On Internal Model Control (IMC) of MIMO Systems

Abstract

Control of MIMO systems offers a challenging problem due to the cross coupling effects present between the inputs and the outputs of MIMO systems. In order to achieve an efficient control decouplers are introduced which eliminate these cross-coupling effects present in MIMO systems. With decouplers properly designed, it is possible to derive control inputs for fully-actuated and over-actuated MIMO systems to achieve reference tracking of the individual outputs. However, the reference tracking for individual outputs is almost unachievable in under-actuated MIMO systems with decoupling control methods. In dealing with this, the present work proposes an internal model control (IMC) applicable as appropriate to all classes of MIMO systems without incorporating any decoupling technique. This paper extends with two unique design methods of the IMC technique. These proposed methods enable one to attain perfect reference tracking of the individual outputs even in presence of the cross-coupling present in the MIMO systems. The conditions for the perfect reference tracking of multi outputs for under-actuated MIMO systems are derived. Different examples are considered to test the efficiency of the methods. The proposed methods are implemented on an experimental test set-up of highly non-linear and unstable cart-inverted pendulum system. The reference tracking goal and disturbance rejection capability of the control scheme are examined well in real-time. The experimental results are portrayed to establish the efficacy of the theoretical claim made.