Data-driven Disturbance Decoupling: Theory and Applications

Recent results on data-driven disturbance decoupling problem (D4P) are applied to two problems arising in practice, namely, the quadruple pendulum setup used in gravitational wave detectors in Laser Interferometer Gravitational-wave Observatory (LIGO) and the four-tank system. The first example is a quadruple pendulum setup used in LIGO. It has eight state variables, four control inputs, a single disturbance input and a single output. The second example is a linearized four tank system which has four state variables, two control inputs, and two outputs. Here disturbance input is considered to affect tanks 2, 3 and 4. For both examples, our recent D4P results are applied to compute the largest control invariant subspace in the kernel of output matrix and a corresponding decoupling feedback matrix by using the data of input, initial state and the noisy output trajectory. Computation is performed in a completely data driven manner and no model parameters are estimated at any stage. Simulation results showing disturbance decoupling are presented for both examples.