Reference no: EM131006380
Question 1: Use the Routh-Hurwitz Stability Criterion to determine the stability of the control systems whose characteristic equations are given by:
a) q(s) = s3 + s2 + 2s + 24 = 0
b) q(s) = s5 + 2s4 + 2s3 + 4s2 + 11s + 10 = 0
c) q(s) = s5 + 2s4 + 24s3 + 48s2 - 25s - 50 = 0
d) q(s) = s4 + 3s3 + 3s2 + 2s + K = 0
Question 2: Use the Jury Stability test to determine the stability of the control systems whose characteristic equations are given by:
a) P(z) = z4 - 1.2z3 + 0.7z2 + 0.4z - 0.2 = 0
b) P(z) = z3 - 0.8z2 - 0.3z + 0.2 = 0
c) P(z) = z3 - 1.1z2 - 0.1z + 0.3 = 0
Question 3: The characteristic equations of 4 DT control systems are as follows:
i) z2 -1.2z + 0.4 = 0 ii) z2 -1.45z +1 = 0
iii) z3 -1.7z2 +1.2z - 0.45 = 0 iv) z3 +0.6z2 -1.5z + 0.24 = 0
a) Use the Routh-Hurwitz test to determine the stability of the system.
b) Use the Jury test to determine the stability of the system.
c) Check your results by finding the roots of the characteristic equations.
Question4: Consider the discrete-time unity feedback control system whose open-loop pulse transfer function is given by:
G(z) = (K (0.37 z + 0.26)) / (z - 0.37 ) (z - 1)
a) Find the closed-loop pulse transfer function of the system.
b) Using the Jury stability test, determine the range of the gain K for stability.
c) Using the Routh-Hurwitz Stability Criterion, determine the range of gain K for stability.
Question 5: Consider a continuous-time unity feedback control system whose open-loop transfer function is given by:
G(s) = 1 - e-s/s .1/(s(s + 2))
a) Determine the Z-transform of G(s) when T = 0.5 sec.
b) Find the closed-loop pulse transfer function for the system.
c) Determine the stability of the closed-loop control system.
Question 6: Consider the control system described by the following block diagram:
The digital filter D(z) is described by D(z)=K.
a) Write the characteristic equation of the closed-loop system.
b) Use the Routh-Hurwitz test to determine the range of K for which the system is stable.
c) Use the Jury test to determine the range of K for which the system is stable.
d) Find the frequency at which the system will oscillate when K > 0.
e) Consider the system with all sampling removed (i.e. remove the sampler and the ZOH).
Find the range of K for which the system is stable.
f) By comparing the results of c) and e), discuss the effects of sampling.
g) If T=0.1, use the Jury test to determine the range of K for which the system is stable.
h) By comparing the results of c) and g), discuss the effects of reducing the sample time T on the stability of the system.
|
Prepare the journal entry to record the purchase of the bond
: Prepare the journal entry to record the purchase of the bonds by Saxton-Bose on January 1, 2011.
|
|
Set of typical family relationships spouse
: Model a set of typical family relationships- spouse, father, and mother-in a single 3NF relation. Also include the nonkey attributes name and birth date. Assume that each person has only one spouse, one father, and one mother.
|
|
What role did contextual factor play in economic development
: What explains Singapore’s economic performance from 1965 - 1992? Why did Singapore outperform most other developing countries? What role did government policies play in Singapore’s economic development? What role did contextual factors (i,e., locatio..
|
|
Present a profile of the chosen company
: Present a profile of the chosen company. Include the following: Demographics of the employees and Health care risk factors or potential areas of high utilization
|
|
Write the characteristic equation of the closed-loop system
: Write the characteristic equation of the closed-loop system - Find the frequency at which the system will oscillate when K > 0.
|
|
How much in dividends were paid to shareholders during the
: In its most recent financial statements, Newhouse Inc. reported $45 million of net income and $585 million of retained earnings. The previous retained earnings were $556 million. How much in dividends were paid to shareholders during the year? Assu..
|
|
Model of information system
: Contact a systems analyst at your university to study the E-R model of any information system. Attempt to understand entities, attri- butes, and relationships in the model. Is the notation the same as described in the text?
|
|
Find an antiderivative of the given function in terms of u
: Use the suggested u to find du and rewrite the integral in terms of u and du. Then find an antiderivative in terms of u, and, finally, rewrite your answer in terms of x.
|
|
What is the price of this coupon bond
: A 20 year coupon bond with face value $100,000 and a 4% coupon rate has a yield to maturity i = 0.08. What is the value of the annual coupon payment? What is the price of this coupon bond?
|