Question: For the inverted-pendulum system shown below, assume that the mass of the inverted pendulum is M/4 and evenly distributed along the length of the rod.

For the inverted-pendulum system shown below, assume that the mass of the inverted pendulum is M/4 and evenly distributed along the length of the rod. Also assume that the center of gravity of the pendulum is located at the center of the rod. If θ is small,

a) Derive mathematical models of the systems in the forms of differential equations

b) Derive related transfer functions

c) Determine state-space equations

У2 -У1 ө - yi У1 M F(t)

Y2 -Y1 - yi Y1 M F(t)

Step by Step Solution

★★★★★

3.43 Rating (156 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

To solve the problem lets break it down into parts a Mathematical Models Differential Equations System Description The system consists of a cart with ... View full answer

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!

Refer to Exercise 9. Assume that the mass of the rock is 288.2 g with negligible uncertainty, the initial volume of water in the cylinder is 400 0.1 mL, and the volume of water plus rock is 516 0.2...

A rod of mass m and length L rests on two pulleys A and B which rotate in opposite directions as shown. Denoting by k the coefficient of kinetic friction between the rod and the pulleys, determine...

A pendulum of length b and mass bob m is oscillating at small angles when the length of the pendulum string is shortened at a velocity of a (db/dt = a). Find Lagranges equations of motion.

Probability and Statistics - Problem Set c Keith M. Chugg October 2, 2015 1 Preliminaries, Combinatorics, Set Probability 1.1. A number of bats are in a cave. 2 bats can see out of their left eye. 3...

Using "On the Spectrum of Hydrogen" by Niels Bohr -What is the main idea of the Author's argument? What is the main essence of the piece? -What ways does the author use to propose and support their...

I need the solution for part 4 and 5 please Wheel inverted pendulums (WIP) are being widely used for short and rapid mobile transfer applications in pedestrian places. A simplified model for the WIP...

Forces on Systems Many real-world systems involve multiple objects and forces acting in different directions. To analyze motion in these complex systems, the first step is to define what objects to...

et quantities for der/reorder large packs Calculate the second U Tetailers exclusively order reorder la Huling retailers exclusively order reorder small packs. Calculate 6 months accounting for the...

1 Distributed Systems In a distributed electronic conference application each participant has a replica of a shared whiteboard. Only one user at a time may write to the whiteboard, after which the...

Formulas to use to solve the questions below are below. And use exactly the same formulas as they are in the images below. Same letters and variables in the formulas should be used to solve the...

The first Starbucks opened in Seattle in 1971 as a purveyor of coffee beans and brewing equipment. It was only in 1987, after the company was sold to Howard Schultz, that it began selling espresso...

Using Euler's method and writing a python the interval [0, 4] program to approximate the solution of the function on dy dr y(0) = 1000 y(x) = 1000e

Which of the following is the term describing a practice where the effective dates on stock options are deliberately changed for the purpose of maximizing management compensation? Backtracking...

Aaron's Agency sells an insurance policy offered by Capital Insurance Company for a commission of $100 on January 2, 2017. In addition, Aaron will receive an additional commission of $10 each year...

Use the normal approximation to the binomial distribution to determine (to four decimals) the probability of getting 7 heads and 7 tails in 14 flips of a balanced coin. Also refer to Table I on pages...

Precipitation, measured in inches, for the month of March in Minneapolis, Minnesota, was recorded for 25 consecutive years. The values ranged from 0.3 up to 4.7, with a mean of 1.7 and an SD of 1.1....

D. Johnston, a physical therapist, opened Johnstons Clinic. His accountant provided the following chart of accounts: Assets Cash Accounts Receivable Office Equipment Office Furniture Liabilities...

As part of a study of natural variation in blood chemistry, serum potassium concentrations were measured in 84 healthy women. The mean concentration was 4.36 mEq/1, and the standard deviation was...

Illustrate the practical application of the economic theory regarding monopolies and monopolistic competition. Research examples of firms that operate under each market structure and explain why you...

Problem Set 9: Collisions AP Physics C Supplementary Problems 1. A ball of mass m and speed v strikes a wall perpendicularly and rebounds with undiminished speed. (a) If the time of collision is t,...

trajectory, this kinetic energy is converted into potential energy. When the ball falls back to the ground, the potential energy is converted back into kinetic energy. The total amount of energy in...

a) Describe in details the system shown in the Figure 1, including the type of configurations, number of components, when will the system work, when will the system fail. b) In the simple...

Question 1 ( 1 6 marks ) Control systems exist in numerous varieties, both in type of applications and level of sophistications. Since most systems are dynamic in nature, to control or regulate...

QUESTION THREE Inverted Pendulum System Fuzzification Combined fuzzy inference with rule tables Defuzzified control angle Next state vector Calculation/software code Answer the questions please 3.1...

Q1) A system is released as shown. Neglect drag, friction and the mass of the string and pulley. Calculate the unknown(s) in each of the following cases. M [kg] m [kg] a [m/s2] 4 - 4 2 4 3 5 3 m MThe...