Explanation Given Information: The given control system is used to pivot the solar platform to track the sun’s movements. Calculation: Consider the motor part of the given system. R a I a ( s ) + L a s I a ( s ) + V b ( s ) = E a ( s ) where R a and L a are the Resistance and Inductance of Motor armature, I a is the current through the armature, E a is the applied armature voltage, and V b is back emf. The torque developed by the motor is directly proportional to the armature current. So, T m ( s ) = K t I a ( s ) ⇒ I a ( s ) = 1 K t T m ( s ) Substitute this value in the previous equation. ( R a + L a s ) I a ( s ) + V b ( s ) = E a ( s ) ⇒ R a + L a s K t T m ( s ) + V b ( s ) = E a ( s ) The back emf is directly proportional to the speed. v b ( t ) = K b d 2 θ m ( t ) d t 2 ⇒ V b ( s ) = K b s θ m ( s ) Substitute this value in previous equation R a + L a s K t T m ( s ) + K b s θ m ( s ) = E a ( s ) Consider the load part, it includes motor inertia J m , motor damping D m , and a spring having spring constant K . T m ( s ) = ( J m s 2 + D m s + K ) θ m ( s ) where J m = J a + J L ( N 1 N 2 ) 2 D m = D a + D L ( N 1 N 2 ) 2 J a , D a are Inertia and Damping of Armature and J L , D L are Inertia and Damping of Load

7th Edition

ISBN: 9781118170519

Author: Norman S. Nise

Publisher: WILEY

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Question

Chapter 2, Problem 65P

To determine

The transfer function θm(s)Ea(s) of the given system.

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Chapter 2, Problem 64P

Chapter 3, Problem 1RQ

Chapter 2 Solutions

Control Systems Engineering

Ch. 2 - Prob. 1RQ Ch. 2 - Prob. 2RQ Ch. 2 - Prob. 3RQ Ch. 2 - Define the transfer function.Ch. 2 - Prob. 5RQ Ch. 2 - What do we call the mechanical equations written...Ch. 2 - If we understand the form the mechanical equations...Ch. 2 - Why do transfer functions for mechanical networks...Ch. 2 - What function do gears perform?Ch. 2 - What are the component parts of the mechanical...

Ch. 2 - The motor’s transfer function relates armature...Ch. 2 - Summarize the steps taken to linearize a nonlinear...Ch. 2 - Prob. 1P Ch. 2 - Prob. 2P Ch. 2 - Prob. 3P Ch. 2 - Prob. 4P Ch. 2 - Prob. 5P Ch. 2 - Prob. 6P Ch. 2 - Prob. 7P Ch. 2 - A system is described by the following...Ch. 2 - For each of the following transfer functions,...Ch. 2 - Write the differential equation for the system...Ch. 2 - Write the differential equation that is...Ch. 2 - Prob. 12P Ch. 2 - Use MATLAB to generate the MATLAB ML transfer...Ch. 2 - Repeat Problem 13 for the MATLAB following...Ch. 2 - Use MATLAB to generate the partial fraction...Ch. 2 - Use MATLAB and the Symbolic Math Symbolic Math...Ch. 2 - Prob. 17P Ch. 2 - Prob. 18P Ch. 2 - Prob. 19P Ch. 2 - Repeat Problem 19 using nodal equations. [Section:...Ch. 2 - Prob. 22P Ch. 2 - Prob. 23P Ch. 2 - Prob. 24P Ch. 2 - Prob. 25P Ch. 2 - Prob. 26P Ch. 2 - Prob. 27P Ch. 2 - Prob. 28P Ch. 2 - Prob. 29P Ch. 2 - Write, but do not solve, the equations of motion...Ch. 2 - For the unexcited (no external force applied)...Ch. 2 - For each of the rotational mechanical systems...Ch. 2 - For the rotational mechanical system shown in...Ch. 2 - Find the transfer function, 1sTs , for the system...Ch. 2 - For the rotational mechanical system with gears...Ch. 2 - For the rotational system shown in Figure P2.21,...Ch. 2 - Prob. 37P Ch. 2 - Find the transfer function, Gs=4s/Ts , for the...Ch. 2 - For the rotational system shown in Figure P2.24,...Ch. 2 - Prob. 40P Ch. 2 - Given the rotational system shown in Figure P226,...Ch. 2 - In the system shown in Figure P2.27, the inertia,...Ch. 2 - Prob. 43P Ch. 2 - Given the combined translational and rotational...Ch. 2 - Prob. 45P Ch. 2 - The motor whose torque-speed characteristics are...Ch. 2 - A dc motor develops 55 N-m of torque at a speed of...Ch. 2 - 48. In this chapter, we derived the transfer...Ch. 2 - Prob. 49P Ch. 2 - Find the series and parallel analogs for the...Ch. 2 - Find the series and parallel analogs for the...Ch. 2 - A system’s output, c, is related to the system’s...Ch. 2 - Prob. 53P Ch. 2 - Consider the differential equation...Ch. 2 - 55. Many systems are piecewise linear. That is,...Ch. 2 - For the translational mechanical system with a...Ch. 2 - 57. Enzymes are large proteins that biological...Ch. 2 - Prob. 58P Ch. 2 - Figure P2.36 shows a crane hoisting a load....Ch. 2 - 60. In 1978, Malthus developed a model for human...Ch. 2 - 61. In order to design an underwater vehicle that...Ch. 2 - 62. The Gompertz growth model is commonly used to...Ch. 2 - A muscle hanging from a beam is shown in Figure...Ch. 2 - A three-phase ac/dc converter supplies dc to a...Ch. 2 - Prob. 65P

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