with Consider the unity-feedback closed loop system shown in Figure 2 G(8) = + 10 8 8 Sketch the Bode plot of G(s). Explain what rules you used to plot it. Draw the frequency response in the polar coordinates, i.e., the magnitude is M(w) and the phase is (w).

Q5) For unity feedback control system with forward transfer function (G(s) ): G(s) = ; By using root locus graph calculate the value K(s+5) (s+2)(s²+12s+50) of gain (K) which must be added to get the dominant root at damping ratio (-0.886) and natural frequency (w = 8 rad/sec )? www CTRICAL ENGIN

The block diagram of a position control system is shown in Figure 3. K₂ Sensor Preamp K K₁ Ki D Power amplifier Current feedback Tachometer feedback K, Figure 3 3.1 Find the open loop transfer function (), with the outer feedback path open. 3.2 Find the closed loop transfer function 8(5) e(s)" 80(5) e(s) Go ratio

Q.4- A model for feedback control system employing both angular position and velocity feedback is shown in figure bellow .The equation describing d²0 do di the system is J di² - = • K.[V₁-K₁0. K₂0-Ka ((1) Summing V,(r) Motor 白口食 amplifier Velocity sensor K₂8 Position sensor Where J is the rotary inertia KandK are the position and velocity feedback gains, and K, is the gain between the input voltages to the motor torque produced. Derive expression for the closed loop system undamped natural frequency and damping ratio.

Please solve the following by hand and without the use of AI. Thank you!

Find the equivalent transfer function of the negative feedback system of figure below: R(s) C(s) G(s) H(s) G(s) K and H(s) =1 s(s +2)? find two values of gain that will yield closed-loop, overdamped, second-order poles. Repeat for underdamped poles find the value of gain, K, that will make the system critically damped. find the value of gain, K, that will make the system marginally stable. Also, find the frequency of oscillation at that value of K that makes the system marginally stable.

1) Consider the system below: Vehicle Controller Steering dynamics Desired Actual bearing angle bearing angle 50 1 K s2 + 10s + 50 s(s + 5) Figure 1: Simplified Block Diagram of a Self-Guiding Vehicle's Bearing Angle Control. • Find a K value that the system has minimum rise time and minimum overshoot. Let us call this proportional gain as Kopt Show each step while finding Kopt- Show the necessary graphical solutions. Simulate the system response with 3 different K values. (Kopt and two other K values close to Kopt) Show the system response (actual bearing angle) in a single graph for different K values. • Comment on the results.

Below is a very common feedback block system. It is a 1dof, and unity-feedback system. The input is the reference command R(s). This is what flows out of thin air, into the system. All other signals in the system (e.g. U, Y, etc.) will depend on R(s). R(s) a. E(s) e. K U(s) G Y(s) Write the algebraic relation between the output Y(s) and the reference R(s) in terms of G and K?. Write it in the format Y = some function of s * R b. What is the TF from R to Y, aka the closed loop TF? What is the "Loop TF" aka the "the open-loop TF"? G has zeros at ZG1, ZG2 etc. and poles at PG1, PG2 etc. C. K has zeros at ZK1, ZK2 etc. and poles at PK1, PK2 etc. What are the zeros and the poles of OLTF? What are the zeros and the poles of CLTF? d. Write the algebraic relation between the error E(s)=R-Y and the reference R(s) in terms of G and K? Write it in the format E = some function of s * R. What is the TF from R to E? Write the algebraic relation between the controller output U(s) and the reference…

If the system is to be arranged in a closed-loop, with a controller gain K in the forward path and a unity negative feedback loop, what is the maximum value of K which could be used without the system becoming unstable? Assuming you use Figure Q5 for this, use a sketch to show how you obtained the values from the plot.

For the following open loop transfer functions, identify the correct Bode plot from the Bode plots given below: Bode Plots: Magnitude (dB) Phase (deg) O 50 -100 -50 -150 -90 0 -135 -180 Magnitude (dB) a 225 Phase (deg) -270 -20 10:2 -40 -60 -80 -100 0 -90 -180 G(s) = -270 Transfer function: a. 1 10-1 101 O b. 2 O c. 3 O d. 4 S Bode Diagram 10° Frequency (rad/s) Bode Diagram (₁² +s+2)(x² +58 + Frequency (rad/s) s+16) 101 10¹ 10² % 2) Magnitude (dB) Phase (deg) Magnitude (dB) Phase (deg) 50 -50 -100 -45 -90 -135 -180 10/2 -60 -80 -100 -120 90 0 -90 -180 -270 10:2 10¹ 10" Bode Diagram 10° Frequency (rad/s) Bode Diagram 10° Frequency (rad/s) 10¹ 101 10² 102