Limitations of Loop Gain in Motion Models of Physical Systems

This paper presents some limitations of the classical concept of loop gain in many mathematical motion models of the real objects. It is well known that there are some advanced concepts in control theory and a lot of them are very heavy on the loop gain. Therefore, the loop gain is heard in many topics like frequency compensation, phase-gain margins, negative feedback systems. However, the loop gain cannot be used to analyze the overshoot phenomenon in many feedback amplifiers because it doesn't show the operating regions of high-order mechatronic systems. In addition, the theoretical calculation, the laboratory simulation and the practical measurement of loop gain are not unique. As a result, this is the biggest limitation in mathematical models of motion that a lot of engineers have trouble with loop gain. To overcome some disadvantages of the loop gain, the use of the self-loop function allows engineers to do the ringing test simpler because it is easily verified in MATLAB calculator, SPICE simulator, and Network Analyzer. In order to extend the application range of the Nichols chart of self-loop function in high-order mechatronic systems, the feasibility of complex functions and the explanation of overshoot phenomena are described in detail. It is shown that complex functions are useful tools for mathematical motion models of mechatronic systems.