Recently, the analyses of sampled data control systems are carried out by means of the Nyquist plot or the root locus method, but they are not always simple for calculation. Therefore, the author tries to extend the merits of the Bode diagram to the sampled data control systems. The open loop pulse transfer function
W(
z) is represented as a rational polynomial in
z by
z-transformation.
Then, a system is amenable to the graphical calculation, representing its components by log modulus and phase shift. In continuous data control systems, the Bode diagram is plotted for ω=0 to ∞, while in this case, it is enough to plot only for ω=0 to π. Then we can easily find the stability criterion of the system and its design will be performed on the concepts of the gain margin and the phase margin. In designing systems by
z-transform method, there is a possibility of missing the hidden instability even in the conservative design. But this can be evaded, if we are scrupulous to design the system for the worst operating condition.
View full abstract