Control loop performance assessment using detrended fluctuation analysis (DFA)

A new index is developed for assessing the performance of a single-input single-output (SISO) linear feedback control loop. The proposed metric is a specific scaling of the generalized Hurst exponent, computed through the method of detrended fluctuation analysis (DFA). We refer to this scaled exponent as the Hurst index. The new method compares favorably with the widely used minimum variance index (MVI), with both indices showing similar trends under changes in controller tunings during closed-loop simulations. The main advantage of the Hurst index over the MVI and other existing performance measures is that its determination does not require a priori knowledge of any loop parameters. Instead, computation of the index relies solely upon process output data collected during routine plant operation. Therefore, this new technique could potentially allow engineers to more efficiently identify problematic control loops.     

Development of fuzzy process accuracy index for decision making problems

Several statistical decision making tools and methods are available to organize evidence, evaluate risks, and aid in decision making. Process capability indices are the summary statistics to point out the process performance. In this paper, these indices are analyzed to obtain a new decision making tool. Process accuracy index (C_a) measures the degree of process centering and gives alerts when the process mean departures from the target value. It focuses on the location of process mean and the distance between mean and target value. We modify the traditional process accuracy index to obtain a new tool under fuzziness. With the proposed tool, specification limits and process mean can be defined as triangular or trapezoidal fuzzy numbers. The proposed tool is illustrated to solve a supplier selection problem.     

线性定常系统的综合性最优控制问题

本文讨论了具有二次型性能指标的线性定常系统的降低性能指标灵敏度、降低轨迹灵敏 度和配置闭环极点的综合性最优控制问题,提出了新的综合性能指标,从而得到了易于计算 的结果;解决了多参数变化时降低轨迹灵敏度的综合性最优控制问题;推导了闭环特征值对 Q阵的梯度阵公式,提出了一种配置互异的全部闭环极点Q阵算法,并给出了算例.     

Simultaneous Fault Detection and Control for Markovian Jump Systems with General Uncertain Transition Rates

This paper investigates the simultaneous control and fault detection of Markovian jump systems with general transition rates allowed to be unknown and known with uncertainties. By introducing slack matrices, a new approach is developed to conquer the nonlinearity induced by unknown and uncertain transition rates. Then, sufficient conditions are presented to ensure the stochastic stability of the resultant closed-loop system and meet the robust and detection performance indices. Finally, an example is given to illustrate the effectiveness of the proposed theoretical results.     

Decentralized robust PI controller design for an industrial boiler

This paper presents a new scheme to design decentralized robust PI controllers for uncertain LTI multivariable systems. Sufficient conditions for closed-loop stability and closed-loop diagonal dominance (almost decoupling) of a multivariable system are obtained. Satisfying these conditions and robust performance of the overall system are modeled as local robust performance problems. Then, by appropriately selecting the time constants of the closed-loop isolated subsystems in the IMC (Internal Model Control) strategy, the defined local robust performance problems are solved. To design a decentralized robust PI controller for a real industrial utility boiler, a control oriented nonlinear model for the boiler is identified. The nonlinearity of the system is modeled as uncertainty for a nominal LTI multivariable system. Using the new proposed method, a decentralized PI controller for the uncertain LTI model is designed. The designed controller is applied to the real system. The simulation results show the effectiveness of the proposed methodology.     

A new validity index for crisp clusters

In this paper, a new cluster validity index which can be considered as a measure of the accuracy of the partitioning of data sets is proposed. The new index, called the STR index, is defined as the product of two components which determine changes of compactness and separability of clusters during a clustering process. The maximum value of this index identifies the best clustering scheme. Three popular algorithms have been applied as underlying clustering techniques, namely complete-linkage, expectation maximization and K-means algorithms. The performance of the new index is demonstrated for several artificial and real-life data sets. Moreover, this new index has been compared with other well-known indices, i.e., Dunn, Davies-Bouldin, PBM and Silhouette indices, taking into account the number of clusters in a data set as the comparison criterion. The results prove superiority of the new index as compared to the above-mentioned indices.     

Robust satisfactory fault-tolerant control of uncertain linear discrete-time systems: an LMI approach

Fault-tolerant control is an important issue in practical systems. Based on satisfactory control and estimation theory, a passive fault-tolerant control strategy is proposed for a class of uncertain linear discrete-time systems in this article. Manipulating linear matrix inequality (LMI) technique, robust fault-tolerant state-feedback controllers are designed which take the possible actuator faults and sensor faults into consideration, respectively. The closed-loop systems are guaranteed by the designed controllers to meet the required constraints on regional pole index φ(q, r), steady-state variance matrix X index and control-cost function V ²(u) index simultaneously. Then, whether possible faults occur or not, the closed-loop systems would maintain the three desirable performance indices accordingly. Meanwhile, the consistency of the performance indices mentioned earlier is also discussed for fault-tolerant control.     

A new separation measure for improving the effectiveness of validity indices

Many validity indices have been proposed for quantitatively assessing the performance of clustering algorithms. One limitation of existing indices is their lack of generalizability, due to their dependence on the specific algorithms and structures of the data space. To handle large-scale datasets with arbitrary structures, this research study proposes a new cluster separation measure for improving the effectiveness of existing validity indices. This is achieved by partitioning the original data space into a grid-based structure which allows the introduction of a new measurement for assessing the true data distribution between any two clusters instead of the distance between the two cluster prototypes. To validate the effectiveness of the proposed separation measure, we adopt two commonly used validity indices, the Davies-Bouldin’s function (DB) and Tibshirani’s Gap statistic (GS). These indices are denoted as R-DB-1 and R-GS-1 for clusters with sphere-shaped structures and R-DB-2 and R-GS-2 for irregular-shaped structures. This integration enables the indices to evaluate both partitional algorithms and hierarchical algorithms. Partitional algorithms including C-Means (CM), Fuzzy C-Means (FCM), and hierarchical algorithms, including DBSCAN and CLIQUE, are used to test the performance of the new indices. Two synthetic datasets with spherical structures and four synthetic datasets with irregular shapes are first compared. Five real datasets from the UCI machine learning repository are then used to further test the measure’s performance. The experimental results provide evidence that the new indices outperform the original indices.     

Issues in performance diagnostics of model-based controllers

The task of diagnosing poorly performing controllers is a challenging one. Process design, controller design, changing process conditions are amongst the common causes of poor performance. In this work, we quantify the effect of factors such as constraints, modelling uncertainty, disturbance uncertainty, process nonlinearity on the achieved closed loop performance. It is important to know the contribution of these factors on the achieved performance in order to attempt diagnosis. The results derived are applicable to the case of deterministic as well as stochastic inputs. Illustrative examples, both SISO and MIMO, are used to demonstrate the key results.     

非高斯系统的建模方法研究*

近年来，高阶统计信息理论广泛应用于非高斯系统的建模问题中，由于高阶统计信息方法特殊的信息结构，难以充分利用具体问题中的统计分布信息，从而对该方法的应用效果产生了影响。针对这一问题，本文提出一种综合应用刘阶统计信息理论与非高斯系统的似然函数指标的建模的方法，为在非高斯系统建模系统建模问题中充分利用问题所提供的统计信息提供了新的途径，仿真研究和应用取得了令人满意的效果。     

Analyzing relationships among ARMA processes based on non-Gaussianity of external influences

The analysis of a relationship among variables in data generating systems is one of the important problems in machine learning. In this paper, we propose an approach for estimating a graphical representation of variables in data generating processes, based on the non-Gaussianity of external influences and an autoregressive moving-average (ARMA) model. The presented model consists of two parts, i.e., a classical structural-equation model for instantaneous effects and an ARMA model for lagged effects in processes, and is estimated through the analysis using the non-Gaussianity on the residual processes. As well as the recently proposed non-Gaussianity based method named LiNGAM analysis, the estimation by the proposed method has identifiability and consistency. We also address the relation of the estimated structure by our method to the Granger causality. Finally, we demonstrate analyses on the data containing both of the instantaneous causality and the Granger (temporal) causality by using our proposed method where the datasets for the demonstration cover both artificial and real physical systems.     

Performance monitoring of model-predictive controllers via model residual assessment

Model quality is a main factor that affects the control performance of model-based controllers. In this paper, a new closed-loop model assessment approach is proposed to assess model deficiency from routine closed-loop data. The proposed model quality index is a minimum variance benchmark for the model residuals obtainable from closed-loop data. From the feedback invariant principle the disturbance innovations are shown to be unaffected by the feedback controller. Then it is shown that the disturbance innovations can be estimated from closed loop data by an orthogonal projection of the current output onto the space spanned by past outputs, inputs or setpoints. With the estimated disturbance innovations as the benchmark, a model quality index is developed by using the ratio of a quadratic form of model residuals and that of the estimated disturbance innovations. The effectiveness of the proposed methods is demonstrated by simulations.     

A cluster validity index for fuzzy clustering

A new cluster validity index is proposed for the validation of partitions of object data produced by the fuzzy c-means algorithm. The proposed validity index uses a variation measure and a separation measure between two fuzzy clusters. A good fuzzy partition is expected to have a low degree of variation and a large separation distance. Testing of the proposed index and nine previously formulated indices on well-known data sets shows the superior effectiveness and reliability of the proposed index in comparison to other indices and the robustness of the proposed index in noisy environments.     

NLPCA as a diagnostic tool for control valve stiction

A significant number of control loops in process plants perform poorly due to control valve stiction. Developing a method to detect valve stiction in the early phase is imperative to avoid major disruptions to the plant operations. Nonlinear principal component analysis (NLPCA), widely known for its capability in unravelling nonlinear correlations in process data, is extended in this paper to diagnose control valve stiction problems. The present work is based on distinguishing the difference between the shapes of the signals caused by stiction and other sources, and utilizes the operating data of controlled variable-controller output (pv–op). The structure of pv–op data used in this work is of sufficiently low dimension such that the NLPCA’s output allows the usage of simple mathematical tests in quantifying the nonlinear behavior of the loop. It is shown that if the underlying structure of pv–op data is linear, the NLPCA output generally approximates to a straight line with a regression coefficient (R²) greater than 0.8, otherwise there is a possibility of presence of nonlinearity or non-Gaussianity. The presence of stiction is then detected via a new and simple NLPCA curvature index, I_NC. Results from simulated and real industrial case studies show that NLPCA is a very promising tool for detecting valve stiction.     

Detection of model-plant mismatch in closed-loop control system

The performance of model-based control systems depends a lot on the process model quality, hence the process model-plant mismatch is an important factor degrading the control performance. In this paper, a new methodology based on a process model evaluation index is proposed for detecting process model mismatch in closed-loop control systems. The proposed index is the ratio between the variance of the disturbance innovation and that of the model quality variable. The disturbance innovations are estimated from the routine operation data by an orthogonal projection method. The model quality variable can be obtained using the closed-loop data and the disturbance model estimated by adaptive Least absolute shrinkage and selection operator (Lasso) method. When the order of the disturbance model is less than 2 or the process time delay is large enough, no external perturbations are required. Besides, the proposed index is independent of the controller tuning and insensitive to the changes in disturbance model, which indicates that the proposed method can isolate the process model-plant mismatch from other factors affecting the overall control performance. Three systems with proportional integral (PI) controller, linear quadratic (LQ) controller and unconstrained model predictive control (MPC) respectively are presented as examples to verify the effectiveness of the proposed technique. Besides, Tennessee Eastman process shows the proposed method is able to detect process model mismatch of nonlinear systems.     

A modified index for control performance assessment

A control performance index which relates actual output variance to minimal achievable variance was first presented by Harris [T.J. Harris, Assessment of control loop performance, The Canadian Journal of Chemical Engineering 67 (1989) 856–861]. In the present paper, a modification of that index is applied. Instead of comparing to minimum variance control — which corresponds to placing all closed-loop poles in the origin — one pole is placed using either control design guidelines or additionally available process knowledge. Some possible choices of the free closed-loop pole are discussed. Based on this modified closed-loop system, a performance index can be calculated which relates actual output variance to the minimum achievable variance using the modified closed-loop system. It is shown that for the calculation of this index no other information apart from the measured process output and the time-delay is necessary. Furthermore, a method is presented which allows the assessment of the accuracy of the calculated index. The original Harris index and the proposed modified index are computed using data from industrial processes.     

带执行器饱和的N 连杆机械臂输出反馈动态面控制

针对带执行器饱和的多关节刚性机械臂系统,提出一种基于RBF神经网络补偿的输出反馈动态面控制.通过观测器实现角速度的观测,采用RBF网络实现执行器饱和的补偿;通过Lyapunov方法证明闭环系统的稳定性,实现高精度的角度和角速度跟踪.仿真结果表明,所提出的方法能够有效补偿系统存在的执行器饱和,显著减小跟踪误差,并且对于外界干扰具有一定的鲁棒性.     

Model predictive control monitoring using multivariate statistics

Control loop monitoring has become an important research field over the past decade. Research has primarily targeted single-input single-output (SISO) feedback control systems with limited progress being made on the monitoring of multi-input multi-output (MIMO) control systems and large scale model predictive control (MPC) systems in particular. The size and complexity of MPC systems means that identifying and diagnosing problems with their operation can be challenging. This paper presents an MPC condition monitoring tool based on multivariate statistical process control (MSPC) techniques. The proposed tool uses intuitive charts to enable casual users of MPC technology to detect abnormal controller operation and to identify possible causes for this behaviour. Through its application to data collected from a large scale MPC system, the proposed technique is shown to be able to identify and diagnose poor control performance resulting from various issues including inappropriate interaction by process operators.     

SWIR-based spectral indices for assessing nitrogen content in potato fields

Nitrogen (N) is an essential element in plant growth and productivity, and N fertilizer is therefore of prime importance in cultivated crops. The amount and timing of N application has economic and environmental implications and is consequently considered to be an important issue in precision agriculture. Spectral indices derived from handheld, airborne and spaceborne spectrometers are used for assessing N content. The majority of these indices are based on indirect indicators, mostly chlorophyll content, which is proven to be physiologically linked to N content. The current research aimed to explore the performance of new N spectral indices dependent upon the shortwave infrared (SWIR) region (1200–2500 nm), and particularly the 1510 nm band because it is related directly to N content. Traditional nitrogen indices (NIs) and four proposed new SWIR-based indices were tested with canopy-level spectral data obtained during two growing seasons in potato experimental plots in the northwest Negev, Israel. Above-ground biomass samples were collected at the same location of the spectral sampling to provide in-situ N content data. The performance of all indices was evaluated by three methods: (1) correlations between the existing and proposed indices and N as well as correlations among the indices themselves; (2) the root mean square error prediction (RMSEP) of the N content; and (3) the indices relative sensitivity (S _r) to the N content. The results reveal a firm advantage for the proposed SWIR-based indices in their ability to predict, and in their sensitivity to, N content. The best index is one that combines information from the 1510 and 660 nm bands but no significant differences were found among the new SWIR-based indices.     

Improved Controller Design with Two Gain-scaling Factors for Global Asymptotic Stabilization of Nonlinear Systems via Matrix Inequality Approach

In this paper, we consider a problem of global asymptotic stabilization for nonlinear systems with the perturbed nonlinearity. We provide a stabilizing controller with two gain-scaling factors and a new controller design method with matrix inequality approach. In particular, we provide a new procedure for selecting gain-scaling factors which are associated with stabilizing the closed-loop system. As a result, our proposed control method widens the class of considered nonlinear systems and yields better control performance over the existing methods. Via several comparison examples, we illustrate the improved features of the proposed control method over the existing ones.