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Need solution urgently what is the proportional–integral–derivative controller and what calculations are made for a line following a car?

Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)

8th Edition

ISBN:9781305387102

Author:Kreith, Frank; Manglik, Raj M.

Publisher:Kreith, Frank; Manglik, Raj M.

Chapter4: Numerical Analysis Of Heat Conduction

Section: Chapter Questions

Problem 4.6P

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Thermodynamic Relations

Thermodynamics is the division of physics that deals with the transfer of any kind of energy, whether it be heat, temperature, or work, from one object to another.

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Q1 (a) A plant is modelled by the differential equation d²y 3. +2 + y = u dt² dy dt Assume that the initial condition y(0) = 1 and y(0) = 0. Use the Laplace transform to show that Y(s): = U(s) 3s² + 2s +1 3s +2 + 3s² + 2s +1 (b) The transfer function of a digital control system is given by (၁) G(z) = (z z² - 1 0.5)(z+0.2 + 0.6j) (z + 0.2 - 0.6j) where j is the imaginary unit. Find poles and zeros of the system. Then, determine the stability of the digital system. The block diagram of a fluidic speed control system is shown in Figure 1 where the actual speed C(s) is system output and R(s) is reference speed. Show that the closed-loop transfer function is given by Reference Speed R(s) Ka C(s) 100s²+s+K₂ R(s) Valve Amplifier actuator Turbine Actual Speed 1 1 Ка S 1+100s C(s) Figure 1
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Question 4 a) A control engineer has modelled the suspension system of a new model car using a 2nd order differential equation. Using Laplace Transform, the engineer has managed to work out the transfer function, which is given below: 0.001 s2 + 12s+81 What is the natural frequency, the damping ratio and the constant K of the system? Please show all calculations. b) The same engineer has studied the suspension system of a SUV vehicle and modelled it using again a 2nd order differential equation, which has resulted into the following 2nd order transfer function: Y(s) 32 U(s) 4s² +8s + 16 For this system first calculate the damping ratio and its natural frequency and state whether the system is underdamped, overdamped or critically damped. Then calculate the peak time, peak value, settling time and damped natural frequency of the system.
A velocity of a vehicle is required to be controlled and maintained constant even if there are disturbances because of wind, or road surface variations. The forces that are applied on the vehicle are the engine force (u), damping/resistive force (b*v) that opposing the motion, and inertial force (m*a). A simplified model is shown in the free body diagram below. From the free body diagram, the ordinary differential equation of the vehicle is: m * dv(t)/ dt + bv(t) = u (t) Where: v (m/s) is the velocity of the vehicle, b [Ns/m] is the damping coefficient, m [kg] is the vehicle mass, u [N] is the engine force. Question: Assume that the vehicle initially starts from zero velocity and zero acceleration. Then, (Note that the velocity (v) is the output and the force (w) is the input to the system): A. Use Laplace transform of the differential equation to determine the transfer function of the system.
A velocity of a vehicle is required to be controlled and maintained constant even if there are disturbances because of wind, or road surface variations. The forces that are applied on the vehicle are the engine force (u), damping/resistive force (b*v) that opposing the motion, and inertial force (m*a). A simplified model is shown in the free body diagram below. From the free body diagram, the ordinary differential equation of the vehicle is: m * dv(t)/ dt + bv(t) = u (t) Where: v (m/s) is the velocity of the vehicle, b [Ns/m] is the damping coefficient, m [kg] is the vehicle mass, u [N] is the engine force. Question: Assume that the vehicle initially starts from zero velocity and zero acceleration. Then, (Note that the velocity (v) is the output and the force (w) is the input to the system): 1. What is the order of this system?
For the system shown in the figure below: 1. Derive the system differential equations of motion. 2. Use Laplace transform to solve for the displacement x:(t) and x2(t), when K,=k2 =k3=1, m,= m;=1, and x1(0) =0, x1(0) = -1, x2(0) =0, and x{0) =1 3. Sketch x:(t) and X2(t) m, X1 X2
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