Control Systems Engineering
7th Edition
ISBN: 9781118170519
Author: Norman S. Nise
Publisher: WILEY
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Textbook Question
Chapter 6, Problem 66P
The system shown in Figure P6.16 has
a. The value of K2for which the inner loop will have two equal negative real poles and the associated range of K1for system stability.
b. The value of K1at which the system oscillates and the associated frequency of oscillation.
c. The gain K1at which a real closed-loop pole is at
d. If the response in Part d can be approximated as a second-order response, find the %OS and settling time, Ts, when the input is a unit step, r(t) = u(t).
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An underdamped second order system forward transfer function is given as:
3a + b + 2d +e
G(s) =
s2 + as + (3a + b + 2d + e)
Answer the following questions:
Manual Calculation
Find the poles of the system and sketch it in an s-plane.
Determine the natural frequency and damping ratio of G(s).
Find the peak time, Tp, percent overshoot, %OS, settling time, Ts, and rise time, T,
under unit step input.
2. Consider the closed-loop system shown below. Determine the range of K for stability. Assume that K > 0.
R(s)
K
S-2
(s + 1)(s² + 6s+25)
C(s)
For the control system shown in Fig. 3.16:
(a) plot the root loci of the system
(b) find the value of gain K such that the damping ratio of the dominant closed-loop
poles is 0.5
(c) obtain all the closed-loop poles using MATLAB
(d) plot the unit-step response curve using MATLAB.
K
Input
s(s²+5s+7)
Output
Chapter 6 Solutions
Control Systems Engineering
Ch. 6 - Prob. 1RQCh. 6 - Prob. 2RQCh. 6 - What would happen to a physical system chat...Ch. 6 - Why are marginally stable systems considered...Ch. 6 - Prob. 5RQCh. 6 - Prob. 6RQCh. 6 - Prob. 7RQCh. 6 - Prob. 8RQCh. 6 - Prob. 9RQCh. 6 - Why do we sometimes multiply a row of a Routh...
Ch. 6 - Prob. 11RQCh. 6 - Prob. 12RQCh. 6 - 13. Does the presence of an entire row of zeros...Ch. 6 - Prob. 14RQCh. 6 - Prob. 15RQCh. 6 - Prob. 16RQCh. 6 - Tell how many roots of the following polynomial...Ch. 6 - Tell how many roots of the following polynomial...Ch. 6 - Using the Routh table, tell how many poles of the...Ch. 6 - Prob. 4PCh. 6 - Determine how many closed-loop poles lie in the...Ch. 6 - Determine how many closed-loop poles lie in the...Ch. 6 - MATLAB ML 7. Use MATLAB to find the pole location...Ch. 6 - Symbolic Math SM 8. Use MATLAB and the Symbolic...Ch. 6 - Determine whether the unity feedback system of...Ch. 6 - Use MATLAB to find the pole locations for the...Ch. 6 - Consider the unity feedback system of Figure P6.3...Ch. 6 - In the system of Figure P6.3, let Gs=Ks+1ss2s+3...Ch. 6 - Given the unity feedback system of Figure P6.3...Ch. 6 - Using the Routh-Hurwitz criterion and the unity...Ch. 6 - Given the unity feedback system of Figure P6.3...Ch. 6 - Repeat Problem 15 using MATLAB.Ch. 6 - Prob. 17PCh. 6 - For the system of Figure P6.4, tell how many...Ch. 6 - Using the Routh-Hurwitz criterion, tell how many...Ch. 6 - Determine if the unity feedback system of Figure...Ch. 6 - For the unity feedback system of Figure P6.3 with...Ch. 6 - In the system of Figure P6.3, let Gs=Ksassb Find...Ch. 6 - For the unity feedback system of Figure P63 with...Ch. 6 - Find the range of K for stability for the unity...Ch. 6 - For the unity feedback system of Figure P6.3 with...Ch. 6 - find the range of K for stability. [Section: 6.41]...Ch. 6 - Find the range of gain, K, to ensure stability in...Ch. 6 - Using the Routh-Hurwitz criterion, find the value...Ch. 6 - Use the Routh-Hurwitz criterion to find the range...Ch. 6 - Prob. 32PCh. 6 - Given the unity feedback system of Figure P63 with...Ch. 6 - Repeat Problem 33 for [Section: 6.4]...Ch. 6 - For the system shown in Figure P6.8, find the...Ch. 6 - Given the unity feedback system of Figure P6.3...Ch. 6 - For the unity feedback system of Figure P6.3 with...Ch. 6 - For the unity feedback system of Figure P6.3 with...Ch. 6 - Given the unity feedback system of Figure P6.3...Ch. 6 - Using the Routh-Hurwitz criterion and the unity...Ch. 6 - Find the range of K to keep the system shown in...Ch. 6 - Prob. 43PCh. 6 - The closed-loop transfer function of a system is...Ch. 6 - Prob. 45PCh. 6 - Prob. 46PCh. 6 - An interval polynomial is of the form...Ch. 6 - A linearized model of a torque-controlled crane...Ch. 6 - The read/write head assembly arm of a computer...Ch. 6 - A system is represented in state space as...Ch. 6 - State Space SS 52. The following system in state...Ch. 6 - Prob. 54PCh. 6 - A model for an airplane’s pitch loop is shown in...Ch. 6 - Prob. 57PCh. 6 - Prob. 58PCh. 6 - Prob. 59PCh. 6 - Prob. 60PCh. 6 - Prob. 61PCh. 6 - Look-ahead information can be used to...Ch. 6 - Prob. 63PCh. 6 - It has been shown (Pounds, 2011) that an unloaded...Ch. 6 - Prob. 65PCh. 6 - The system shown in Figure P6.16 has G1s=1/ss+2s+4...Ch. 6 - Prob. 67PCh. 6 - Prob. 68PCh. 6 - Hybrid vehicle. Figure P6.l8 shows the HEV system...Ch. 6 - Prob. 70P
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- Figure 1 shows an electrical system comprising a series RLC circuit and input voltagesource ein(t).(a) Derive the input-output equation with output y = I and input u = ein(t). (b) Using the derived input-output equation, drive the system transfer function G(s)that relates output to input. Use the following numerical values for the electrical systemparameters: resistance R = 2Ω, inductance L = 0.25H, and capacitance C = 0.4F. (c) Using the derived transfer function, derive the time-domain ordinary differentialequation for the input-output equation of this electrical system. (d) Draw the complete block diagram of this series RLC circuit using the derived transferfunction.arrow_forwardFigure Q2 shows the block diagram of a unity-feedback control system Proportional Controller Plant R(s) C(s). s(3s +1) 5+2s² +4 K 2.1- Determine the characteristic equation. 2.2- Using the Routh-Hurwitz criterion to determine the range of gain, K to ensure stability and marginally stability in the unity feedback syste m.arrow_forwardThe close loop system block diagram is given below .Find the transfer function of the given system. 02 G Error Harrow_forward
- 1.block diagram physical meaning and the time response for different inputsarrow_forwardConsider the system shown in Figure .Plot the root loci with MATLAB. Locate the closed-loop poles when the gain K is set equal to 2. K(s+1) s(s²+2s+6) Figure s+1arrow_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
- A system can be approximately expressed as X₁ = −T₁×₁ +σx2 x2=-T2x2 + ku a. Given ₁ = 8,σ = 4, k = 0, find the range of T2 such that the system x = Ax is asymptotical stable. b. Given ₁ = 8, t₂ = −1, σ = k = 1, design a state-feedback controller, such that the system x = Ax+Bu is asymptotical stable. LG 11-7 IZ-N 13-arrow_forwardP4. The open loop transfer function of a unity feedback system is given by G (s) = K s(as+1)(Bs+1) Determine the range of K for stability in terms of a and B.arrow_forward6. Consider the mechanical system shown in Fig. 8. Let V(t) be the input and the acceleration of the mass be the output. Derive the state equations and the output equation using linear graphs and normal trees. B m V₁(t) Figure 8: A mechanical system with an across-variable sourcearrow_forward
- Selecting the new closed-loop poles in a location where the dominant closed- loop poles are located will result in state-feedback gains: s^2+4s+10arrow_forwardASAParrow_forwardIf a system transfer function has two complex roots in the denominator, it is described as: O being underdamped being overdamped being critically damped O having no dampingarrow_forward
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