Use of the magnitude invariance method for digital emulation of analog controllers

Use of digital computers for controlling physical systems has become more and more popular due to the many advantages of digital control. Because continuous time design tools are abundant and more common with many control engineers, design by emulation is often preferred over direct digital design. Unfortunately, when a controller is mapped from the s-domain to the z-domain using traditional techniques, the magnitude of the resulting discrete-time controller does not match its continuous-time counterpart. In this paper the Magnitude Invariance Method (MIM), which was recently developed in the field of signal processing, is used for digital emulation. This technique produces a discrete time transfer function with a magnitude response nearly the same as its analog prototype. The open-loop frequency and closed-loop step responses of systems designed using this approach are investigated to demonstrate the effectiveness of this approach.