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The heading control of the traditional bi-wing aircraft, shown in Figure I(2), is represented by the...
Convert following the transfer function into state space representation (Marks 5) 3 +45² T($) = 54...
Convert following the transfer function into state space representation (Marks 5) 3 +45² T($) = 54 +52 +7 Convert the following state space into a transfer function. (Marks 5) x = 11 * = x + ( u 21 y = [02]x + [2]u Evaluate the steady-state error of state-space system. (Marks 5) i [ 10] [21. *= 15 2]* +11 y = [ 02]x + [2]u Evaluate the steady-state error of state-space system. (Marks 5) -1 0x+lu x =...
Question 4 (a) A feedback control system with a proportional controller is shown in Figure Q4...
Question 4 (a) A feedback control system with a proportional controller is shown in Figure Q4 (a). (i) Sketch the root locus of the system, (ii) Design the proportional controller (choose the value of K) such that the damping ratio does not exceed 0.5 and the time constant is less than 1 second. [All necessary steps of root locus construction and controller design must be shown). C(s) R(S) + s(s+4)(s + 10) Figure Q4 (a). A feedback control system [11...
Consider the aircraft model shown in Figure 1. We will assume that the aircraft is in steady-crui...
Consider the aircraft model shown in Figure 1. We will assume that the aircraft is in steady-cruise at constant altitude and velocity; thus, the thrust, drag, weight and lift forces balance each other in the x- and y directions. We will also assume that a change in pitch angle will not change the speed of the aircraft under any circumstance (unrealistic but simplifies the problem a bit). Under these assumptions the longitudinal equations of motion for the aircraft can be...
2. (disturbances & sensitivity) For the control system shown in the figure below, do the following:...
2. (disturbances & sensitivity) For the control system shown in the figure below, do the following: i. Simplify the block diagram to form a negative unity feedback system ii. Determine the system type. ii. Find the steady-state error for r(t) 2tu(t) and d(t) 0 iv. Find the steady-state error for r(t) 0 and d(t) -0.2ut) v. Find the total error to both the input and the disturbance vi. Find the sensitivity of the total steady-state error to changes in Ki...
Question 4 A control system is shown in Figure 3, where Ge(s) is the controller, R(s)...
Question 4 A control system is shown in Figure 3, where Ge(s) is the controller, R(s) is the setpoint temperature, Tw is the measured water temperature, Ta is the ambient temperature and u(t) is the rate of heat supplied to the heater. The mathematical model of a simple thermal system consisting of an insulated tank of water is given by: dTW = c(1, - Iw) +u dt where c is the heat insulation coefficient. Heater Water R(s) Ta Gc/s) u(1)...
Question 3 A high quality telescope is represented using a transfer function, shown in Figure 3. It needs to follow a trajectory described by input E(s) exactly in order to track a star. The outp...
Question 3 A high quality telescope is represented using a transfer function, shown in Figure 3. It needs to follow a trajectory described by input E(s) exactly in order to track a star. The output C(s) is the angle of the telescope E(s) 7 C) Figure 3: A System expressed as a Transfer Function (a) Convert the system into state space form (b) Find the steady state error when a unity step input is applied. (c) Is your answer to...
control system System Description: The figure 1 and 2 below show, respectively, components and block diagram...
control system
System Description: The figure 1 and 2 below show, respectively, components and block diagram of a motor and the measurements of velocity (via the tacho unit) and position (via the potentiometer). n represents the gearbox ratio between the rotating shaft and the output shaft. The left-hand side of the diagram represents the controller. A reference set point for the rotating shaft is entered in degrees and this is equivalent voltage. The error is calculated by subtracting the measured...
Problem 4 (25%) Consider the attitude control system of a rigid satellite shown in Figure 1.1....
Problem 4 (25%) Consider the attitude control system of a rigid satellite shown in Figure 1.1. Fig. 1.1 Satellite tracking control system In this problem we will only consider the control of the angle e (angle of elevation). The dynamic model of the rigid satellite, rotating about an axis perpendicular to the page, can be approximately written as: JÖ = tm - ty - bė where ) is the satellite's moment of inertia, b is the damping coefficient, tm is...
Convert following the transfer function into state space representation (Marks 5) 3 +45² T($) = 54 +52 +7 Convert the following state space into a transfer function. (Marks 5) x = 11 * = x + ( u 21 y = [02]x + [2]u Evaluate the steady-state error of state-space system. (Marks 5) i [ 10] [21. *= 15 2]* +11 y = [ 02]x + [2]u Evaluate the steady-state error of state-space system. (Marks 5) -1 0x+lu x =...
Question 4 (a) A feedback control system with a proportional controller is shown in Figure Q4 (a). (i) Sketch the root locus of the system, (ii) Design the proportional controller (choose the value of K) such that the damping ratio does not exceed 0.5 and the time constant is less than 1 second. [All necessary steps of root locus construction and controller design must be shown). C(s) R(S) + s(s+4)(s + 10) Figure Q4 (a). A feedback control system [11...
Consider the aircraft model shown in Figure 1. We will assume that the aircraft is in steady-cruise at constant altitude and velocity; thus, the thrust, drag, weight and lift forces balance each other in the x- and y directions. We will also assume that a change in pitch angle will not change the speed of the aircraft under any circumstance (unrealistic but simplifies the problem a bit). Under these assumptions the longitudinal equations of motion for the aircraft can be...
2. (disturbances & sensitivity) For the control system shown in the figure below, do the following: i. Simplify the block diagram to form a negative unity feedback system ii. Determine the system type. ii. Find the steady-state error for r(t) 2tu(t) and d(t) 0 iv. Find the steady-state error for r(t) 0 and d(t) -0.2ut) v. Find the total error to both the input and the disturbance vi. Find the sensitivity of the total steady-state error to changes in Ki...
Question 4 A control system is shown in Figure 3, where Ge(s) is the controller, R(s) is the setpoint temperature, Tw is the measured water temperature, Ta is the ambient temperature and u(t) is the rate of heat supplied to the heater. The mathematical model of a simple thermal system consisting of an insulated tank of water is given by: dTW = c(1, - Iw) +u dt where c is the heat insulation coefficient. Heater Water R(s) Ta Gc/s) u(1)...
Question 3 A high quality telescope is represented using a transfer function, shown in Figure 3. It needs to follow a trajectory described by input E(s) exactly in order to track a star. The output C(s) is the angle of the telescope E(s) 7 C) Figure 3: A System expressed as a Transfer Function (a) Convert the system into state space form (b) Find the steady state error when a unity step input is applied. (c) Is your answer to...
control system
System Description: The figure 1 and 2 below show, respectively, components and block diagram of a motor and the measurements of velocity (via the tacho unit) and position (via the potentiometer). n represents the gearbox ratio between the rotating shaft and the output shaft. The left-hand side of the diagram represents the controller. A reference set point for the rotating shaft is entered in degrees and this is equivalent voltage. The error is calculated by subtracting the measured...
Problem 4 (25%) Consider the attitude control system of a rigid satellite shown in Figure 1.1. Fig. 1.1 Satellite tracking control system In this problem we will only consider the control of the angle e (angle of elevation). The dynamic model of the rigid satellite, rotating about an axis perpendicular to the page, can be approximately written as: JÖ = tm - ty - bė where ) is the satellite's moment of inertia, b is the damping coefficient, tm is...
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