文档介绍：INSTRUMENTATION AND CONTROL
TUTORIAL 5 – SYSTEM RESPONSE
This tutorial is a continuation of tutorial 4 and is of interest to any student studying control
systems and in particular the EC module D227 – Control System Engineering.
pletion of this tutorial, you should be able to do the following.
• Explain the standard second order transfer function in detail
• Examine the various ways of writing the standard second order transfer function.
• Define the roots and poles of the standard second order transfer function.
• Explain and calculate the response of a standard 2nd order system to a step change in
the input.
• Explain and define design parameters of the second order step response.
• Explain and calculate the response of a standard 2nd order system to a ramp
(velocity) change in the input.
• Explain the response of a standard 2nd order system to a sinusoidal change in the
input.
• Explain how to find the overall gain of a system.
• Explain how to find the steady state error of systems.
• Explain the relationship between pole positions and dynamic response.
• Explain the relationship of plex pole position with the damping ration and
natural frequency.
• Explain the root locus diagram for plex poles with respect to damping ratio.
If you are not familiar with instrumentation used in control engineering, you should
complete the tutorials on Instrumentation Systems.
In order plete the theoretical part of this tutorial, you must be familiar with basic
mechanical and electrical science.
You must also be familiar with the use of transfer functions and the Laplace Transform
(see maths tutorials).
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1. STANDARD 2 ORDER SYSTEM
FORMS OF THE STANDARD TRANSFER FUNCTION
The standard second order transfer function can be expressed in many ways. Here are the most useful.
θ k
In terms of the time constant T o (s ) =
θi T2s2