Abstract
Modeling is the most important component in predictive controller design. It should predict outputs precisely and fast. Thus, it must be adequate for the ship dynamics while having as simple a structure as possible. In a good ship model the standard deviation of a particular coefficient should not exceed 10% of its value. Fitting the validation data to 80% for short-term prediction and 65% for long-term prediction is treated as a declared benchmark for model usage in ship course predictive controller. Regularization was proposed to ensure better state-space models to fit the real ship dynamics and more accurate standard deviation value control. Usage of the simulation results and real-time trials, as model estimation and validation data, respectively, during the identification procedure is proposed. In the first step a predictive linear model is identified conventionally, and then coefficients are regularized, based on the validation data, using a genetic algorithm. Particular linearized model coefficient standard deviations were decreased from more than 100% of their values to approximately 5% of them using genetic algorithm tuning. Moreover, the proposed method eliminated model output signal oscillations, which were observed during the validation process based on experimental data, gained during ship trials. Improved mapping of ship dynamics was achieved. Fit to validation data increased from 71% and 54% to 89% and 76%, respectively, for short-term and long-term prediction. The proposed method, which may be applied to real applications, is easily applicable and reliable. The tuned model is sufficiently suited to plant dynamics and may be used for future predictive control purposes.
Highlights
Modeling is the most important element in the model-based control techniques (e.g., Model Predictive Control)
Nonlinear ones are based on Kalman Filters [1], identified during model tests as the nonlinear mathematical model parameters [2], based on the backstepping procedure and the tuning design method using the complex model of Wagner–Smith [3]
The first method seems to be better because we identify real objects, not its mathematical model
Summary
Modeling is the most important element in the model-based control techniques (e.g., Model Predictive Control). The identification procedure is a demanding and time-consuming issue, and it should be done as precisely as possible. It is still a growing branch in the field of control. Nonlinear ones are based on Kalman Filters [1], identified during model tests as the nonlinear mathematical model parameters [2], based on the backstepping procedure and the tuning design method using the complex model of Wagner–Smith [3]. These nonlinear models may be based on neural networks, e.g., conventional [4] or probabilistic [5]
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