Discrete Time LQG/LTR Applied To A Practical Quadruple Tank System

Discrete time robust linear quadratic Gaussian controller with loop transfer recovery (LQG/LTR) considering the augmented system with the addition of backward Euler integrator at controller output is applied to a practical quadruple tank system. The plant developed in this work is a benchmark of a multivariable two-input-two-output (TITO) system with coupled channels, frequently used in academic works, mainly due to its versatility for generating minimum phase or non-minimum phase systems and to the coupled channels characteristic. For the LQG/LTR controller, the singular values of the open loop transfer function are matched in the frequency range from zero up to the Nyquist rate using the same approach considered for continuous time system design. Simulation and practical experiments are performed in order to validate the controller design considering set-point tracking and disturbance rejection. It is possible to observe that the resulting controller performs very well tracking step and sinusoidal inputs and rejecting sinusoidal disturbances. Practical and simulated results are very similar to each other.