A numerically computed constrained multivariable generalized predictive control algorithm is proposed. The solution of the optimization problem is achieved using an orthogonal matrix decomposition. Apart from improving the numerical integrity of the solution, Singular Value Decomposition also provides additional useful information that can be used to enhance the robustness of the closed loop control system. The proposed algorithm has been applied to two high purity distillation column physiochemical models, and the closed loop control performances studied. These have demonstrated the validity of the algorithm in respect of being able to respond to process operating constraints. In addition, the algorithm has been shown to be capable of stabilizing systems in which the nominal plant dynamic gain matrix was ill-conditioned.