Indian Institute of Information Technology, Allahabad
Department of Electronics and Communication Engineering
Course Name: Control System Lab
EXPERIMENT NO: 6
DETERMINATION OF BODE PLOT USING MATLAB CONTROL SYSTEM TOOLBOX FOR 2ND ORDER
SYSTEM AND OBTAIN CONTROLLER SPECIFICATION PARAMETER.
Objective:To determine
Bode plot of a 2nd order system
II. Frequency domain specification parameters
Materials Required: MATLAB Software.
THEORY: The frequency response method may be less intuitive than other methods you
have studied previously. However, it has certain advantages, especially in real-life situations
such as modeling transfer functions from physical data. The frequency response of a system
can be viewed two different ways: via the Bode plot or via the Nyquist diagram. Both
methods display the same information; the difference lies in the way the information is
presented. We will explore both methods during this lab exercise. The frequency response is
a representation of the system's response to sinusoidal inputs at varying frequencies. The
output of a linear system to a sinusoidal input is a sinusoid of the same frequency but with a
different magnitude and phase. The frequency response is defined as the magnitude and phase
differences between the input and output sinusoids. In this lab, we will see how we can use
the open-loop frequency response of a system to predict its behavior in closedloop. To plot
the frequency response, we create a vector of frequencies (varying between zero or "DC" and
infinity i.e., a higher value) and compute the value of the plant transfer function at those
frequencies. If G(s) is the open loop transfer function of a system and ω is the frequency
vector, we then plot G( jω) vs. ω . Since G( jω) is a complex number, we can plot both its
magnitude and phase (the Bode plot) or its position in the complex plane (the Nyquist plot).
The gain margin is defined as the change in open loop gain required to make the system
unstable. Systems with greater gain margins can withstand greater changes in system
parameters before becoming unstable in closed loop.
The phase margin is defined as the change in open loop phase shift required to make a closed
loop system unstable.
