Consider an n-dimensional linear time-invariant system x Ax+ Bu. = a) What is the state space?...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
Consider an n-dimensional linear time-invariant system x Ax+ Bu. = a) What is the state space? b) c) Suppose that u E R². What are the dimensions of matrices A and B? Discretize the system into discrete time with step size 8. You need to express x((k+1)8) in terms of A, B, 8, x(k8), u(k8). To make the notation easier to read, you can use x[k + 1] instead of x((k+1)8) to denote the discrete-time state and express x[k +1] in terms of x[k]; note that you still need to consider the impact of 8. d) Suppose that we use a linear controller u(x) = -Kx. Write the difference equation for the discretized system; i.e., write how to obtain x[k+1] from x[k]. Find x[k] in terms of A, B, K and the initial condition x[0] = x₁ € R¹. Consider an n-dimensional linear time-invariant system x Ax+ Bu. = a) What is the state space? b) c) Suppose that u E R². What are the dimensions of matrices A and B? Discretize the system into discrete time with step size 8. You need to express x((k+1)8) in terms of A, B, 8, x(k8), u(k8). To make the notation easier to read, you can use x[k + 1] instead of x((k+1)8) to denote the discrete-time state and express x[k +1] in terms of x[k]; note that you still need to consider the impact of 8. d) Suppose that we use a linear controller u(x) = -Kx. Write the difference equation for the discretized system; i.e., write how to obtain x[k+1] from x[k]. Find x[k] in terms of A, B, K and the initial condition x[0] = x₁ € R¹.
Expert Answer:
Answer rating: 100% (QA)
a The state space of the system is the set of all possible states that the system can be in In this ... View the full answer
Related Book For
Modern Advanced Accounting In Canada
ISBN: 9781259066481
7th Edition
Authors: Hilton Murray, Herauf Darrell
Posted Date:
Students also viewed these general management questions
-
You are the Chairperson of the Business Program at InterState Community College (ICC). Recently it has come to that attention of ICC Administration that there is a need for Project Management...
-
Planning is one of the most important management functions in any business. A front office managers first step in planning should involve determine the departments goals. Planning also includes...
-
Managing Scope Changes Case Study Scope changes on a project can occur regardless of how well the project is planned or executed. Scope changes can be the result of something that was omitted during...
-
The following data relates to direct labor costs for August: Actual costs: 5,500 hours at $24.00 per hour. Standard Costs: 5,000 hours at $23.70 per hour. What is the direct labor rate variance?
-
An alternating current of frequency w = 314 s-1 is fed to a circuit consisting of a capacitor of capacitance C = 73F and an active resistance R = 100 connected in parallel. Find the impedance of the...
-
Consider four mutually exclusive alternatives: The analysis period is 8 years. At the end of 2, 4, and 6 years Alt A will have an identical replacement. Alternative B will have a single identical...
-
Santiago, Inc., began operations as an importer of fine Chilean wine the United States. Sales and purchase information is provided below. Santiago, Inc., uses the LIFO method of inventory valuation....
-
FINS produces three products from its fish farm: fish, fish oil, and fishmeal. During July 2010, FINS produced the following average quantities of each product from each pound (16 ounces) of fish...
-
You are the manager of a U . S . company situated in Los Angeles and manages the import / export division of the company. The company distributes ( resells ) a variety of consumer products imported...
-
On January 1, 2024, LLB Industries borrowed $200,000 from Trust Bank by issuing a two-year, 10% note, with interest payable quarterly. LLB entered into a two-year interest rate swap agreement on...
-
Bramble Unlimited is considering purchasing an additional delivery truck that will have a seven-year useful life. The new truck will cost $33,500. Cost savings with this truck are expected to be...
-
For a sample of size n = 15, the following values were obtained: b0 = 3.71, b1 = 8.38, se = 1.13, (x x)2 = 7.71, x = 13.16. Construct a 95% prediction interval for an individual response when x = 8.
-
What does the responding party need to do to object to a motion for summary judgment?
-
Which of the following is least likely to be detected by an internal control system? a. Duplicate payments to suppliers. b. Deviations from written procedures. c. Fraudulent actions by an individual...
-
Assume that as a government auditor you have been asked to evaluate an energy growth model. The model relies on historical data and uses econometric techniques to estimate the parameters in the...
-
Organization charts of the activity being audited are useful to the internal auditor because they: a. Depict informal lines of communication. b. Provide good internal control. c. Ensure a proper...
-
Suppose there is a monopoly firm operating in the Home market in the no-trade situation. When Home opens up to trade, many foreign firms are willing to sell in the Home market at the world price...
-
Without solving, determine the character of the solutions of each equation in the complex number system. 3x 2 3x + 4 = 0
-
The balance sheets of X Ltd. and Y Ltd. on December 30, Year 7, are as follows: On December 31, Year 7, X issued 150 common shares for all 60 outstanding common shares of Y. The fair value of each of...
-
Baskin purchased 20,000 common shares (20%) of Robbin on January 1, Year 5, for $275,000 and classified the investment as FVTPL. Robbin reported net income of $85,000 in Year 5 and $90,000 in Year 6,...
-
Explain the application of lower of cost and net realizable value to inventory that was purchased from a foreign supplier.
-
The Rankine Corporation reported net income of \($10\) million in 2016, and it appears that net income for 2017 will be the same. During 2017, the company made the following expenditures: 1....
-
The following cash flow information was taken from the 2015 annual report for Johnson & Johnson. Compute the missing values in the table (amounts are in millions). Based on this data, how does the...
-
The following cash flow information was taken from the 2015 annual report for General Electric. Compute the missing values in the table (amounts are in millions). Based on this data, describe GEs...
Study smarter with the SolutionInn App