How can I create the Mathematica model of the inverted pendulum with a moving vertically base? To
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
To dos For the described system do the following: (a) Prepare the Mathematica model of the inverted pendulum with a moving vertically base (1): i. define a function which returns the pendulum base position, ii. define a function which returns the mass m position, iii. define the differential equation 1. Analyze the model behavior for an initial value equal to 0 and 0.2, and the steady base (y=0). Plot the joint angle as a function of time. Animate the pendulum movement. Investigate the influence of the dumping coefficient on the pendulum behavior. (b) Equip the pendulum with the oscillator (2): i. define the rule which introduces the controller (2), ii. apply the defined rule to the system. Examine the correctness of the provided solution. (c) Simulate the system behavior for both the initial values with different values of oscil- lations amplitude and frequency. Try A = 0.2, w = 4; A = 0.2, w = 40; A = 0.2, w = 400; A = 0.02, w 400; A= 0.002, w = 400; A 0.002, w 4000. Try to derive some conclusions about the influence of the oscillator amplitude and its frequency on the system behaviors. = = To dos For the described system do the following: (a) Prepare the Mathematica model of the inverted pendulum with a moving vertically base (1): i. define a function which returns the pendulum base position, ii. define a function which returns the mass m position, iii. define the differential equation 1. Analyze the model behavior for an initial value equal to 0 and 0.2, and the steady base (y=0). Plot the joint angle as a function of time. Animate the pendulum movement. Investigate the influence of the dumping coefficient on the pendulum behavior. (b) Equip the pendulum with the oscillator (2): i. define the rule which introduces the controller (2), ii. apply the defined rule to the system. Examine the correctness of the provided solution. (c) Simulate the system behavior for both the initial values with different values of oscil- lations amplitude and frequency. Try A = 0.2, w = 4; A = 0.2, w = 40; A = 0.2, w = 400; A = 0.02, w 400; A= 0.002, w = 400; A 0.002, w 4000. Try to derive some conclusions about the influence of the oscillator amplitude and its frequency on the system behaviors. = =
Expert Answer:
Related Book For
Income Tax Fundamentals 2013
ISBN: 9781285586618
31st Edition
Authors: Gerald E. Whittenburg, Martha Altus Buller, Steven L Gill
Posted Date:
Students also viewed these databases questions
-
Let A, B be sets. Define: (a) the Cartesian product (A B) (b) the set of relations R between A and B (c) the identity relation A on the set A [3 marks] Suppose S, T are relations between A and B, and...
-
Answer the following question based on the information presented for Cloud 9 in the appendix to this text and the current and earlier chapters. You should also consider your answers to the case study...
-
A researcher is testing the effectiveness of a skills mastery imagery program for soccer players. A sample of n = 25 college varsity players is selected and each player is tested on a ball-handling...
-
A 50.0-kg block and a 100-kg block are connected by a string as in Figure P8.36. The pulley is frictionless and of negligible mass. The coefficient of kinetic friction between the 50.0 kg block and...
-
According to an article in the Wall Street Journal, in 2022, the Walt Disney Company hired 50 people for a new division of the company to develop metaverse strategiesfinding ways to tell interactive...
-
Yi Min started an engineering firm called Min Engineering. He began operations and completed seven transactions in May, which included his initial investment of $18,000 cash. After those seven...
-
_____ redirects a user from a legitimate website to a malicious website by changing hosts files on a DNS server. A. Exploitation framework B. ARP poisoning C. DDoS DNS attack D. DNS...
-
Find the following derivates: 1) f(x) = x5 2) H(x) = 3x4 3) y(x) = 1/x2 = x2 4) f(t) = t2 = t2/3 %3D
-
In Problems 23-34, find the value of each annuity at the end of the indicated number of years. Assume that the interest is compounded with the same frequency as the deposits. Amount of Deposit m 30....
-
Use estimation to select the best response in Problems 7-24. Do not calculate. A reasonable APR to pay for a 3 -year installment loan is A. \(1 \%\) B. \(12 \%\) C. \(32 \%\)
-
Find the present value of the ordinary annuities in Problems 21-32. Amount of Deposit m 28. $400 Frequency n quarterly Rate r 11% Time t 20 yr
-
Use a calculator to evaluate an ordinary annuity formula \[A=m\left[\frac{\left(1+\frac{r}{n}ight)^{n t}-1}{\frac{r}{n}}ight]\] for \(m, r\), and \(t\) (respectively) given in Problems 7-22. Assume...
-
Explain summation notation.
-
in February 2009, bushfires raced across the Australian state of Victoria. this terrible tragedy resulted in the loss of over 300 lives, Australias highest ever loss of life from a bushfire. In...
-
Wimot Trucking Corporation uses the units-of-production depreciation method because units-of-production best measures wear and tear on the trucks. Consider these facts about one Mack truck in the...
-
While preparing Massie Miller's 2012 Schedule A, you review the following list of possible charitable deductions provided by Massie: Cash contribution to a family whose house burned...
-
Carl and Jenny adopt a Russian orphan. The adoption takes 2 years and two trips to Russia and is final in 2012. They pay $6,000 in 2011 and $7,500 in 2012 of qualified adoption expenses, and have AGI...
-
Ray and Maria Gomez have been married 3 years. They live at 1610 Quince Ave., McAllen, TX 78701. Ray works for Palm Oil Corporation and Maria works for the City of McAllen. Maria's Social Security...
-
In a boiler trial observations made are as: Feed water temperature \(=30^{\circ} \mathrm{C}\) Boiler pressure \(\quad=12 \mathrm{bar}\) Dryness fraction of steam \(=0.80\) Coal consumption...
-
How much heat is to be added to convert \(4 \mathrm{~kg}\) of water at \(20^{\circ} \mathrm{C}\) in to steam at 8 bar and \(200^{\circ} \mathrm{C}\). Take \(C_{p}\) of superheated steam as \(2.1...
-
What do you understand by mechanical and thermal efficiency? A steam plant uses 3 tonne of \(\mathrm{coal} / \mathrm{h}\). The steam is fed to turbine the output of which is \(4 \mathrm{MW}\). The...
Study smarter with the SolutionInn App