Control system design and analysis using closed-loop Nyquist and Bode arrays

TLDR: In this article, a method is described for designing linear multivariable control schemes which have a closed-loop frequency response as close as possible, in a least squares sense, to a desired response.

Abstract: In this paper a method is described for designing linear multivariable control schemes which have a closed-loop frequency response as close as possible, in a least squares sense, to a desired response. After using characteristic gain loci to ensure system stability, the closed-loop Bode array gives easily understood information about the controlled system in terms of bandwidth, speed of response, resonance and interaction. The closed-loop Nyquist array indicates the robustness of the control scheme for sensor failures ; it also indicates the extent to which state and input noise will be suppressed, since the feedback just multiplies the open-loop disturbances by a unit matrix minus the closed-loop frequency response. Bands of Gershgorin and Ostrowski circles are used to indicate the behaviour for changes in the characteristics of more than one sensor at a time. A similar frequency-response array, obtained by breaking the feedback loops next to the actuators instead of next to the sensors, can be used to p...