Determine the transfer function of the controller

Assignment Help Mechanical Engineering

Reference no: EM131444808

Problem 1: The control design block diagram of a mechanical system is shown below:

Where the controller and the system are given by:

(a) Determine the transfer function of the "Controller" from E(s) to U(s).

(b) Determine the transfer function of the closed loop system from R(s) to Y(s).

(C/s³+As²+Bs+C)

Determine the values of 'A', 'B' and 'C' in terms of 'K₁', 'K₂' and 'K₃'. Determine the steady state value of the system for a unit step input E(s) in terms of A, B, and C.

Problem 2: The following figure shows a simple model of a furnace. A packing of temperature T₁ is being heated in the furnace by an electric heater supplying heat at the rate qi. The amount of heat supplied is a function of the pressure head (liquid height), h: q_i = 2(1.5-h)². The temperature inside the furnace is T₂. An insulation layer of resistance R₁ surrounds the packing and another one of resistance R₂ surrounds the furnace. The outside wall is at temperature T₃ and the ambient temperature is T_a. The thermal capacitances of the packing, the air inside the furnace, and the outside furnace wall are C₁, C₂ and C₃, respectively.

(a) Derive the dynamic equations for this system assuming that the heat is transferred by conduction only.

(b) Draw the equivalent electric circuit.

Problem 3: The differential equation for a certain second order dynamic system is given below:

y^··(t) + y^·2(t) + 6√(y(t)) = 12

(a) Determine the equilibrium/operating point of the system, y₀.

(b) Linearize the given differential equation about the equilibrium/operating point as obtained in part (a).

Problem 4: Consider the block diagram representation of a feedback control system given below. It is your task to select values of the real parameters K and H such that the unit step response of the closed loop system (from r to y) has all of the following characteristics:

a) the final value of y(t) is 1

b) the 1% settling time for the response is less than 3 (seconds)

c) the overshoot in the response is between 10% and 20%.

If there is a possible combination of H and K, show how you arrived at these choices. If not, explain why the objectives cannot be met.

Problem 5: Find the range of the controller gains (K, K₁) so that the feedback system is stable.

Attachment:- Assignment File.rar

Reference no: EM131444808

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