Consider the dynamical system, * = Ax + Bu; y = Cx + Du, given by...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
Consider the dynamical system, * = Ax + Bu; y = Cx + Du, given by -1 0 0 1 0 0 0 0 -1 -1 0 -1 1 [****** B= D a. Find the transfer function of the underlying dynamical system b. Determine the controllability for the following inputs: (i) u₁, (ii) U₂, (iii) all u a. Compute the infinity controllability Gramian (P) and hence deduce the energy required to reach the ith unit vector e,, i.c, vector of zeros with 1 on the ith. position using (1) u₂, (ii) u₂, (iii) all u respectively. Comment your results. c. Determine the observability from each of the outputs: (i) y₁. (ii) y₂2. (iii) all y a. Compute the infinity observability gramian (0) and hence deduce the energy obtained by observing the ith unit vector e,, i.e, vector of zeros with 1 on the ith. position using (1) y₁, (ii) y₂, (iii) all y respectively. Comment your results. d. What can you say with regard to minimality of the system? Consider the dynamical system, * = Ax + Bu; y = Cx + Du, given by -1 0 0 1 0 0 0 0 -1 -1 0 -1 1 [****** B= D a. Find the transfer function of the underlying dynamical system b. Determine the controllability for the following inputs: (i) u₁, (ii) U₂, (iii) all u a. Compute the infinity controllability Gramian (P) and hence deduce the energy required to reach the ith unit vector e,, i.c, vector of zeros with 1 on the ith. position using (1) u₂, (ii) u₂, (iii) all u respectively. Comment your results. c. Determine the observability from each of the outputs: (i) y₁. (ii) y₂2. (iii) all y a. Compute the infinity observability gramian (0) and hence deduce the energy obtained by observing the ith unit vector e,, i.e, vector of zeros with 1 on the ith. position using (1) y₁, (ii) y₂, (iii) all y respectively. Comment your results. d. What can you say with regard to minimality of the system?
Expert Answer:
Answer rating: 100% (QA)
a To find the transfer function of the underlying dynamical system we need to transform the statespa... View the full answer
Related Book For
Posted Date:
Students also viewed these accounting questions
-
Jorgansen Lighting, Incorporated, manufactures heavy-duty street lighting systems for municipalities. The company uses variable costing for internal management reports and absorption costing for...
-
Two partners have decided to acquire a more expensive manufacturing facility. One of the partners researched and found a factory selling for $25 million. The partners went to a local bank to discuss...
-
The figure shows a rotating wheel with radius 40 cm and a connecting rod AP with length 1.2 m. The pin P slides back and forth along the -axis as the wheel rotates counterclockwise at a rate of 360...
-
A fuel, Cx Hy, is burned with dry air and the product composition is measured on a dry basis to be: 9.6% CO2, 7.3% O2 and 83.1% N2. Find the fuel composition (x/y) and the percent theoretical air...
-
List and describe the various tools for conducting primary market research.
-
In July 2008, Brian, Dale, and Sandra Allen signed a contract with East Resources, Inc., concerning 148 acres of the Allens property. East wanted to develop and exploit the oil and gas resources...
-
Lager Dental Clinic is a medium-sized dental service specializing in family dental care. The clinic is currently preparing the master budget for the first 2 quarters of 2014. All that remains in this...
-
Fickle Sickles collects 15,000 checks per 365-day year with average amount $170 and total delay 5 days. A lockbox system would reduce that delay to 3 days, and it would also reduce FISI's check...
-
A textile company produces shirts and pants. Each shirt requires two square yards of cloth, and each pair of pants requires three square yards of cloth. During the next two months the following...
-
Outcome Probability Return Boom 60% 30.4% Normal 25% 15.5% Recession 10% 10.1% Depression 5% 5.7% What is the arithmetic expected return on this asset?
-
Go to the consolidated balance sheet in the 2010 annual report for Kelloggs Company at http://investor.kelloggs.com/annuals.cfm. What is the amount of retained earnings in 2010? What is the par value...
-
In a market in which demand is price inelastic, producers can gouge consumers and the government must set high standards of conduct for producers to ensure that consumers gets a fair deal. Do you...
-
Find the most current listing of the CICAs Top Ten IT Issues Compare the listing to prior years listings. Identify and discuss trends among the years. Your professor will tell you how long your paper...
-
Explain the three key drivers of complexity in manufacturing operations in the new millennium.
-
What is systems development?
-
You have just passed ACST1001 and started a summer internship at Harrison Bank, with Peter as your supervisor. As your first task, Peter has given you some client accounts and asked you to verify...
-
Write a program to move a signed number from smaller register to bigger register. Hint: movzx ax, bl Topic: Data Related Operators and Directives in assembly language
-
Because a sailboat cannot sail directly into the wind, and traveling straight downwind is usually slow, the shortest sailing distance is rarely a straight line. Thus sailboats tack upwind-the...
-
Consider the system represented in state variable form v = Cx + Du, where C = [1000 0]. and D = [0] Sketch the Bode plot. A= 0 100
-
Consider the system represented in state variable form x = Ax + Bu y = Cx + Du, where Determine the characteristic equation and then sketch the root locus as 0 C= [1 0], and D=[0].
-
Using Mendels data from the experiment in Figure 2.8, conduct a chi square test to determine if the data agree with Mendels law of independent assortment. Mendels data: THE DATA P cross F1 generation...
-
On rare occasions, an organism may have three copies of a chromosome and therefore three copies of the genes on that chromosome (instead of the usual number of two copies). The alleles for each gene...
-
Explain how the miR-200 family of miRNAs behave as tumorsuppressor genes. What happens when their expression is blocked or decreased?
Study smarter with the SolutionInn App