Dual-driver standing wave tube: acoustic impedance matching with robust repetitive control

In many applications of acoustic standing wave tubes, for instance thermoacoustic heat pumping systems, it is desirable to make a shorter tube operate like a longer standing wave tube at the same driving frequency. The basic idea here is to reduce the physical length of the tube, and replace the removed section with a secondary driver. The problem is then to match the acoustic impedance at the boundary where the secondary driver is installed to that of the original system. A two-input-two-output (TITO) formulation directly tracks the two acoustic variables related to the impedance, while a SISO formulation minimizes the impedance matching error. The desired impedance containing a very lightly damped mode is embedded in the augmented plant for feedback control design. In addition to the balance realization method, the Schur method was used in model reduction for the high-order non-minimum phase plants. Since the standing wave tubes are driven by tonal signals, repetitive control was incorporated into the control frameworks to achieve the desired performance. Good impedance matching performance was obtained for both formulations. The formulations are compared.