UESTC4003 - Control
Computer Lab Exercise 2
MATLAB for Control Engineering
1.0 Objectives
The primary aim of this class is to use MATLAB to:
• Create and analyse Bode Diagrams and Nyquist plots
• Analyse Dynamic models
2.0 Bode Diagrams and Nyquist plots
2.1 Consider the system that has the forward transfer function:
a) Draw the Bode log-magnitude and phase plots for this system.
b) Also obtain the Nyquist plot for the same system.
c) Find the real-axis crossings by clicking on the appropriate points on the plotted Nyquist plot.
d) Plot the Nichols chart, with grid, for the same system.
2.2 Consider unity feedback system that has the below forward transfer function:
a) Draw the Bode log-magnitude and phase plots for this system.
b) Obtain the Nyquist plot for the same system, find gain, and phase margins. Also, find associated frequencies for gain and phase margins.
3.0 Analysis of Dynamic Models (Exercise 2A)
Consider a general second-order transfer function:
wn is the natural frequency of a second-order system (the frequency of oscillation of the system without damping and ζ is the damping ratio. Without damping, the poles would be on the jω-axis, and the response would be anundamped sinusoid. Second- order response as a function of damping ratio can be shown as in Figure 1 below:
Figure 1
3.1 Calculate the eigenvalues, natural frequencies and damping factors of the continuous transfer function model:
3.2 Define below MIMO transfer function model in MATLAB and find DC gain.
3.3 Now generate the Bode plot for the system defined in part 3.2.
3.4 Builds a second-order transfer function, G(s), with damping factor 0.35 and natural frequency 3.4 rad/sec.
3.5 Computes a closed-loop model as shown in Figure 2,using H(s) from part 3.1 and G(s) from part 3.4.
Figure 2
3.6 Plot the closed-loop poles and zeros, with grid, of the model shown in Figure 2. Also, plot the impulse response of the system.
3.7 Plot also the response of the system when the input is given by:
4.0 Analysis of Electrical Networks (Exercise 2B)
Figure 3
Consider the electrical network shown in Figure 3. Note, Laplace domain values for each inductor, resistor and capacitor are shown in the figure.
4.1 Write down the mesh equations for the network.
4.2 Using MATLAB, find all of the mesh currents in the network.
4.3 Hence obtain the transfer function, I3(s)/V(s), where I3(s) is the current through the capacitor.
References
Gene F. Franklin, J. Da Powell, Abbas Emami-Naeini, Feedback Control of Dynamic Systems, 7th Edition.
Katsuhiko Ogata, Modern Control Engineering, 5th Edition.
Norman S. Nise, Control Systems Engineering, 7th Edition.