Multivariate Control Techniques Research Articles

Comparison of Advanced Multivariable Control Techniques for Axial-Piston Pump

This article is devoted to a comparison of two advanced control techniques applied to the same plant. The plant is a certain type of axial-piston pump. A linear-quadratic (LQR) controller and an H-infinity (H∞) controller were synthesized to regulate the displacement volume of the pump. The classical solution to such a problem is to use a hydro-mechanical controller (by pressure, flow rate, or power) but, in the available sources, there are solutions that implement proportional-integral-derivative (PID), LQR, model predictive control (MPC), etc. Unlike a classical solution, in our case, the hydro-mechanical controller is replaced by an electro-hydraulic proportional valve, which receives a reference signal from an industrial microcontroller. It is used as the actuator of the pump swash plate. The pump swash plate swivel angle determines the displacement volume, respectively, and the flow rate of the pump. The microcontroller is capable of embedding various control algorithms with different structures and complexities. The developed LQR and H∞ controllers are compared in the simulation and real experiment conditions. For this purpose, the authors have developed a laboratory experimental test bench, enabling a real-time function of the control system via USB/CAN communication. Both controllers are compared under different pump loading modes. Also, this paper contributes an uncertain model of an axial-piston pump with proportional valve control that is obtained from experimental data. Based on this model, the robust stability of the closed-loop system is investigated by comparing the structure of a singular value (μ). The investigations show that both control systems achieved robust stability. Moreover, they can tolerate up to four times larger uncertainties than modeled ones. The system with the H∞ controller attenuates approximately at least 30 times the disturbances with frequency up to 1 rad/s while the system with the LQR controller attenuates at least 10 times the same disturbances.

Copula deep learning control chart for multivariate zero inflated count response variables

With the increasing popularity of big data analysis, research on zero-inflated count data with the copula method has garnered significant attention because zero-inflated count data do not follow a normal distribution and have high correlation among variables. Within the domain of quality control, there has been limited emphasis on multivariate statistical process control (SPC) techniques that specifically address the challenge of multicollinearity within regression models for multivariate zero-inflated count responses. In this paper, we explain a computational challenge in handling big data with parametric generalized linear models, such as the zero-inflated Poisson model. This challenge motivates us to introduce a copula-based deep learning and neural network model involving multivariate zero-inflated count response variables with highly correlated explanatory variables. This approach builds upon existing deep learning and neural network models designed for univariate count responses, expanding them to encompass multivariate count response models through the integration of a copula regression framework. To evaluate the performance of our proposed methodology, we conduct a comparative analysis of accuracies using the zero-inflated Poisson model, univariate deep learning and neural network models, multivariate count response deep learning and neural network models, and our proposed copula deep learning and neural network models. This assessment involves employing metrics such as root mean square error (RMSE), weighted mean absolute percentage error (WMAPE), and mean absolute deviation (MAD). We include both copula-based asymmetrical zero-inflated simulated data and real-world data. We also propose a temporal dependence control chart for assessing the temporal dependence between bivariate zero-inflated count response variables. Our proposed copula deep learning and neural network temporal control charts can check time-varying dependence and outliers by leveraging the Shewhart statistical process control chart and t-copula ARMA-GARCH dynamic control correlation.

Portable spectroscopy, digital imaging colorimetry and multivariate statistical tools in contaminant identification: A case study of mint (Mentha) and basil (Ocimum basilicum)

The advent of portable Fourier-Transform Infrared (FTIR) and Raman spectrometers has revolutionized analysis capabilities, presenting the possibility of on-site contaminant identification without the need for specialized laboratory settings. Compared to laboratory instrumentation, portable spectroscopy is more prone to noise, and appropriate spectral processing procedures need to be established. This paper introduces a comprehensive methodology that integrates acquisition techniques, spectral analysis, and mathematical tools necessary for utilizing handheld spectrometers to diagnose plant contamination. It focuses on determining the efficacy of handheld FTIR, Raman spectroscopy, and digital imaging for detecting contaminants in two food plants, Basil (Ocimum basilicum) and Mint (Mentha). The study examines the impact of three pollutants: iron (II) sulphate (FeSO4), zinc (II) sulphate (ZnSO4), and copper (II) sulphate (CuSO4), on these plants, but also the necessary amount of measurements to spot the pollutants' effects. Measurements were conducted at the start, after 24 hours, and after 48 hours of exposure, on both fresh and dried plant leaves, as well as in solution. Spectral effects of each of the pollutants were identified with the use of multivariate statistical process control techniques. With the help of the developed methodologies, researchers can identify in-situ contaminant effects, exposure times and run diagnostics directly on the leaf both in alive and dried plants.

New Anomaly Detection Method based on the Multivariate Generalized Pareto Distributions

The extreme events of floods, rainfalls, waves, and wind often cause serious damage. The observed data can be used to detect the sign of abnormal phenomena and can prevent the crucial damage. Anomaly detection techniques, the techniques of distinguishing between normal and abnormal cases from the data, have been one of the most used methods for detecting suspicious events from the collected data. Although many methods of the anomaly detection have appeared in the literature, almost all of them are based on multivariate statistical process control techniques and machine learning techniques. Recently, under the idea that information for suspicious and critical events is more likely to be involved in the largest or smallest values than values around the mean or median, the anomaly detection methods are based on the “Extreme Value Theory” (EVT), which is the statistical theory dealing with the largest or smallest data, attract the variety of areas. However, they can be applied to only univariate data since they have been based on the EVT for univariate data, and hence there has been little work for the multivariate anomaly detection based on the EVT. The multivariate anomaly detection method is important in applications because almost all data for anomaly detection are multivariate and can be misleading by applying univariate methods to multivariate data independently. In this paper, we propose the new anomaly detection method based on the multivariate EVT. The performance of the proposed methods is evaluated by the Monte Carlo simulation. To illustrate all the proposed methods of anomaly detection for multivariate data, we apply them to analyze the new real data of precipitation events in 2021. The numerical results show that the proposed method outperforms the existing methods.

Control Chart T2Qv for Statistical Control of Multivariate Processes with Qualitative Variables

The scientific literature is abundant regarding control charts in multivariate environments for numerical and mixed data; however, there are few publications for qualitative data. Qualitative variables provide valuable information on processes in various industrial, productive, technological, and health contexts. Social processes are no exception. There are multiple nominal and ordinal categorical variables used in economics, psychology, law, sociology, and education, whose analysis adds value to decision-making; therefore, their representation in control charts would be useful. When there are many variables, there is a risk of redundant or excessive information, so the application of multivariate methods for dimension reduction to retain a few latent variables, i.e., a recombination of the original and synthesizing of most of the information, is viable. In this context, the T2Qv control chart is presented as a multivariate statistical process control technique that performs an analysis of qualitative data through Multiple Correspondence Analysis (MCA), and the Hotelling T2 chart. The interpretation of out-of-control points is carried out by comparing MCA charts and analyzing the χ2 distance between the categories of the concatenated table and those that represent out-of-control points. Sensitivity analysis determined that the T2Qv control chart performs well when working with high dimensions. To test the methodology, an analysis was performed with simulated data and with a real case applied to the graduate follow-up process in the context of higher education. To facilitate the dissemination and application of the proposal, a reproducible computational package was developed in R, called T2Qv, and is available on the Comprehensive R Archive Network (CRAN).

Integrating PCA and structural model decomposition to improve fault monitoring and diagnosis with varying operation points

Fast and efficient fault monitoring and diagnostics methods are essential for fault diagnosis and prognosis tasks in Health Monitoring Systems. These tasks are even more complicated when facing dynamic systems with multiple operation points. This article introduces a symbiotic solution for fault detection and isolation, based on the integration of two complementary techniques: Possible Conflicts (PCs), a model-based diagnosis technique from the Artificial Intelligence (AI) community, and Principal Component Analysis (PCA), a Multivariate Statistical Process Control (MSPC) technique. Our proposal improves the PCA-based fault detection in systems with multiple operation points and transient states and provides a straightforward fault isolation stage for PCA. At the same time, the proposal increases the robustness for fault detection using PCs through the application of PCA to the residual signals. PCA has the ability to filter out residual deviations caused by model uncertainties that can lead to a high number of false positives. The proposed method has been successfully tested in a real-world plant with accurate fault detection results. The plant has noisy sensors and a system model without the same accuracy at each operation point and transient states.

The model predictive control strategy of the transcritical CO2 air conditioning system used in railway vehicles

• A transcritical CO 2 air conditioning system was developed for use in a railway vehicle. • The model predictive control strategy was used to optimize the system performance. • The proposed control method maximized the real-time COP without sacrificing comfort. • The simulation results showed that the proposed control strategy is effective. This paper presented a model predictive control strategy to optimize the operation of the transcritical CO 2 air conditioning system used in railway vehicles, which had to balance the needs of the passengers' comfort with energy-saving effects. In this work, the discharge pressure and evaporator air volume flow rates were optimized while maintaining comfort using a multi-variable control technique called model predictive control strategy. The objective function and the predictive model, which were proposed in this work combining data and physical laws, were the basis for the model predictive controller's ability to foresee future operation-conditions and calculate the optimal inputs. The validation results showed that the prediction error was less than 4.5%. The model predictive controller was adopted in GT-SUITE platform to realize the real-time maximization of the energy efficiency and maintain comfort requirement by adjusting discharge pressure, evaporator air volume flow rate and compressor speed. The simulation was conducted under fixed conditions and realistic conditions. As for the fixed conditions, the coefficient of performance achieved at 2.24, equaling to the maximum value of the map. Under the realistic conditions, the overall energy consumption of the control method using the MPC strategy was lower than that using the PID control strategy, and the average COP was increased by 7.4%. Further, there was a 1% error in coefficient of performance between the extreme value gained by the model predictive control method and the extreme value offered by the map method, which validated that the model predictive control strategy can be an effective control method for the optimal operation of the transcritical CO 2 air conditioning system.

HVAC multivariable system modelling and control

Heating, Ventilation and Air Conditioning (HVAC) is a multivariable process where any alteration with one system input affects most or all of the system’s outputs simultaneously. Owing to its comprehensiveness, a readily derived multivariable HVAC mathematical model is selected for this work, mainly a hybrid distributed-lumped parameters model. As the transfer function matrix was not established in the selected HVAC model, it was exclusively developed in this study, using the time domain graphical responses of the chosen model. Based on the developed transfer function matrix, a conceptual two-step approach was followed to control HVAC model performance. The first was decoupling the interactions that affect all the system outputs, and the second was designing proper PID controllers for each decoupled loop similar to those used for single input single output (SISO) systems. A direct Nyquist Array (DNA) multivariable control strategy was used for this purpose and successfully decoupled the HVAC system into three separate (SISO) loops. Three PID controllers afterwards were applied for each decoupled loop. The results showed quite decoupled system outputs with a minor coupling percentage so that any change in a system input only affected the corresponding system output. The output responses are also underdamped with almost zero steady-state error confirming the effectiveness of the selected PID parameters. The values of steady-state responses are obtained in (10–15) s compared with (200–600) s of open-loop response time. However, various overshoot percentages in the responses are encountered but are relatively small, with a short settling time, so they don’t affect the thermal comfort of the ventilated volume. System stability using the Nyquist criterion has also been examined and found to satisfy the criterion. The multivariable DNA control technique and the SISO closed-loop PID controllers have shown the capability to suppress external disturbances and restore the system to its original functional steady-state values.

Control of a Three-Input DC-DC Converter Suitable for DC Motors

A new multivariable control technique is introduced in this paper. This method is applied to a three-input DC-DC converter. First, the dynamic model of the converter is obtained in the state space, and then, the transfer function is achieved from the state space model to design a controller. In the second step, the input-output sets must be paired using a relative gain array (RGA) matrix. In the third step, the system is decoupled in the steady state by a simple matrix. The PI controller tracks the reference inputs of the controller. If the designed controller has proper performance in the transfer function of the converter, it can be applied to a real system. This multivariable control method has suitable performance and simple implementation, which results in an inexpensive controller. The DC motor must work in a constant power region if the practical application is the aim. In this case, the torque can be directly controlled to regulate the speed of the DC motor without needing a gearbox, which promotes total efficiency. Real-time simulation and experimental results verify the effectiveness of the proposed system.

Autogenerated Multilocal PLS Models without Pre-classification for Quality Monitoring of Nonlinear Processes with Unevenly Distributed Data

To achieve the desired product qualities for an operating process, the operational status must be monitored. Operating conditions are changed because of the variability in the quality of raw materials and equipment characteristics. The operating conditions are also changed to produce various product grades and to meet time-to-market demands. This makes the process data collected within a wide region to be distributed unevenly, so conventional multivariate statistical process control techniques that use a single global model are not suited to monitoring. Data is partitioned to construct each local model, but partitioning data without considering variable correlations can cause the information to be lost. This study uses a multilocal partial least-squares (ML-PLS) model to monitor a wide operation process. Without pre-selecting the data for each local model, ML-PLS automatically reinforces the data that pertains to each local model and weakens the data that does not pertain to other local models. The entire range of operation is clustered, and multiple PLS models are constructed using this clustered data. Statistical indices for quality-based process monitoring in the latent and observed variable spaces are derived using the learned ML-PLS models. The effectiveness and accuracy of the proposed method are demonstrated using a numerical example and a practical application for a chemical process.

Modelling and controlling A new PV/FC/battery DC–DC converter suitable for DC motor

Here, a new hybrid DC–DC converter is presented to enable controlling a DC motor. Since renewable energy sources, including PV, FC, and batteries, are projected to be used extensively in the future, using interface converters becomes essential. Firstly, these converters must have a suitable voltage gain because PV and FC have a low voltage at the output. Secondly, such converters must be controlled correctly because PV and FC do not provide a constant voltage, they have different characteristics, and they may work in any operating point instead of the maximum power point. Therefore, a suitable controller is essential for extracting maximum power values from these energy sources. In this paper, the decentralized control method, as a multivariable control technique, has been used to control a PV/FC/battery DC–DC converter.

A variable relevant multi-local PCA modeling scheme to monitor a nonlinear chemical process

In chemical plants, operated processes require different conditions to produce various product grades and meet the time-to-market demand. Conventional multivariate statistical process control techniques based on a single global model are certainly poor. In the past, data were partitioned first without considering variable correlations before each local model was constructed. This may cause information loss. This study proposes a multi-local principal component analysis (ML-PCA) modeling strategy to monitor a nonlinear process over a large operating region. ML-PCA can automatically enhance the data of the clustered model and weaken those data of the other local models. The operating data are collected from the whole range of operations to cluster and construct the corresponding PCA for each operating condition simultaneously. Once ML-PCA models are constructed, two statistical indices are designed for process monitoring. The effectiveness and accuracy of the proposed ML-PCA are demonstrated through a numerical example and a real industrial process.

Adaptive Predictive Control with Neuro-Fuzzy Parameter Estimation for Microgrid Grid-Forming Converters

Model predictive control (MPC) is a flexible and multivariable control technique with better dynamic performance than linear control. However, MPC is sensitive to parametric mismatches that reduce its control capabilities. In this paper, we present a new method of improving the robustness of MPC to filter parameter variations/mismatches by easily implementable parameter estimation. Furthermore, we extend the proposed technique for wider operating conditions by novel neuro-fuzzy estimation. The results, which are demonstrated by both simulations and real-time hardware-in-the-loop tests, show a steady-state parameter estimation accuracy of 95%, and at least 20% improvement in total harmonic distortion (THD) than conventional non-adaptive MPC under parameter mismatches up to 50% of the nominal values.

Robust multivariate control chart based on shrinkage for individual observations

A robust multivariate quality control technique for individual observations is proposed, based on the robust reweighted shrinkage estimators. A simulation study is done to check the performance and compare the method with the classical Hotelling approach, and the robust alternative based on the reweighted minimum covariance determinant estimator. The results show the appropriateness of the method even when the dimension or the Phase I contamination are high, with both independent and correlated variables, showing additional advantages about computational efficiency. The approach is illustrated with two real data-set examples from production processes.

Comparative Study of Optimal Multivariable LQR and MPC Controllers for Unmanned Combat Air Systems in Trajectory Tracking

Guidance, navigation, and control system design is, undoubtedly, one of the most relevant issues in any type of unmanned aerial vehicle, especially in the case of military missions. This task needs to be performed in the most efficient way possible, which involves trying to satisfy a set of requirements that are sometimes in opposition. The purpose of this article was to compare two different control strategies in conjunction with a path-planning and guidance system with the objective of completing military missions in the most satisfactory way. For this purpose, a novel dynamic trajectory-planning algorithm is employed, which can obtain an appropriate trajectory by analyzing the environment as a discrete 3D adaptive mesh and performs a softening process a posteriori. Moreover, two multivariable control techniques are proposed, i.e., the linear quadratic regulator and the model predictive control, which were designed to offer optimal responses in terms of stability and robustness.

Managing the energy of the air conditioning systems using a modified multi-variable control technique

This research is a continuation of our previous work [19], in which, I’ve investigated many control techniques for the multi-input multi-output (MIMO) control systems for air conditioners. In the present work, I’ve suggested another control technique which exhibited better performance in the cases where permanent disturbances are present. I’ve applied the technique to a model room that simulates a computer room and is conditioned by a simple, less expensive, and energy-saver HVAC system. The two control inputs are; the opening angle of a fresh air gate and the steam flow rate from a humidifier. The two controlled outputs are the temperature and humidity. The control technique and the in-door conditions are simulated using a written program that works along with a commercial code. The sampling interval for each controlled variable is modified to allow more accuracy for measured data. When applying accidental and permanent disturbances in both controlled variables, the suggested technique exhibited accepted performance. The controlled variables that are affected with permanent disturbances achieved their set-point values after longer time intervals than those of the cases where only accidental disturbances are present. Two comparisons were made between the controlled and uncontrolled system by operating the system for a certain period, and fixing the fresh air opening at 25% and 50% of the full opening area. The consumed energy in the two cases was compared with that of the case when applying the control technique for the same period. An energy-saving of about 15.3% was recorded in the first case and about 37.6% for the second case. The present technique is a case-independent and may be applied to any MIMO control system with little modifications.

Statistical Control of Multivariant Processes through the Artificial Neural Network Multilayer Perceptron and the MEWMA Graphic Analysis

Nowadays the supervision of the quality in the production systems is a very important task. In order to reach this goal, it is necessary that quality of the products is supervised from a global approach where all the quality characteristics are considered. In addition, it is necessary to apply multivariate statistical process control techniques to guarantee a correct control of the manufacturing systems. An important disadvantage of multivariate statistical control is the lack of a complementary analysis that identify the presence of variations or out of control signals that allow locate the source of the instability in the manufacturing process. In order to solve this problem, this research proposes using a multilayer perceptron artificial neural network as an analysis mechanism for each out-of-control signal detected by the multivariate exponentially weighted moving average control chart which is able to identify small changes in the quality of any process. The monitoring and control procedure were used in a process of bearings manufactured for the automotive industry, the results show that the mechanism detected and interpreted small variations and significant changes successfully, identifying the origin of the variation generated in the productive system with an accuracy of 99.85%.

Multivariate statistical monitoring strategy for an automotive manufacturing part facility

In this article an attempt has been made to devise a statistical monitoring strategy based on multivariate projection based method. The projection based method that was employed for development for the strategy was Principle Component Analysis (PCA) which is primarily used as a dimension reduction technique. The strategy thus devised was applied to a connecting rod manufacturing facility. Connecting rods are primarily produced via hot forging process accompanied by a litany of other finishing processes. Each process in turn is characterized by their own set of process characteristics which requires simultaneous monitoring so as to produce good quality end product. Simultaneous monitoring of characteristics and moreover correlated characteristics can be achieved via the employment of multivariate statistical control technique. Projection based techniques viz., PCA and partial least squares regression fall under special category MSPC techniques owning to their ability to deal with highly correlated and ill-conditioned data. The PCA based monitoring strategy thus devised in this article was found to be efficient in detection of faults indicated by out-of-control observations and thus aiding in producing good quality connecting rods.

Multivariate analyses to determine fungicide efficacy on Ecuadorian bananas for consumption

Half maximal effective concentration EC 50 is considered the main reference for evaluating the efficacy of the products in any plantation using doses and inhibition percentages from laboratory data. However, EC 50 is not the best representation when other relevant variables and their relationships could be involved. As an agricultural case study, fungicide sensitivity of Pseudocercospora fijiensis , the causal agent of black sigatoka, was evaluated on bananas’ plantations in three provinces of Ecuador. In this study, multivariate statistical process control was adjusted to a fungicide efficacy evaluation case considering multiple data tables from different locations and years at the same time. The threshold conveyed by inhibition percentages, related to the EC , along with locations and years allowed the multivariate analyses carried out in the proposal. The multivariate statistical control techniques applied were Multilinear Principal Component Analysis (MPCA) and Dual STATIS-Parallel Coordinates approach (DS-PC). A comparison was developed and showed that both methods discriminate correctly between the normal and anomalous conditions within plantations along years, validating the ability of the novel method DS-PC for exhibiting better signaling of anomalous plantations and performing variable-wise analysis to find out possible causes of this behavior in an easier time-saving graphical framework.

Dynamic Non-parametric Monitoring of Air-Pollution

Air pollution poses a major problem in modern cities, as it has a significant effect in poor quality of life of the general population. Many recent studies link excess levels of major air pollutants with health-related incidents, in particular respiratory-related diseases. This introduces the need for city pollution on-line monitoring to enable quick identification of deviations from “normal” pollution levels, and providing useful information to public authorities for public protection. This article considers dynamic monitoring of pollution data (output of multivariate processes) using Kalman filters and multivariate statistical process control techniques. A state space model is used to define the in-control process dynamics, involving trend and seasonality. Distribution-free monitoring of the residuals of that model is proposed, based on binomial-type and generalised binomial-type statistics as well as on rank statistics. We discuss the general problem of detecting a change in pollutant levels that affects either the entire city (globally) or specific sub-areas (locally). The proposed methodology is illustrated using data, consisting of ozone, nitrogen oxides and sulfur dioxide collected over the air-quality monitoring network of Athens.