A process whose dynamics is described by a double integrator is controlled by an ideal PD controller with the transfer function C(s) kas kp, where the gains are ka 25wo and kp wf, and 0 1 1 (a) What is the loop transfer function (L(s) P(s)C(s)) for this system (b) The gain margin is 9m where L(iwpc) ' Wpc is the phase crossover frequency (the frequency at which the Nyquist curve crosses the nega tive real axis ImL(iwpc) 0 and ReL(iwpc) 0) When the Nyquist curve never intersects the (strictly) negative real axis, we define the gain margin to be infinite Show that the gain margin is infinite for any value of $ (c) The phase margin is m arctan(Rege)), where wgc is the gain crossover frequency (the frequency at which the Nyquist curve crosses through the unit circle L(iwgc) 1) Calculate the phase margin m, and plot m vs C Hint if you do the algebra correctly, you will not need to know the value of wo for your plot (d) The stability margin is the shortest distance from the Nyquist curve to the critical point Sm minw L(iw) 1 you Calculate the stability margin sm, and plot sm vs C Hint 1 if do the algebra correctly, you will not need to know the value of wo for your plot Hint 2 the minimizer wmin may depend on the value of C

The Answer is in the image, click to view ...

Question: A process whose dynamics is described by a double integrator is controlled by an ideal PD controller with the transfer function C(s) = kas

A process whose dynamics is described by a double integrator is controlled by an ideal PD controller with the transfer function C(s) = kas + kp, where the gains are ka = 25wo and kp = wf, and 0 < < 1. 1 (a) What is the loop transfer function (L(s) = P(s)C(s)) for this system? (b) The gain margin is 9m = where |L(iwpc)|' Wpc is the phase crossover frequency (the frequency at which the Nyquist curve crosses the nega- tive real axis: ImL(iwpc) = 0 and ReL(iwpc)

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mechanical Engineering Questions!

The Wood Connection decided to offer cash discounts toits regular credit customers, provided the credit customers have a proven trackrecord of on-time payment. The Wood Connection is offering Monkey...

Write a short paragraph about "What should a hiring process be?" In HRM

Read the Citizens Guide to the Federal Budget that is posted in this week's module. Review the federal budget historical tables at the following website and provide your answers to the following...

EXPERIMENT G1: Dynamic Response Modelling & Temperature Controller Tuning in a Jacketed Flow Reactor Objective This experiment involves a jacketed, mixed flow reactor in which an exothermic (heat...

Please read the question Question : What are "spaced practice", "varied practice", and "interleaved practice"? Give a definition for each. Then give an example of each from your own experience as a...

Project 1: Analysis of a 10- K (10%) 1. Locate a 10-K of your choice from the SEC website (www.sec.gov). Present your choice in the conference set up for same in Week #1 for approval by stating the...

Pick a case and become familiar with the case requirements. Use what you learned on chapter 19. For formatting, use times new roman 12 pt font and double space your answers. You must include...

Consider the mechanical system in Example 2-2 on page 32 of the textbook, whose dynamics are described by (2-16)(2-21) and whose block diagram is shown in Figure 2-16. Suppose the system parameters...

Dymac Appliances uses the periodic inventory system. Details regarding the inventory of appliances at January 1, purchases invoices during the next 12 months, and the inventory count at December 31...

Evelyn Carter started Carter Manufacturing Company to make a universal television remote control device that she had invented. The companys labor force consisted of part-time employees. The following...

MONARCH INSTITUTE The partners have all replied to your email approving the financial report. They have also asked to complete additional analysis of the financial data. The business would like to...

Armstrong Helmet Company Developed by Dick Wasson, Southwestern College The Business Situation Armstrong Helmet Company manufactures a unique model of bicycle helmet. The company began operations...

Go to the "Governmental Affairs" webpage on the American Counseling Association website, located in the Topic 4 Resources, to find options to advocate for the counselors and the counseling profession...

X P X10. You need to add another current so that B]; = D. A classmate suggests that you run a current through point R parallel to all the others. Could this work? lfit could: determine the direction...

Answer all . 4. The Uris & Warren Ratings Agency rates bonds on a simplified scale with just three categories: A, B, and C. The Professors Pension Fund has all its money invested in two bonds, X and...

Large Industries annual bonds are selling at 95.70 (i.e., the price is $957 for the $1,000 bond). There are 8 years remaining until maturity on the bonds and the yield to maturity is 6.25%. Find the...

Should we separate the debt and equity features of convertible debt? Team 1: Pro separation: Present arguments in favor of separating the debt and equity features of convertible debt. Team 2: Against...

A manufacturer of light bulbs finds that the mean lifetime of a bulb is 1200 hours. Assume the life of a bulb is exponentially distributed. a. Find the probability that a bulb will last less than its...

Find the lengths of the curves. x = (y 3 /12) + (1/y), 1 y 2

The instructions for the integrals have two parts, one for the Trapezoidal Rule and one for Simpsons Rule. I. Using the Trapezoidal Rule a. Estimate the integral with n = 4 steps and find an upper...

7. How does testosterone infl uence emotional and cognitive responses to a facial expression of anger?

10. What change in diet can alter the production of serotonin?

9. Given that monkeys with low serotonin turnover pick many fi ghts and in most cases die young, what keeps natural selection from eliminating the genes for low serotonin turnover?