Daoping Huang

Adaptive Fuzzy Control With Guaranteed Convergence of Optimal Approximation Error

With no a priori knowledge of plant boundary functions, a novel direct adaptive fuzzy controller (AFC) for a class of single-input single-output (SISO) uncertain affine nonlinear systems is developed in this paper. Based on the theory of fuzzy logic systems (FLSs) with variable universes of discourse (UDs), sufficient conditions that guarantee that the optimal fuzzy approximation error (FAE) is locally convergent are given. By the use of the output tracking error and its derivatives as input variables and by the selection of suitable adjusting parameters, a variable UD FLS with an optimal FAE local convergence is constructed, and its parameter adaptive law is derived by virtue of the Lyapunov stability theorem. Under the assumption that the optimal FAE is bounded, it is proved that the closed-loop system is asymptotically stable in the sense that all variables are uniformly ultimately bounded and that the tracking errors converge to zero. The proposed approach eliminates the influence of the FAE on the tracking errors by means of the inherent mechanism of the variable UD FLS. Thus, it has the potential to achieve high control performance without additional compensation under only a few fuzzy rules. Simulation studies demonstrate the superiority of the proposed AFC in terms of the settling time, tracking accuracy, smoothness of the control input, and robustness against external disturbances and parameter variations.

Fire-rule-based direct adaptive type-2 fuzzy H∞ tracking control

This paper presents a novel H^~ tracking-based direct adaptive fuzzy controller (HDAFC) for a class of perturbed uncertain affine nonlinear systems involving external disturbances and measurement noise. A practical interval type-2 (IT2) fuzzy logic system (FLS) is introduced to approximate the ideal control law. To eliminate the tradeoff between H^~ tracking performance and high gain at the control input, a modified output tracking error is introduced. Based on the proposed fired-rule-determination algorithm, a practical average defuzzifier expressed in parameterized and closed formula is developed for the IT2 FLS. Without the restriction that the control gain function is exactly known, the IT2 HDAFC is constructed and its adaptive law is derived by virtue of the Lyapunov synthesis. To improve control performance under measurement noise, the recursive linear smoothed Newton predictor is further introduced as a delayless output filter. Simulated application of a single-link robot manipulator demonstrates the superiority of the proposed approach over the previous approach in terms of the settling time, tracking accuracy, energy consumption and smoothness of the control input.

A probabilistic self-validating soft-sensor with application to wastewater treatment

Abstract In the wastewater treatment plants (WWTPs), soft sensors are viewed as a simple signal estimator for hard-to-measure quantities. However, the presence of unreliable data, coupled with increasing demands for measurement quality assurance, has rendered inadequate such a simplistic view. In this paper, a probabilistic self-validating soft-sensor is proposed with the capability of performing self-diagnostics, self-reconstruction and online uncertainty measurement. In this framework, data collecting for soft-sensor modeling (easy-to-measure data) is validated by a Variational Bayesian Principal Component Analysis (VBPCA) model before performing a soft-sensor model construction. By integrating Relevant Vector Machine (RVM) as a predictive model, not only prediction values are obtained, but also the credibility of information for easy-to-measure and hard-to-measure quantities can be generated. The performance of the proposed soft-sensor is validated through two simulation studies of WWTPs with different process characteristics. The results suggest that the proposed strategy significantly improves the prediction performance.

Direct adaptive fuzzy control for a class of nonlinear systems with unknown bounds

For a class of uncertain single-input single-output (SISO) nonlinear systems with unknown bound functions and unknown function control gain, a novel approach of direct adaptive fuzzy controller (AFC) without supervisory controller is proposed by Lyapunov synthesis. Based on the direct AFC with projection operator, it is developed a fuzzy approximation error estimator as adaptive compensator, which is used to estimate optimal approximation error (OAE) dynamically and reduce the influence of approximation error on system performance. In closed-loop system analysis, it is not required that the OAE is square-integrable or the OAE supremum is known. It is proved that controlled object being bounded is the sufficient condition of the OAE being bounded. The overall controller guarantees that the closed-loop system is global asymptotically stable in sense that all variables are bounded. The proposed controller is demonstrated to be simple and effective by simulation studies for inverted pendulum system. It achieves favorable performance with smooth controller output, small tracking error and strong robustness.

Indirect Adaptive Fuzzy Control with Approximation Error Estimator for Nonlinear Systems

For a class of single-input single-output (SISO)nonlinear systems with unknown bound functions and unknown function control gain, a novel approach of indirect adaptive fuzzy controller (AFC) without supervisory controller is proposed by Lyapunov synthesis. Firstly, it is presented a novel indirect AFC with adaptive laws using improved projection operator. Then an adaptive compensator with approximation error estimator is developed, which is used for estimating optimal approximation error (OAE) dynamically and reducing the influence of approximation error on system performance.In closed-loop system analysis, it does not require that the OAE is square-integrable or the OAE supremum is known. It is proved that the overall controller guarantees the global asymptotical stability of the closed-loop system in sense that all variables are bounded. Control simulation results of inverted pendulum system demonstrate that this approach achieves favorable performance with smooth controller output, small tracking error and strong robustness.

Prediction of Filamentous Sludge Bulking using a State-based Gaussian Processes Regression Model

Activated sludge process has been widely adopted to remove pollutants in wastewater treatment plants (WWTPs). However, stable operation of activated sludge process is often compromised by the occurrence of filamentous bulking. The aim of this study is to build a proper model for timely diagnosis and prediction of filamentous sludge bulking in an activated sludge process. This study developed a state-based Gaussian Process Regression (GPR) model to monitor the filamentous sludge bulking related parameter, sludge volume index (SVI), in such a way that the evolution of SVI can be predicted over multi-step ahead. This methodology was validated with SVI data collected from one full-scale WWTP. Online diagnosis and prediction of filamentous bulking sludge with real-time SVI prediction was tested through a simulation study. The results showed that the proposed methodology was capable of predicting future SVIs with good accuracy, thus providing sufficient time for predicting and controlling filamentous sludge bulking.

Semiadaptive Fault Diagnosis via Variational Bayesian Mixture Factor Analysis with Application to Wastewater Treatment

Mainly due to the hostile environment in wastewater plants WWTPs, the reliability of sensors with respect to important qualities is often poor. In this work, we present the design of a semiadaptive fault diagnosis method based on the variational Bayesian mixture factor analysis VBMFA to support process monitoring. The proposed method is capable of capturing strong nonlinearity and the significant dynamic feature of WWTPs that seriously limit the application of conventional multivariate statistical methods for fault diagnosis implementation. The performance of proposed method is validated through a simulation study of a wastewater plant. Results have demonstrated that the proposed strategy can significantly improve the ability of fault diagnosis under fault-free scenario, accurately detect the abrupt change and drift fault, and even localize the root cause of corresponding fault properly.

H∞ direct adaptive fuzzy control with unknown control gain for uncertain nonlinear systems

With unknown control gain function and plant bound functions, a H∞ direct adaptive fuzzy controller (AFC) for a class of single-input single-output (SISO) uncertain affine nonlinear systems under external disturbance is proposed. A conventional fuzzy logic system (FLS) is used to approximate the control gain function, and a FLS with variable universes of discourse, which has the characteristic of high fuzzy output precision with only one adjusting parameter, is used to approximate a ideal controller. A novel fuzzy approximation theorem is introduced to solve the problem of unknown control gain function in direct AFC scheme. Both adaptive laws of conventional FLS and variable universe FLS are derived by virtue of the Lyapunov stability theorem. Under the assumption that the total approximation error is bounded, it is proved that the closed-loop system not only is stable in sense that all variables are bounded, but also achieves the H∞ tracking performance and the tracking error convergence. Simulation example is demonstrated to confirm the effectiveness of this approach.