Zero-pole gain model is important for digital control

1. FACULTY OF ELECTRONIC
ENGINEERING
Digital Control System

2. Creating Zero-Pole-Gain Models
Learning the basics of zero-pole-gain
models to explore the mathematical
representation of systems and how to
create a transfer function.

3. What are Zeros, Poles, and Gains?
Zeros
In a transfer function, zeros are the values
of s that cause the numerator to be zero.
Poles
In a transfer function, poles are the values
of s that cause the denominator to be
zero.
Gains
In a transfer function, the gain is the
constant that multiplies the transfer
function.
Why do we care?
Understanding zeros, poles, and gains
allows us to analyze the behavior of
systems and design controllers to achieve
desired performance.

4. Mathematical Representation of a
System
1
State Space Model
A mathematical model that describes how
a system evolves over time in response to
inputs.
2
Transfer Function
A mathematical model that relates the
output of a system to its input.
3
Block Diagram
A graphical representation of a system that
shows its inputs, outputs, and internal
components.

5. How to Create a Transfer Function
Formulate a
differential equation
that relates the
output of a system to
its input.
Take the Laplace
transform of the
differential equation.
Manipulate the
Laplace transform to
obtain the transfer
function.

6. Types of Transfer Functions
1 Proper Transfer
Function
A transfer function where
the degree of the
numerator polynomial is
less than or equal to the
degree of the denominator
polynomial.
2 Strictly Proper
Transfer
Function
A transfer function where
the degree of the
numerator polynomial is
strictly less than the
degree of the denominator
polynomial.
3 Non-Proper
Transfer
Function
A transfer function where
the degree of the
numerator polynomial is
greater than the degree of
the denominator
polynomial.
4 Real and
Complex
Transfer
Function
A transfer function where
the coefficients of the
numerator and
denominator polynomials
are real or complex
numbers.

7. Examples of Zero-Pole-Gain
Models
RC Circuit
Modeling an
RC circuit with
zero, pole, and
gain
Inverted
Pendulum
Modeling an
inverted
pendulum with
state space
and transfer
function
DC Motor
Modeling a DC
motor with
state space
and transfer
function

8. Conclusion and Practical
Applications
Conclusion
Zero-pole-gain models are
powerful tools for analyzing
and designing control systems.
Practical Applications
Zero-pole-gain models are
commonly used in fields such
as electrical engineering,
mechanical engineering, and
aerospace engineering.

9. References
1. Franklin, G. F., Powell, J. D., & Workman, M. L.
(2014). Digital control of dynamic systems.
Pearson.
2. Ogata, K. (2009). Modern control engineering.
Pearson.
3. Nise, N. S. (2011). Control systems engineering.
Wiley.