A Methodology to Obtain Analytical Models That Reduce the Computational Complexity Faced in Real Time Implementation of NMPC Controllers

Ribeiro, Leonardo D.; Secchi, Argimiro Resende

doi:10.1590/0104-6632.20190363s20180457

Cited by 7 publications

(5 citation statements)

References 43 publications

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“…Due to the fact that the dynamic matrix A k changes, in general, in every time step, then in each time step, the formula (46) or (48) allowing calculating the control action should be used by the algorithm. As a consequence, appropriate rows of the matrix…”

Section: Utilization Of Analytical Versions Of the Algorithmsmentioning

confidence: 99%

“…The control plant is a nonlinear, isothermal CSTR in which the van de Vusse reaction takes place. These CSTRs are a popular benchmark due to their nonlinearity and difficult dynamics, willingly used to test newly developed control algorithms; see, e.g., [48][49][50][51][52][53]. The process model of the reactor is composed of two composition balance equations; see, e.g., [54]:…”

Section: Example 31 Control Plantmentioning

confidence: 99%

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

Marusak

2021

Algorithms

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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.

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Section: Utilization Of Analytical Versions Of the Algorithmsmentioning

confidence: 99%

Section: Example 31 Control Plantmentioning

confidence: 99%

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

Marusak

2021

Algorithms

View full text Add to dashboard Cite

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“…, ∆ ǔm k+s−1|k(i w ) . (46) This prediction should then be used to formulate the optimization task in the same way as in the basic algorithm. After solving this task, one can either use the result to control the process or to perform another internal iteration of the algorithm.…”

Section: Iterative Improvement Of the Predictionmentioning

confidence: 99%

“…The steady-state characteristic of the control plant is depicted in Figure 1. The CSTRs in which the van de Vusse reaction takes place are a popular benchmark due to their nonlinearity and difficult dynamics, willingly used to test newly developed control algorithms; see for example, References [46][47][48][49][50][51]. The process model of the reactor is composed of two composition balance equations; see for example, Reference [52]:…”

Section: Examplementioning

confidence: 99%

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

Marusak

2020

Algorithms

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In Model Predictive Control (MPC) algorithms, control signals are generated after solving optimization problems. If the model used for prediction is linear then the optimization problem is a standard, easy to solve, quadratic programming problem with linear constraints. However, such an algorithm may offer insufficient performance if applied to a nonlinear control plant. On the other hand, if a model used for prediction is nonlinear, then non–convex optimization problem must be solved at each algorithm iteration. Then the numerical problems may occur during solving it and the time needed to calculate the control signals cannot be determined. Therefore approaches based on linearized models are preferred in practical applications. A fuzzy algorithm with an advanced generation of the prediction is proposed in the article. The prediction is obtained in such a way that the algorithm is formulated as a quadratic optimization problem but offers performance very close to that of the MPC algorithm with nonlinear optimization. The efficiency of the proposed approach is demonstrated in the control system of a nonlinear chemical control plant—a CSTR (Continuous Stirred–Tank Reactor) with van de Vusse reaction.

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“…The moderate computational requirements mean that the computational resources (fundamentally processor and memory) that need to solve the problem are within the acceptable costs. Being inside these limits facilitates implementation and helps in reaching the system performance specifications [7]. The acronyms used here are summarized in Table 1.…”

Section: Introductionmentioning

confidence: 99%

Experimental Design of an Adaptive LQG Controller for Battery Charger/Dischargers Featuring Low Computational Requirements

Montenegro-Oviedo

Ramos‐Paja

Orozco-Gutierrez

et al. 2023

WEVJ

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The growing use of DC/DC power converters has resulted in the requirement that their complex controllers be cheaper and smaller, thus using cost-effective implementations. For this purpose, it is necessary to decrease the computational burden in controller implementation to minimize the hardware requirements. This manuscript presents two methods for tuning an adaptive linear–quadratic–Gaussian voltage controller for a battery charger/discharger, implemented with a Sepic/Zeta converter, to work at any operating point. The first method is based on a lookup table to select, using the nearest method, both the state feedback vector and the observer gain vector, solving the Riccati’s differential equation offline for each practical operating point. The second method defines a polynomial function for each controller element that is based on the previous data corresponding to the system operating points. The adaptability of the two controllers to fixed voltage regulation and reference tracking was validated using simulations and experimental tests. The overshoot and settling time results were lower than 11% and 3.7 ms, which are in the same orders of magnitude of a control approach in which the equations are solved online. Likewise, three indices were evaluated: central processing unit capacity, cost, and performance. This evaluation confirms that the controller based on polynomial interpolation is the best option of the two examined methods due to the satisfactory balance between dynamic performance and cost. Despite the advantages of the controllers in being based on a lookup table and polynomial interpolation, the adaptive linear–quadratic–Gaussian has the benefit of not requiring an offline training campaign; however, the cost saving obtained with the lookup table controllers and polynomial interpolation controllers, due to the possible implementation on small-size microcontrollers with development tool simple and easy maintenance, will surely be desirable for a large number of deployed units, ensuring that those solutions are highly cost-effective.

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A Methodology to Obtain Analytical Models That Reduce the Computational Complexity Faced in Real Time Implementation of NMPC Controllers

Cited by 7 publications

References 43 publications

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

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

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

Experimental Design of an Adaptive LQG Controller for Battery Charger/Dischargers Featuring Low Computational Requirements

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