Control Systems Engineering
7th Edition
ISBN: 9781118170519
Author: Norman S. Nise
Publisher: WILEY
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Textbook Question
Chapter 5, Problem 5RQ
For a simple, second-order feedback control system of the type shown in Figure 5.14, describe the effect that variations of forward-path gain, K, have on the transient response.
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Give a physical example for feedback control systems. Sketch the block diagram with input and output variables:
Missile launch system
B) For a unity feedback system with the forward transfer function:
G(S)
K
s (1+0.4 s)(1 + 0.25 s)
Find the range of (K) to make the system stable (Apply Routh's stability criterion).
Chapter 5 Solutions
Control Systems Engineering
Ch. 5 - Prob. 1RQCh. 5 - Name three basic forms for interconnecting...Ch. 5 - For each of the forms in Question 2, state...Ch. 5 - Besides knowing the basic forms as discussed in...Ch. 5 - For a simple, second-order feedback control system...Ch. 5 - Prob. 6RQCh. 5 - Prob. 7RQCh. 5 - How are summing junctions shown on a signal-flow...Ch. 5 - If a forward path touched all closed loops, what...Ch. 5 - Name five representations of systems in state...
Ch. 5 - Prob. 11RQCh. 5 - Which form of the state-space representation leads...Ch. 5 - When the system matrix is diagonal, what...Ch. 5 - What terms lie along the diagonal for a system...Ch. 5 - Prob. 15RQCh. 5 - Prob. 16RQCh. 5 - For what kind of system would you use the observer...Ch. 5 - Describe state-vector transformations from the...Ch. 5 - Prob. 19RQCh. 5 - Prob. 20RQCh. 5 - Prob. 21RQCh. 5 - Find the closed-loop transfer function, T(s) =...Ch. 5 - Find the equivalent transfer function, T(s) =...Ch. 5 - Reduce the system shown in Figure P5.4 to a single...Ch. 5 - Reduce the block diagram shown in Figure P5.6 to a...Ch. 5 - Find the unity feedback system that is equivalent...Ch. 5 - 8. Given the block diagram of a system shown in...Ch. 5 - 9. Reduce the block diagram shown in Figure P5.9...Ch. 5 - Reduce the block diagram shown in Figure P5.10 to...Ch. 5 - 11. For the system shown in Figure P5.11, find the...Ch. 5 - 12. For the system shown in Figure P5.12, find the...Ch. 5 - Prob. 13PCh. 5 - For the system of Figure P5.14, find the value of...Ch. 5 - 15. For the system shown in Figure P5.15, find K...Ch. 5 - For the system of Figure P5.16, find the values of...Ch. 5 - Find the following for the system shown in Figure...Ch. 5 - 18. For the system shown in Figure P5.18, find ,...Ch. 5 - Prob. 19PCh. 5 - Prob. 20PCh. 5 - Find the transfer function G(s) = Eo(s)/T(s) for...Ch. 5 - Prob. 22PCh. 5 - Prob. 23PCh. 5 - State Space SS
24. Given the system below, draw a...Ch. 5 - Prob. 25PCh. 5 - Using Mason’s rule, find the transfer function,...Ch. 5 - Using Mason’s rule, find the transfer function,...Ch. 5 - Prob. 28PCh. 5 - Use block diagram reduction to find the transfer...Ch. 5 - State Space SS 30. Represent the following systems...Ch. 5 - Prob. 31PCh. 5 - State Space SS 32. Repeat Problem 31 and represent...Ch. 5 - Prob. 33PCh. 5 - Prob. 34PCh. 5 - Repeat Problem 34 for the system shown in Figure...Ch. 5 - Prob. 37PCh. 5 - State Space SS 38. Consider the rotational...Ch. 5 - Prob. 40PCh. 5 - Prob. 41PCh. 5 - State Space SS
42. Consider the subsystems shown...Ch. 5 - Prob. 43PCh. 5 - Prob. 44PCh. 5 - State Space SS
45. Diagonalize the following...Ch. 5 - Prob. 46PCh. 5 - Prob. 48PCh. 5 - Prob. 51PCh. 5 - Figure P5.33 shows a noninverting operational...Ch. 5 - Figure P5.34 shows the diagram of au inverting...Ch. 5 - Prob. 54PCh. 5 - A car active suspension system adds an active...Ch. 5 - Prob. 58PCh. 5 - Prob. 60PCh. 5 - Some medical procedures require the insertion of a...Ch. 5 - Prob. 62PCh. 5 - Prob. 64PCh. 5 - Prob. 65PCh. 5 - The purpose of an Automatic Voltage Regulator is...Ch. 5 - 68. Integrated circuits are manufactured through a...Ch. 5 - Prob. 69PCh. 5 - Prob. 72PCh. 5 - Prob. 73PCh. 5 - Assume ideal operational amplifiers in the circuit...Ch. 5 - Parabolic trough collector. Effective controller...
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- Homework: For a unity feedback system with the forward transfer function: K(s + 20) G(s) = s(s + 2)(s+3) find the range of K to make the system stable.arrow_forwardA stock-flow system models the level of water in a lake. Near a certain equilibrium point, there are three feedback loops: an amplifying feedback loop with strength of +0.55 per month, a stabilizing feedback loop with strength of -0.09 per month, and an amplifying feedback loop with strength of +0.79 per month. Calculate the strength of the overall feedback.arrow_forwardA Block diagram of a feedback control system is shown in Figure Q3. Using the Block Diagram Reduction Method, solve for the output Y(s) when:(i) Input D(s) = 0,(ii) Input R(s) = 0,(iii) Input R(s) and D(s) are both applied (i.e., R(s) ≠ 0 , D(s) ≠ 0).arrow_forward
- For the system whose block diagram is shown in Fig.1, find the overall transfer function by using only one method of the followings: 1-Mason's Gain Formula. 2- Block diagram reduction techniques. R R G3 G1 G2 H1 Fig.1 H2arrow_forwardB6arrow_forwardQUESTION 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.arrow_forward
- P.5: For the unity feedback system shown K(s + a) (s+B)² G(s) is to be designed to meet the following specifications: steady-state unit step input = 0.1; damping ratio = 0.5; natural frequency K, a, and B. = error for a √10. Find R(s) + E(s) G(s) C(s)arrow_forwardWe consider a dynamical system represented by the block diagram: Simple negative feedback: U(s) E(s) input, + with T₁(s) T₂(s) = 2 = a 1+5² T,(s) T₂(s) X(S) output measurement with a 4 and Calculate the closed-loop transfer function at s=10.arrow_forwardIt is known that G(s)= $4 and the closed-loop structure is shown below: R(s) + E(s) A (7 K(s + 2) G(s) +s C(s) Find the range of K for which the closed-loop system will have at least two right half-plane poles. (Tip: consider no zeros in 1st column of Routh table and special cases separately)arrow_forward
- Briefly explain the terms time constant, damping ratio, undamped natural frequency and damped natural frequency in relation to the transient response of systems. For each of the systems with transfer funtions given below, determine the closed-loop poles and sketch the response c(t) when the input, r(t), is a unit step. Indicate the steady-state value of c(t) in each case. (i) (ii) (iii) C(s) 1 R(s) s+0.5 = C(s) 1 = R(s) s² +5.5s +2.5 C(s) 1 = R(s) s² +s+1 b y(t) m d k₂ wwwx(1) For the system in the figure shown above, x(t) and y(t) are displacements, k, and k2 are spring constants and b is a damping coefficient. Derive the transfer function Y(s) x(s)arrow_forwardFor a unity negative feedback control system having an open-loop transfer function, G(s) as given below. Find out the value of "K" such that the system will be in the stable region. (K/s) (s3 + 12. 5s2 + 50. 5s + 66) G(s) =arrow_forwardA vibrating spring-mass system has the feedback control system shown in Fig Q3 below. (figure attached as image ACT)If K = 12.25 determine:6.1 the transfer function ; (3)6.2 the characteristic equation with a impulse input; (1)6.3 the un-damped natural frequency of the system; (2)6.4 the damping ratio; (2)6.5 the damped natural frequency; (2)6.6 the maximum percentage overshoot; (2)6.7 the peak time; (1)6.8 the settling time for the response within 2%. (2)arrow_forward
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