A novel multi-loop QFT robust control methodology for cascade control systems

In attempt to improve the conventional method, we proposed a new iterative methodology. The new methodology starts with the inner loop to design a controller with desired control specifications formulated as quadratic inequalities and QFT-bounds. Then, with the resulting inner controller the outer loop is designed in a similar way as the inner one, and as a function of the inner loop design. Subsequently new control specifications, quadratic inequalities and QFT-bounds based on sensitivity functions of two controllers already designed are formulated and added to the original set of QFT-bounds of the inner loop, restarting the design of the controllers in an iterative methodology. By Cascade-Control theory, the inner loop must be faster; therefore, adding QFT-bounds of the outer loop to the inner loop will be helpless because the inner loop is more demanding one. Therefore, we add a new cascade controller external to the outer loop (new loop) and apply our theory on the outer and the new loops. We continue this process, adding additional external loops, until we meet our objective function. Alternatively, gradual decrease of sensitive function at low frequency for each loop leads to the same conclusion. In this paper we present this new control design methodology and expand it to "n" cascade control loops. We also validate the methodology improving a classical electrical motor cascade control system with current, velocity and position loops.