Routh-Hurwitz Stability Criterion: Solving Feedback Control Systems Homework

In summary, the method for approaching the second question is to form an auxiliary equation and solve for the roots, which will give the oscillation frequency of the system when K = 1.
  • #1
l46kok
297
0

Homework Statement



http://img24.imageshack.us/img24/9028/72841137.jpg [Broken]

Homework Equations



Routh-Hurwitz Stability Criterion

The Attempt at a Solution



For first question, you just write the Routh Array, make sure that the first row is all positive and you get Kmax = 1. Simple enough

How would I approach the second question though? Any starters would be sincerely appreciated.
 
Last edited by a moderator:
Physics news on Phys.org
  • #2
l46kok said:

Homework Statement



http://img24.imageshack.us/img24/9028/72841137.jpg [Broken]

Homework Equations



Routh-Hurwitz Stability Criterion

The Attempt at a Solution



For first question, you just write the Routh Array, make sure that the first row is all positive and you get Kmax = 1. Simple enough

How would I approach the second question though? Any starters would be sincerely appreciated.

You got the value K = 1 by making the line [tex]s^1[/tex] equal to zero. Now, you form an auxiliary equation with the coefficients of the [tex]s^2[/tex] line. The roots of the auxiliary equation are also roots of the characteristic equation. Solve it and you get two imaginary roots, whose module is the oscillation frequency when K = 1.
 
Last edited by a moderator:

1. What is a feedback control system?

A feedback control system is a type of control system in which the output of a system is continuously compared to a desired input, and adjustments are made based on the difference between the two. This allows the system to maintain a desired output and correct for any errors or disturbances.

2. What are the components of a feedback control system?

A feedback control system typically consists of four main components: a sensor or measuring device, a controller, a plant or process being controlled, and an actuator or final control element. The sensor measures the output of the system, the controller calculates the appropriate action to take, the plant carries out the action, and the actuator translates the control signal into a physical response.

3. What is the purpose of a feedback control system?

The main purpose of a feedback control system is to maintain or regulate a desired output of a system. This can be achieved by continuously comparing the output to a desired input and making adjustments to ensure that the output remains within a specified range or meets a certain setpoint.

4. What are the advantages of using feedback control systems?

Feedback control systems have several advantages, including the ability to maintain system stability, adapt to changes or disturbances, and improve accuracy and precision. They also allow for remote or automated control of systems, reducing the need for manual intervention.

5. What are some examples of feedback control systems?

Feedback control systems are used in a wide range of applications, including temperature control in thermostats, speed control in motor vehicles, and flight control in airplanes. They are also commonly used in industrial processes, such as manufacturing and chemical production, to maintain precise and consistent outputs.

Similar threads

  • Engineering and Comp Sci Homework Help
Replies
0
Views
710
  • Engineering and Comp Sci Homework Help
Replies
4
Views
2K
Replies
1
Views
894
  • Engineering and Comp Sci Homework Help
Replies
1
Views
3K
  • Engineering and Comp Sci Homework Help
Replies
1
Views
2K
  • Engineering and Comp Sci Homework Help
Replies
16
Views
4K
  • Engineering and Comp Sci Homework Help
Replies
1
Views
1K
  • Engineering and Comp Sci Homework Help
Replies
8
Views
2K
  • Engineering and Comp Sci Homework Help
Replies
1
Views
4K
  • Introductory Physics Homework Help
Replies
12
Views
740
Back
Top