Question: Consider a rotating robot where you can control the angular velocity around a fixed axis. (a) Model this as a system where the input is

Consider a rotating robot where you can control the angular velocity around a fixed axis.

(a) Model this as a system where the input is angular velocity and the output is angle . Give your model as an equation relating the input and output as functions of time.

(b) Is this model BIBO stable?

(c) Design a proportional controller to set the robot onto a desired angle. That is, assume that the initial angle is (0) = 0, and let the desired angle be (t) = au(t), where u is the unit step function. Find the actual angle as a function of time and the proportional controller feedback gain K. What is your output at t = 0? What does it approach as t gets large?

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 Databases Questions!

Consider a turntable to be a circular disk of moment of inertia It rotating at a constant angular velocity i around an axis through the center and perpendicular to the plane of the disk ( the disk's...

P10.1: In this exercise problem, we will review how to find equilibriums of a nonlinear system, and how to obtain a linearized state-space model of the nonlinear system at a chosen equilibrium. Then...

A 55-kg runner runs around the edge of a horizontal turntable mounted on a vertical, frictionless axis through its center. The runner's velocity relative to the earth has magnitude 2.8 m/s. The...

A 5 5 . 0 k g runner runs around the edge of a horizontal turntable mounted on a vertical, frictionless axis through its center. The runner's velocity relative to the earth has magnitude 2 . 7 0 m s...

Review | Constants A 50.0 kg runner runs around the edge of a horizontal turntable mounted on a vertical, frictionless axis through its center. The runner's velocity relative to the earth has...

Exercise 4. Roll control under periodic disturbance (10pt) Consider the feedback loop represented in Fig. 1 where 1 P(s) = S is the normalized transfer function of a body rotating around one of its...

Motion in space of physical objects can be represented with six degrees of freedom. Three of these represent position in three-dimensional space,and three represent orientation in space. We assume...

Chapter 10 Getting Dizzy with Rotational Dynamics In This Chapter Calculating moments of Inertia Doing rotational work Rolling with rotational work and ramps Handling angular momentum Working with...

A model rocket is constructed with a motor that can provide a total impulse of 24.0 N-s. The mass of the rocket is 0.202 kg. What is the speed that this rocket achieves when it is launched from rest?...

. Thinkabout 35.1 - Forces on a circle a+ Consider the Figure below for the following Thinkabout. You may want to refer to the Angular Conservation of Momentum Model Sheet Please do the following: 1....

Kropf Inc. has provided the following data concerning one of the products in its standard cost system. Variable manufacturing overhead is applied to products on the basis of direct labor-hours....

Roofs of houses are sometimes blown off (or are they pushed off?) during a tornado or hurricane. Explain, using Bernoullis principle.

active versus passive management of a bond portfolio, including a discussion of issues in performance measurement of both approaches. the key points on General Challenges in Performance Measurement...

On December 1 0 , a company pays $ 5 0 0 for advertising to appear on December 2 0 . On which date should the expense be recorded under accrual - basis accounting?

How is the chairperson of the Federal Reserve System selected? Describe the relationship between the Board of Governors of the Federal Reserve System and the 12 Federal Reserve Banks. What is the...

KEY QUESTION What are the components of the M 1 money supply? What is the largest component? Which of the components of M 1 is legal tender? Why is the face value of a coin greater than its intrinsic...

KEY QUESTION Trace the cause-and-effect chain through which financing and refinancing of the public debt might affect real interest rates, private investment, the stock of capital, and economic...