Stability Test for Multivariable NCbT Using Input/Output Data

Abstract

In model-free controller syntheses, we have no idea whether the designed controller stabilizes the resulting closed-loop system before its implementation. From the view point of safety of the experimental equipment, we should develop the stability test for model-free controller synthesis using the acquired input/output data. Karimi et al. introduced the sufficient stability condition for the closed-loop system and proposed the stability test for NCbT (Noniterative Correlation-based Tuning) for SISO systems. However, since the positions of the plant and the controller have to be swapped in NCbT, its applicability is restricted to SISO systems.
This paper proposes to extend the stability test for NCbT to MIMO systems. The basic idea is to use the special reference r^[i](t) and to acquire input/output data as many times as the number of plant inputs. The small-gain theorem introduces the sufficient stability condition for the closed-loop system in terms of the H_∞ norm of the specific transfer function matrix, which is estimated from the acquired input/output data by the spectral analysis method.
The effectiveness of the proposed stability test is confirmed by the numerical experiment for LV100 gas turbine engine model and the experiment for tension-and-speed control apparatus.