Elsevier

Journal of Process Control

Volume 19, Issue 2, February 2009, Pages 187-204
Journal of Process Control

Intelligent state estimation for fault tolerant nonlinear predictive control

https://doi.org/10.1016/j.jprocont.2008.04.006Get rights and content

Abstract

There is growing realization that on-line model maintenance is the key to realizing long term benefits of a predictive control scheme. In this work, a novel intelligent nonlinear state estimation strategy is proposed, which keeps diagnosing the root cause(s) of the plant model mismatch by isolating the subset of active faults (abrupt changes in parameters/disturbances, biases in sensors/actuators, actuator/sensor failures) and auto-corrects the model on-line so as to accommodate the isolated faults/failures. To carry out the task of fault diagnosis in multivariate nonlinear time varying systems, we propose a nonlinear version of the generalized likelihood ratio (GLR) based fault diagnosis and identification (FDI) scheme (NL-GLR). An active fault tolerant NMPC (FTNMPC) scheme is developed that makes use of the fault/failure location and magnitude estimates generated by NL-GLR to correct the state estimator and prediction model used in NMPC formulation. This facilitates application of the fault tolerant scheme to nonlinear and time varying processes including batch and semi-batch processes. The advantages of the proposed intelligent state estimation and FTNMPC schemes are demonstrated by conducting simulation studies on a benchmark CSTR system, which exhibits input multiplicity and change in the sign of steady state gain, and a fed batch bioreactor, which exhibits strongly nonlinear dynamics. By simulating a regulatory control problem associated with an unstable nonlinear system given by Chen and Allgower [H. Chen, F. Allgower, A quasi infinite horizon nonlinear model predictive control scheme with guaranteed stability, Automatica 34(10) (1998) 1205–1217], we also demonstrate that the proposed intelligent state estimation strategy can be used to maintain asymptotic closed loop stability in the face of abrupt changes in model parameters. Analysis of the simulation results reveals that the proposed approach provides a comprehensive method for treating both faults (biases/drifts in sensors/actuators/model parameters) and failures (sensor/ actuator failures) under the unified framework of fault tolerant nonlinear predictive control.

Introduction

The need to operate continuous processes over wide operating ranges and semi-batch/batch processes efficiently has motivated the development of nonlinear MPC (NMPC) techniques over last two decades. These techniques employ nonlinear models for prediction. The prediction model is typically developed once in the beginning of implementation of an NMPC scheme. However, as time progresses, slow drifts in unmeasured disturbances and changes in process parameters can lead to significant mismatch in plant and model behavior. Also, NMPC schemes are typically developed under the assumption that sensors and actuators are free from faults. However, soft faults, such as biases in sensors or actuators, are frequently encountered in the process industry. In addition to this, some sensor(s) and/or actuator(s) may fail during operation, which results in loss of degrees of freedom for control. Occurrences of such parametric changes, soft faults and failures progressively result in severe model-plant mismatch. This can lead to a significant degradation in the closed loop performance of the NMPC scheme and may also lead to instability. Thus, to arrest the degradation in controller performance, it is extremely important to isolate the root causes of the plant model mismatch and, if possible, compensate for them on-line.

The conventional approach to deal with the model-plant mismatch in the NMPC formulations is through the introduction of additional artificial states in the state observer [2], [3], [4]. The main limitation of this approach is that the number of extra states introduced cannot exceed the number of measurements. This implies that it is necessary to have a priori knowledge of which subset of faults are most likely to occur or which parameters are most likely to drift. In such a formulation where the state vector is permanently augmented with subset of parameters to be estimated, the state estimates can become biased when unanticipated abrupt changes/faults occur. Moreover, the permanent state augmentation approach cannot systematically deal with the difficulties arising out of sensor biases or actuator/sensor failures. The difficulties encountered while selecting such a subset in design of extended Kalman filter (EKF) for a complex large dimensional system (Tennessee Eastman problem) have been highlighted by Ricker and Lee [2].

Attempts to develop fault-tolerant MPC schemes have mainly focused on dealing with sensor or actuator failures [5], [6], [7]. Yu et al. [6] have proposed to develop a failure tolerant cascaded Kalman filter with online tuning parameters. This approach involves the design of main and auxiliary Kalman filter (KF) based on reliable set of measurements and complete set of measurements, respectively. The auxiliary KF is used to remove the bias from the estimates given by the main KF. The steady state gain of auxiliary KF is modified online based on the failed measurements. Though this approach achieves fault tolerance while maintaining the integrity in the estimate of the lost output, the fault detection and isolation aspect does not feature in the formulation. Recently, Prakash et al. [8] have proposed an active fault tolerant linear MPC (FTMPC) scheme, which can systematically deal with soft faults in a unified framework. The FTMPC scheme is developed by integrating generalized likelihood ratio (GLR) method, a model based fault detection and identification (FDI) scheme, with the state space formulation of MPC based on Kalman filter. The GLR method performs fault identification using innovation sequence generated by the Kalman filter over a moving window of data in the past and this facilitates very close integration of the FDI and MPC schemes. The main limitation of these approaches arises from the use of linear perturbation model for performing control and diagnosis tasks. The use of linear models not only restricts its applicability to a narrow operating range but also limits the diagnostic abilities of fault detection and identification (FDI) components to only linear additive type faults. As a consequence, many faults that have a nonlinear effect on the system dynamics, such as abrupt changes in model parameters or unmeasured disturbances, have to be approximated as linear additive faults. Moreover, the FTMPC scheme does not deal with failures of sensors or actuators.

Recently, Mhaskar et al. [9], [10] have presented an approach that deals with control system or actuator failure in nonlinear processes subject to constraints. They have presented an approach for design of robust hybrid predictive candidate controllers, which guarantees stability from an explicitly characterized set of initial conditions, subject to uncertainty and constraints. Reconfiguration or controller switching is done to activate or deactivate the constituent control configuration in order to achieve fault tolerance. The Fault tolerant controller uses the knowledge of the stability regions of the back up control configurations to guide the state trajectory within the stability regions of the back up control configurations to enhance the fault tolerance capabilities. Their approach, however, requires nonlinear system under consideration to have input affine structure. In another article, Mhaskar et al. [11] have presented an integrated fault detection and fault-tolerant control structure, for SISO nonlinear systems with input constraints subject to control failures. A bounded Lyapunov based controller has been developed, which depends on construction of control Lyapunov function. Upon failure of the primary controller, the faulty configuration is shut down and a well functioning fall back configuration is switched on. It may be noted that various control structures are developed by exploiting specific structural features of a nonlinear system, as no standard method is available for construction of these control Lyapunov functions. Also, these approaches, as proposed, do not address difficulties arising from abrupt changes in model parameters, mean shift in unmeasured disturbances, sensor/actuator biases and failed sensors.

Examination of various fault tolerant MPC/NMPC formulations proposed in literature reveals that the design of state observer is the key to integration of fault tolerance with predictive control. If it is desired to achieve tolerance with respect to a broad spectrum of faults (abrupt changes in unmeasured disturbance, parameter drifts, sensor/actuator biases) and sensor/actuator failures in a typical situation where the number of degrees of freedom available for observer design (synonymous with the number of measurements available for observer construction) is limited (i.e. far less than the number faults and failures to be dealt), then it becomes imperative to introduce some degree of intelligence in the state estimation to overcome these limitations [12]. In the present work, an intelligent nonlinear state estimation strategy is proposed, which keeps diagnosing the root cause(s) of the plant model mismatch by isolating the subset of active faults and auto-corrects the model on-line so as to accommodate the isolated faults. To carry out the task of fault diagnosis in multivariate nonlinear time varying systems, we propose a nonlinear version of the generalized likelihood ratio (GLR) based FDI scheme, which is referred to as nonlinear GLR (NL-GLR) in the rest of the text. The NL-GLR scheme, along with the fault location, also generates an estimate of the fault magnitude, which is used to correct the prediction model used in the proposed fault tolerant NMPC (FTNMPC) formulation. As the proposed NL-GLR scheme is computationally demanding, it is further simplified for online implementation (SNL-GLR). This simplification is based on linearization of nonlinear process model around a nominal trajectory. The significant contributions of the work described in this paper are

  • Development of an active fault tolerant control scheme for nonlinear processes by suitably integrating a nonlinear version of the GLR method for FDI with a nonlinear model based controller.

  • Development of fault/failure isolation strategy when multiple faults and failures occur simultaneously.

  • Development of a comprehensive method for treating both faults (biases/drifts in sensors/actuators/model parameters) and failures (sensor/actuator failures) in fault diagnosis and accommodation.

The above contributions allow application of the fault tolerant scheme to nonlinear and time varying processes including batch and semi-batch processes. The proposed fault tolerant scheme also overcomes the limitation on the number of extra states that can be added to the state space model in NMPC for offset removal and allows bias compensation for more variables than the number of measured outputs. The advantages of the proposed state estimation and control scheme are demonstrated by conducting simulation studies on a benchmark CSTR system, which exhibits input multiplicity and change in the sign of steady state gain, and a fed batch bioreactor, which exhibits strongly nonlinear dynamics. By simulating regulatory control problem associated with a unstable nonlinear system given by Chen and Allgower [1], we also demonstrate that the proposed intelligent state estimation strategy can be used to recover closed loop stability in the face of abrupt changes in model parameters.

The rest of this article is organized as follows. To begin with, we develop the nonlinear version of GLR method. A fault tolerant NMPC formulation is presented in the subsequent section. We then proceed to present the results of simulation case studies. The main conclusions reached based on the analysis of these results are presented in the last section.

Section snippets

Fault diagnosis

In this section we develop an FDI method based on a nonlinear version of GLR scheme for diagnosing faults in nonlinear dynamic systems. To begin with, the method is described as applied once when a single fault is detected for the first time. Modifications necessary for on-line implementation of the FDI scheme when multiple faults occur sequentially are described later.

Intelligent state estimation for fault tolerant NMPC

NMPC techniques use nonlinear model for prediction, which is typically developed once in the beginning of implementation of an NMPC scheme. However, as time progresses, slow changes in unmeasured disturbances and/or process parameters and faults such as biases in sensors or actuators results in significant mismatch in plant and model behavior (behavior mismatch). In addition, hard failures, like failures of actuators and sensors can lead to significant structural plant model mismatch (structure

Simulation case studies

Simulation studies are carried out to evaluate the proposed intelligent state estimation (referred to as intelligent EKF in the rest of the text) and FTNMPC schemes by simulating control problems associated with the following highly nonlinear systems:

  • CSTR exhibiting input multiplicity [20], [21].

  • Unstable nonlinear system described in Chen and Allgower [1].

  • Fed-batch bioreactor [22].

The performance of the conventional NMPC (CNMPC) that employs conventional EKF for state estimation is compared

Conclusions

In this work, a novel intelligent nonlinear state estimation strategy has been proposed, which keeps diagnosing the root cause(s) of the plant model mismatch by isolating the subset of active faults (abrupt changes in parameters/disturbances, biases in sensors/actuators, actuator/sensor failures) and auto-corrects the model on-line so as to accommodate the isolated faults/failures. To facilitate the diagnosis of faults and failures in nonlinear and time varying processes, we develop a nonlinear

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