Control Systems Engineering
7th Edition
ISBN: 9781118170519
Author: Norman S. Nise
Publisher: WILEY
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Chapter 12, Problem 5RQ
Under what conditions can inspection of the signal-flow graph of a system yield immediate determination of controllability?
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QUESTION 1
A vertical vibrating system of 5 kg of mass and 500 N/m of spring stiffness is
critically damped. The system is excited by a step input force f(t) = 50 N to
generate an output vertical motion y(t), in metres, and t-is the time in seconds.
1.1.
Determine the transfer function of the system
1.2.
Provide an equivalent block diagram with a unitary negative feedback to
control the motion y(t)
1.3.
Using s-plane, locate the closed loop pole(s) and zero (s) of the system
and provide the reasons of stability or non-stability of the system
1.4.
Using the technique of partial fractions, establish the analytical
expression of the time response of the vibrating system.
Characteristic equation of a system is given by:
C = s³ + 4s² + 25s + K = 0
%3D
determine the range of values of K for which the system is stable. Use Roth Hurwitz stability criteria.
Q4) A particular control system yielded a steady state error of 0.20 for unit step input. A
unit integrator is cascaded to this system and unit ramp input is applied to this
modified system. What is the value of steady-state error for this modified system?
Chapter 12 Solutions
Control Systems Engineering
Ch. 12 - Prob. 1RQCh. 12 - Prob. 2RQCh. 12 - 3. Different signal-flow graphs can represent the...Ch. 12 - Prob. 4RQCh. 12 - Under what conditions can inspection of the...Ch. 12 - In order to determine controllability...Ch. 12 - Prob. 7RQCh. 12 - Prob. 8RQCh. 12 - Prob. 9RQCh. 12 - Prob. 10RQ
Ch. 12 - Prob. 11RQCh. 12 - Prob. 12RQCh. 12 - Prob. 13RQCh. 12 - Prob. 14RQCh. 12 - 15. In order to effect a complete observer design,...Ch. 12 - Under what conditions can inspection of the...Ch. 12 - 17. In order to determine observability...Ch. 12 - Prob. 1PCh. 12 - Prob. 2PCh. 12 - 3. The following open-loop transfer functions can...Ch. 12 - Prob. 4PCh. 12 - Prob. 5PCh. 12 - Prob. 6PCh. 12 - Prob. 7PCh. 12 - Prob. 8PCh. 12 - Prob. 9PCh. 12 - Prob. 10PCh. 12 - Prob. 11PCh. 12 - Prob. 12PCh. 12 - Prob. 13PCh. 12 - Prob. 14PCh. 12 - Prob. 15PCh. 12 - Repeat Problem 14 assuming that the plant is...Ch. 12 - The open-loop system of Problem 14 is represented...Ch. 12 - Prob. 18PCh. 12 - Prob. 20PCh. 12 - Prob. 21PCh. 12 - Prob. 22PCh. 12 - Prob. 23PCh. 12 - Prob. 24PCh. 12 - Prob. 26PCh. 12 - Prob. 27PCh. 12 - Prob. 29PCh. 12 - Prob. 30PCh. 12 - Prob. 31PCh. 12 - Prob. 32PCh. 12 - Prob. 33PCh. 12 - Prob. 41PCh. 12 - Prob. 42PCh. 12 - Prob. 44P
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- QUESTION 5 Consider the system whose block diagram is shown below. D(s) R(s) + + C(s) K G(s) G(8) R(s) is the reference input or target, and D(s) is the disturbance input. Gp(t) is the plant (house, motor, car,...) transfer function, Gc(t) is the compensator transfer function, and K is the compensator gain given by 1 G (s) G (s) = P s+10 1 3s+2 and K=5. Find the transfer function, C(s)/R(s). 3 s²+16s+14 8 3s²+32s+25 S 382+8+6 8(s+ 10) 3s² + 32s+25 3s+2 3s²+32s+25 5 3x²+32x+25arrow_forward1. Verify Eqs. 1 through 5. Figure 1: mass spring damper In class, we have studied mechanical systems of this type. Here, the main results of our in-class analysis are reviewed. The dynamic behavior of this system is deter- mined from the linear second-order ordinary differential equation: where (1) where r(t) is the displacement of the mass, m is the mass, b is the damping coefficient, and k is the spring stiffness. Equations like Eq. 1 are often written in the "standard form" ď²x dt2 r(t) = = tan-1 d²r dt2 m. M +25wn +wn²x = 0 (2) The variable wn is the natural frequency of the system and is the damping ratio. If the system is underdamped, i.e. < < 1, and it has initial conditions (0) = zot-o = 0, then the solution to Eq. 2 is given by: IO √1 x(1) T₁ = +b+kr = 0 dt 2π dr. dt ل لها -(wat sin (wat +) and is the damped natural frequency. In Figure 2, the normalized plot of the response of this system reveals some useful information. Note that the amount of time Ta between peaks is…arrow_forwardP.4: R(s) + E(s) K(s+7) s(s+5)(5 + 8)(5 + 12) C(s) a. What value of K will yield a steady-state error in position of 0.01 for an input of (1/10)? b. What is the K, for the value of K found in (a)? c. What is the minimum possible steady-state position error for the input given in (a)? s(1/s²) e(00) = Cramp (00) = lim1+G(s) 1 05+sG(s) = lim 1 lim sG(s) 5-0arrow_forward
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