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This paper discusses state space realization algorithm from general multiple   input multiple output (MIMO) step response data with or without input   delays. It uses the factored form of the block Hankel matrix formed from the   Markov parameters of the equivalent impulse response of the step response   model to obtain an equivalent state space model. Though the state space   model that best approximates the step response model has number of states   equal to the rank of the block Hankel matrix, much lower rank state space   model, adequate for use as internal model for model predictive control   (MPC), can also be obtained. By using an empirical step response model of a   pilot distillation plant, a simple state space MPC, which use a full rank,   and then a low-rank approximation of the model as its internal model, is   implemented on the plant model. The setpoint tracking trends of the control   outputs of the two approximations match closely.

State space model realization using step response data of MIMO system with input delays for model predictive control