Reference no: EM13965192
Control System Stability - Homework - MATLAB
Discussion Question
Given the denominator of a closed-loop transfer function, ??4+ 20????3+ ??1??2+ 4?? + ??2= 0 , discuss what values of K1 and K2 will lead to a stable system.
Solve the following problems:
1. For the given system below:
Determine the range of K for the system to become unstable.
2. Determine the stability of the following polynomials: (a) 2??4 + ??3 + 3??2 + 5?? + 10
(b) ??3 + 3408.3??2 + 1,204,000?? + 1.5 × 107??
(c) ??3 + 3????2 + (?? + 2)?? + 4
3. for the following system:
(a) Determine the range of K for stability.
(b) Develop an m-file to calculate the closed-loop poles for K from 0 to 5 with an increment of 0.1 (you may want to use the for loop in MATLAB). What are the poles when K = 4?
Design Project
The altitude control of a rocket is shown in the following figure:
The controller given is ???? (??) = (??+??)(??+2)/?? (this is called a PID controller - we will cover PID controllers in Module 7) and the rocket transfer function ??(??) = ??/??2-1. Note that the rocket itself is open-loop unstable (a pole is on the right hand side of the complex plane) and feedback with a controller is needed to stabilize the system.
1. Using the Routh-Hurwitz criterion, determine the range of K and m so that the system is stable, and plot the region of stability (m vs. K).
2. Select K and m so that the steady-state error due to a ramp input is less or equal to 10% of the input magnitude.
With K and m you selected from Part 2, write a MATLAB program to obtain and plot the unit step response of the system, and determine the percent overshoot (P.O.) of the system from your plot.
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