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The fiber length and the Canadian standard freeness (CSF) are two key indices in measuring pulp quality of the refining process with non-Gaussian stochastic distribution dynamics. Among them, it is defective to use the conventional 1-D average fiber length (AFL) as a pulp quality index because the AFL is insufficient to describe the 2-D probability density function (pdf) shaping of fiber length distribution (FLD) with non-Gaussian types. In this article, a data-driven multiobjective predictive optimal control method is proposed to control the 2-D pdf shaping of FLD and the 1-D CSF, simultaneously. First, a radial basis function neural network (RBF-NN) based stochastic distribution model is developed to approximate the 2-D pdf shaping of FLD, and the parameters of RBF basis functions are updated by an iterative learning rule. Then, taking the developed pulp quality models, including the 2-D pdf model of FLD and the model of 1-D CSF as two predictors, a multiobjective predictive controller is designed by solving the nonlinear programming problems with constraints. Then, the stability of the resulted closed-loop system is also analyzed. Ultimately, the industrial experiments demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper proposes the energy-based controller (EC) incorporated with radical basis function (RBF) neural-network compensation (ECRBFC), which is used to swing up the Pendubot and raise it to its uppermost unstable equilibrium position. First, for the known dynamics model of the two-link arm, the EC is designed. In the EC, the singularity is successfully avoided by constructing an appropriate energy evaluation function. Second, as for the friction of the Pendubot, because of the time-varying characteristics, an accurate friction dynamics model cannot be known absolutely; thus, the RBF neural network is introduced to offset the bad effect of friction. Finally, in order to evaluate the performance of ECRBFC, the numerical simulations and the experimental results are given, and by comparing the results with that of other algorithms, it is found that ECRBFC proposed in this paper has better performance under the same conditions. [ABSTRACT FROM PUBLISHER]