Control Systems Engineering
Control Systems Engineering
7th Edition
ISBN: 9781118170519
Author: Norman S. Nise
Publisher: WILEY
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Chapter 6, Problem 47P

An interval polynomial is of the form

P s = a 0 + a 1 s + a 2 s 2 + a 3 s 3 + a 4 s 4 + a 5 s 5 + ...

with its coefficients belonging to intervals x 1 a i y i , where xi, yiare prescribed constants. Kharitonov's theorem says that an interval polynomial has all its roots in the left half-plane if each one of the following four polynomials has its roots in the left half-plane (Minichelli, 1989):

k 1 s = x 0 + x 1 s + y 2 s 2 + y 3 s 3 + x 4 s 4 + x 5 s 5 + y 6 s 6 + ... k 2 s = x 0 + y 1 s + y 2 s 2 + x 3 s 3 + x 4 s 4 + y 5 s 5 + y 6 s 6 + ... k 3 s = y 0 + x 1 s + x 2 s 2 + y 3 s 3 + y 4 s 4 + x 5 s 5 + x 6 s 6 + ... k 4 s = y 0 + y 1 s + x 2 s 2 + x 3 s 3 + y 4 s 4 + y 5 s 5 + x 6 s 6 + ...

Use Kharitonov’s theorem and the Routh-Hurwitz criterion to find if the following polynomial has any zeros in the right half-plane.

P s = a 0 + a 1 s + a 2 s 2 + a 3 s 3 2 a 0 4 ; 1 a 1 2 ; 4 a 2 6 ; a 3 = 1

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Chapter 6 Solutions

Control Systems Engineering

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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