(a) Find the damping ratio and natural frequency for each second-order system of Problem 4.17.6 and show that the value of the damping ratio conforms to the type of response (underdamped, overdamped, and so on) predicted in that problem. [Section: 4.5]

Problem 5a: Consider the first-order system given below. T₁ = 8/s+8 i) Find the 2% settling time. ii) Find the rise time. iii) Given the quantities above, sketch and label the time response of the system. Problem 5b: In class, you have derived the response of a first-order system to a unit-step input. Given a first-order system of the form G(s) = K/(1+Ts), where T is the time-constant, and K is the constant, find: i) The time-response to a unit-ramp input r(t) = t. ii) The steady-state error for error measured as e(t) = r(t)- c(t). (Hint: the steady-state error is measured as t tends to infinity).

Problem 2. Find the transfer function Vo(5)/Vtn(5) of the circuit below

Purpose This discussion activity supports the following module learning outcomes (MLOS): • Identify and compute the effect of basic control structures such as proportional, integral, derivative control. Task For this discussion, you will work with your group to complete the following task: Discuss the pros and cons of PID control. Once you are all in agreement on your answer, the group leader will post the final answer to the Discussion 2: Final Group Answer discussion thread. our final group post should be no more than 10 sentences.

Question (1) Fig. I shows the armature controlled de motor with IR drop compensation. Draw the block diagram of the system, then simplify the block diagram. Find the transfer function e(s)/E(s). Assume the suitable notations for the system constants.

Question (2) Consider a unity feedback control system with an open loop transfer function of (a) Determine the steady-state error for: (i) unit step input (ii) unit ramp input (b) Derive any formula used

Consider a multiple inputs control system described by a block diagram shown in Fig. 2. Find the complete output for the system when both inputs act simultaneously.

2. Compute the transfer function Y(s)/R(s) for the following system in state space representation. You will need to use the inverse function inv() in Matlab for this. For full credit, write the formula for computing the transfer function, show the code for computing transfer, and the result.

For this discussion, you will work with your group to complete the following task: Take a control system. Illustrate the design choices/parameters that impact its performance specifications.

(a) Assuming an uncharged capacitor in the figure below, use Laplace tranform to find an expression for the voltage across the capacitor after the switch closes at t = 0. Find the time constant, rise time, and settling time for the calculated voltage. [Sections: 4.2, 4.3]