equation for VR1 in terms of other components (not with their numerical values, just symbolic equation) 1.. C1 = 16 L1 =.. 26 R1 = 100 Q C1 L1 'R1 V1