Convenient representation of a linear, dynamic model.
A transfer function (TF) relates one input and one output:
u (t )
y (t )
The following terminology is used:
Frequency Response Analysis
Sinusoidal Forcing of a First-Order Process
For a first-order transfer function with gain K and time constant ,
the response to a general sinusoidal input, x t A sin t is:
et / cos t sin t
Dynamic Behavior and Stability of
Closed-Loop Control Systems
In this chapter we consider the dynamic behavior of
processes that are operated using feedback control.
This combination of the process, the feedback controller,
and the instrument
Controller Tuning: A Motivational Example G s
Fig. 11.1. Unit-step disturbance responses for the candidate controllers
(FOPTD Model: K = 1, 4, 20).
PID Controller Design, Tuning, and
Mathematical Modeling of
Mathematical Model (Eykhoff, 1974)
a representation of the essential aspects of an existing
system (or a system to be constructed) which
represents knowledge of that system in a usable form
Figure 7.1 Schematic diagram for a stirred-tank blending
Basic Control Modes
Next we consider the three basic control modes starting with the
simplest mode, proportional control.
More General Transfer Function Models
Poles and Zeros:
The dynamic behavior of a transfer function model can be
characterized by the numerical value of its poles and zeros.
General Representation of TF:
There are two equivalent representation
A Career in Process Control
Provides professional mobility.
There is a
shortage of experienced process control engineers.
Well paid technical profession for chemical
Importance of Process Control
Process Control directl
In analyzing process dynamic and process control systems, it is
important to know how the process responds to changes in the
A number of standard types of input changes are widely used for
1. They ar
Problem 4.6 c
Comments: It is underdamped process with nominator terms
(check the response in Simulink)