Controller Design for Non-Minimum Phase Systems

The figure is a closed-loop control block diagram of a non-minimum phase system, where H(s) is the transfer function of the voltage detection element.

Figure 1 Block diagram of closed-loop control for non-minimum phase system

Given a non-minimum phase system, whose transfer function is G(s), including RHP zeros, that is, (1-Tzs), design a controller with transfer function K(s). The design steps are as follows:

(1) For unstable systems (with right half-plane poles), the inner loop should be designed first to make it stable.

(2) Try to design, for example, let the low-order controller transfer function be

(3) The corrected system open-loop transfer function is:

For example, the current-mode controlled Boost converter is

That is, the corrected system open-loop transfer function retains the RHP zeros in G(s), so the controller will not contain RHP poles.

During design, the To(s) parameter can be selected so that the low frequency band meets the high gain requirement, the mid-frequency band meets the stability and response speed requirement, and the high frequency band meets the noise suppression requirement.

For example, the controller design of the current-mode controlled Boost converter.

If a current-mode controlled Boost converter is used, the voltage loop open-loop transfer function of the system after correction is expected to be