# “Transfer Function Analysis of Dynamic Systems” Courseware

## Course Materials Include:

#### Transfer Function Analysis of Dynamic Systems

This curriculum module contains interactive live scripts and a MATLAB app that teach transfer function analysis of dynamic systems. The contents include an interactive live script review lesson on Laplace transforms. The main lessons for the module are covered in three live scripts:

• Transfer Function Basics
• Pole-Zero Analysis
• Frequency Domain Analysis

Throughout the module, students apply transfer functions to analyze the dynamics of physical and electrical systems. In the final lesson, students perform a frequency domain analysis of an LC filter in a buck converter. The MATLAB app lets students construct a transfer function by graphically positioning the poles and zeros, as well as compute and plot the impulse and step responses. These lessons can be used as part of a lecture, as activities in an instructional setting, or as interactive assignments to be completed outside of class.

Learning Goals

• ConceptReview.mlx
• Compute Laplace transforms by hand and using symbolic math.
• Describe the properties of the Laplace transform.
• Apply Laplace transforms to solve initial value problems.
• Recall the definition of a linear time-invariant (LTI) operator.
• TransferFunctionBasics.mlx
• Derive transfer functions by hand.
• Derive transfer functions using symbolic math.
• Numerically evaluate and plot the impulse, step, and forced responses of a system.
• Analytically derive the step and forced responses of a system.
• Explain the physical significance of time responses.
• PoleZeroAnalysis.mlx
• Describe how the transfer function of a DC motor is derived.
• Identify the poles and zeros of a transfer function.
• Assess the stability of an LTI system based on the transfer function poles.
• Relate the position of poles in the s-plane to the damping and natural frequency of a system.
• Explain how poles of a second-order system relate to its dynamics.
• Examine how transfer function zeros affect the dynamics of a system.
• FrequencyDomainAnalysis.mlx
• Explain how a Bode plot is generated.
• Use MATLAB to numerically calculate the frequency response of a transfer function.
• Discuss how features of the Bode plot relate to characteristics of physical systems.
• Describe how to derive a differential equation model for a buck converter with an LC filter.
• Apply the Bode plot to analyze an LC filter in a buck converter.

• Have any questions or feedback? Contact the MathWorks online teaching team.