Consider the unity feedback negative system with an open-loop function G(s)= K (s^2+10s+24)/(s^2+3s+2). a. Plot the...

Consider the unity feedback negative system with an open-loop function G(s)= K (s^2+10s+24)/(s^2+3s+2).

a. Plot the locations of open-loop poles with X and zeros with O on an s-plane.

b. Find the number of segments in the root locus diagram based on the number of poles and zeros.

c. The breakaway point (the point at which the two real poles meet and diverge to become complex conjugates) occurs when K = 0.02276. Show that the closed-loop system has repeated poles for this K.

d. The break-in point (the point at which the complex conjugate poles meet and diverge to become real) occurs when K = 10.97. Show that the closed-loop system has repeated poles for this K.

e. Find the poles of the closed-loop system when K = 6.

f. Sketch the two segments of the root locus.

g. Check your work using MATLAB. It is not necessary to submit the output.

Solutions

Expert Solution

Manojponduru answered 10 months ago

Next > < Previous

Related Solutions

A Unity feedback system has an open loop transfer function of G(s) = K / s...

A Unity feedback system has an open loop transfer function of G(s) = K / s (s+1) (s+5) Draw the root locus plot and determine the value of K to give a damping ratio of 0.3 A network having a transfer function of 10(1 +10s) /(1 +100s) is now introduced in tandem. Find the new value of K, which gives the same damping ratio for the closed -loop response. Compare the velocity error constant and settling time of the original...

Rana Abdelal Ex. 350. Consider a unity feedback system where the forward TF is: G(s) =...

Rana Abdelal Ex. 350. Consider a unity feedback system where the forward TF is: G(s) = K (s+18)/(s(s+17)). Find the breakaway and entry points on the real axis (Enter the one closest to the origin first). One point on the root locus is -18+jB. Find K there and and also find B. It is possible to work this one without MATLAB, but it requires some intense algebra. Answers: s1,s2,K, and B. ans:4 Can you show me how to do the...

A function of the feedback control system is desired: = (2 (s + 1)) / (s...

A function of the feedback control system is desired: = (2 (s + 1)) / (s ^ 2 + 3s + 2). If the function transfer process is second order with gain = 4, time constant = 1, damping factor = 1.5, arrange the form of the PID controller function transfer using the direct synthesis method.

Q1): Consider the following third-order transfer function for open loop system: (25 marks) ?(?)?(?) =2 \...

Q1): Consider the following third-order transfer function for open loop system: ?(?)?(?) =2 \ (? + ?. ??)(? + ?. ??)(? + ?. ??) By using the polar plot method, choose the correct answer for the following: 1) When the (ω) equal to one, the magnitude of function is: A) 1.808 B) 1.705 C) 1.642 D) 1.505 2) When the (ω) equal to five, the magnitude of function is: A) 0.368 B) 0.344 C) 0.323 D) 0.312 3) When the...

A servomechanism has an open loop transfer function of G(s) = 10 / s (1+0.5s) (1+0.1s)...

A servomechanism has an open loop transfer function of G(s) = 10 / s (1+0.5s) (1+0.1s) Draw the Bode plot and determine the phase and gain margin. A networks having the transfer function (1+0.23s)/(1+0.023s) is now introduced in tandem. Determine the new gain and phase margins. Comment upon the improvement in system response caused by the network

The plant H(s)=40/(S^2+4) is now put in a unity-feedback connection with a proportionalderivative compensator Cpd(s) =...

The plant H(s)=40/(S^2+4) is now put in a unity-feedback connection with a proportionalderivative compensator Cpd(s) = K(1 + sT), where K and T are real constants to be determined. The closed-loop is stable with a constant step-response error of +20% in steady state. Ignore implementation issues arising from the improperness of the compensator. (a)Determine K. (b)What range of values can T take? (c) What is the gain margin? (d) If the gain cross-over frequency is 10 rad/s, determine the phase...

Consider a system with the following transfer function, G(s) = 10/ [s(s + 1)]. Design a...

Consider a system with the following transfer function, G(s) = 10/ [s(s + 1)]. Design a compensator according to the following design objectives: • Kv = 20 sec−1 ; • PM = 50 oF; • GM ≥ 10 dB. Submit your answer regarding the detailed compensator design procedures, and the corresponding MATLAB code and figures to verify your design. In addition, compare the step response of both uncompensated and compensated systems in MATLAB

For a system with G(s) in forward path and H(s) in feedback path, Derive in details...

For a system with G(s) in forward path and H(s) in feedback path, Derive in details the equivalent transfer function and its zeros/poles?

Consider the equilibrium N2(g) + O2(g) ⇄ 2 NO(g) At 2300 K the equilibrium constant K...

Consider the equilibrium N2(g) + O2(g) ⇄ 2 NO(g) At 2300 K the equilibrium constant K = 1.7 × 10-3. Suppose that 0.0150 mol NO(g), 0.250 mol N2(g), and 0.250 mol O2(g) are placed into a 10.0-L flask and heated to 2300 K. The system is not at equilibrium. Determine the direction the reaction must proceed to reach equilibrium and the final equilibrium concentrations of each species. to the right to the left [N2] =____ mol/L [O2] = ____mol/L [NO]...

1. Give an example of negative feedback system in the body and how it works. 2.What...

1. Give an example of negative feedback system in the body and how it works. 2.What name is given to all chemical reactions that occur within body cells? 3. Why is it necessary to be in a pressured cabin when flying at 30,000 feet ? 4.What process allows us to adjust to either extreme heat or cold? 5. When we begin to get dehydrated , we usually get thirsty, which causes us to drink? Is this a negative or positive...

Subjects