Numerically Efficient Fuzzy MPC Algorithm with Advanced Generation of Prediction—Application to a Chemical Reactor

Initialisation of Optimisation Solvers for Nonlinear Model Predictive Control: Classical vs. Hybrid Methods

In nonlinear Model Predictive Control (MPC) algorithms, the number of cost-function evaluations and the resulting calculation time depend on the initial solution to the nonlinear optimisation task. Since calculations must be performed fast on-line, the objective is to minimise these indicators. This work discusses twelve initialisation strategies for nonlinear MPC. In general, three categories of strategies are discussed: (a) five simple strategies, including constant and random guesses as well as the one based on the previous optimal solution, (b) three strategies that utilise a neural approximator and an inverse nonlinear static model of the process and (c) four hybrid original methods developed by the authors in which an auxiliary quadratic optimisation task is solved or an explicit MPC controller is used; in both approaches, linear or successively linearised on-line models can be used. Efficiency of all methods is thoroughly discussed for a neutralisation reactor benchmark process and some of them are evaluated for a robot manipulator, which is a multivariable process. Two strategies are found to be the fastest and most robust to model imperfections and disturbances acting on the process: the hybrid strategy with an auxiliary explicit MPC controller based on a successively linearised model and the method which uses the optimal solution obtained at the previous sampling instant. Concerning the hybrid strategies, since a simplified model is used in the auxiliary controller, they perform much better than the approximation-based ones with complex neural networks. It is because the auxiliary controller has a negative feedback mechanism that allows it to compensate model errors and disturbances efficiently. Thus, when the auxiliary MPC controller based on a successively linearised model is available, it may be successfully and efficiently used for the initialisation of nonlinear MPC, whereas quite sophisticated methods based on a neural approximator are very disappointing.

Comparing Methods of DC Motor Control for UUVs

Adaptive and learning methods are proposed and compared to control DC motors actuating control surfaces of unmanned underwater vehicles. One type of adaption method referred to as model-following is based on algebraic design, and it is analyzed in conjunction with parameter estimation methods such as recursive least squares, extended least squares, and batch least squares. Another approach referred to as deterministic artificial intelligence uses the process dynamics defined by physics to control output to track a necessarily specified autonomous trajectory (sinusoidal versions implemented here). In addition, one instantiation of deterministic artificial intelligence uses 2-norm optimal feedback learning of parameters to modify the control signal, while another instantiation is presented with proportional plus derivative adaption. Model-following and deterministic artificial intelligence are simulated, and respective performance metrics for transient response and input tracking are evaluated and compared. Deterministic artificial intelligence outperformed the model-following approach in minimal peak transient value by a percent range of approximately 2–70%, but model-following achieved at least 29% less error in input tracking than deterministic artificial intelligence. This result is surprising and not in accordance with the recently published literature, and the explanation of the difference is theorized to be efficacy with discretized implementations.

Advanced Construction of the Dynamic Matrix in Numerically Efficient Fuzzy MPC Algorithms

A method for the advanced construction of the dynamic matrix for Model Predictive Control (MPC) algorithms with linearization is proposed in the paper. It extends numerically efficient fuzzy algorithms utilizing skillful linearization. The algorithms combine the control performance offered by the MPC algorithms with nonlinear optimization (NMPC algorithms) with the numerical efficiency of the MPC algorithms based on linear models in which the optimization problem is a standard, easy-to-solve, quadratic programming problem with linear constraints. In the researched algorithms, the free response obtained using a nonlinear process model and the future trajectory of the control signals is used to construct an advanced dynamic matrix utilizing the easy-to-obtain fuzzy model. This leads to obtaining very good prediction and control quality very close to those offered by NMPC algorithms. The proposed approach is tested in the control system of a nonlinear chemical control plant—a CSTR reactor with the van de Vusse reaction.

Tuning of Multivariable Model Predictive Control for Industrial Tasks

This work is concerned with the tuning of the parameters of Model Predictive Control (MPC) algorithms when used for industrial tasks, i.e., compensation of disturbances that affect the process (process uncontrolled inputs and measurement noises). The discussed simulation optimisation tuning procedure is quite computationally simple since the consecutive parameters are optimised separately, and it requires only a very limited number of simulations. It makes it possible to perform a multicriteria control assessment as a few control quality measures may be taken into account. The effectiveness of the tuning method is demonstrated for a multivariable distillation column. Two cases are considered: a perfect model case and a more practical case in which the model is characterised by some error. It is shown that the discussed tuning approach makes it possible to obtain very good control quality, much better than in the most common case in which all tuning parameters are constant.

The Model Order Reduction Method as an Effective Way to Implement GPC Controller for Multidimensional Objects

The paper addresses issues associated with implementing GPC controllers in systems with multiple input signals. Depending on the method of identification, the resulting models may be of a high order and when applied to a control/regulation law, may result in numerical errors due to the limitations of representing values in double-precision floating point numbers. This phenomenon is to be avoided, because even if the model is correct, the resulting numerical errors will lead to poor control performance. An effective way to identify, and at the same time eliminate, this unfavorable feature is to reduce the model order. A method of model order reduction is presented in this paper that effectively mitigates these issues. In this paper, the Generalized Predictive Control (GPC) algorithm is presented, followed by a discussion of the conditions that result in high order models. Examples are included where the discussed problem is demonstrated along with the subsequent results after the reduction. The obtained results and formulated conclusions are valuable for industry practitioners who implement a predictive control in industry.