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When tuning the parameters of a constrained model predictive controller (MPC), one usually will use closed-loop simulations in order to predict closed-loop performance. Closed-loop simulation can be very time-consuming and inconvenient for large-scale constrained MPC, such as paper machine cross-directional (CD) predictive control. Paper machine CD processes are two-dimensional (2-D) (temporal and spatial) systems with up to 600 inputs and 6000 outputs. It is very important to predict the steady-state values for the closed-loop CD MPC systems during the tuning process, as the variances of these values are used as the control performance indexes in paper making industry. This article proposes to use a direct one-step static optimizer for approximating the closed-loop steady-state performance of constrained CD MPC. The parameters of this static optimizer can be obtained through minimizing the difference of two closed-loop transfer functions. Experiments with industrial data demonstrate that the static optimizer is computationally much more efficient (up to two orders of magnitude) than closed-loop simulation while reliably and accurately predicting the steady-state performance.