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.     

Latent variable MPC for trajectory tracking in batch processes

A novel multivariate empirical model predictive control strategy (LV-MPC) for trajectory tracking and disturbance rejection for batch processes is presented. The strategy is based on dynamic principal component analysis (PCA) models of the batch process. The solution to the control problem is computed in the low dimensional latent variable space of the PCA model. The trajectories of all variables over the future horizon are then computed from the latent variable solution of the controller. The excellent control performance and the modest closed-loop data requirements for identification are illustrated for the temperature tracking in simulations of an emulsion polymerization process, an exothermic chemical reaction system and for MIMO temperature and pressure tracking in a nylon polymerization autoclave.     

Adaptive tracking and asymptotic rejection of unknown but bounded disturbances in nonlinear MIMO systems

The goal of this paper is global disturbance rejection in nonlinear systems. An output feedback controller with disturbance rejection is developed for a class of nonlinear multi input-multi output (MIMO) systems. The availability of state variables and the bound of disturbances are not required to be known in advance and reference tracking will is guaranteed. By the aid of designing an adaptive observer, a robust adaptive nonlinear state feedback controller using the estimated states is proposed. For tracking problem, an adaptive pre-compensator is used. The control methodology is robust against both constant and time varying bounded disturbances, maintaining effective performance. The adaptive laws are derived based on the Lyapunov synthesis method, therefore closed-loop asymptotic stability is also guaranteed. Moreover, for chattering reduction we use a low-pass filter. Consequently, small gain theorem is adopted to prove the stability of the closed-loop system. Simulation results are employed to illustrate the effectiveness of the proposed controller.     

An expert autotuner for multiloop SISO controllers

In this paper, an on-line expert autotuner for a class of 2-input-2-output multivariable process control applications is proposed. The autotuning controller, which uses a pattern-recognition technique is designed with a view to its practical implementation in multivariable processes. The main idea of the autotuning methodology is to use the observed multiloop responses with reference to the single-loop responses such that proper detuning of the SISO controllers is achieved. Customized identification techniques in SISO and MIMO environments based on closed-loop responses are developed for this application. Simulation results for a range of 2-input-2-output multivariable processes characterized by the Relative Gain (RG) and the relative dynamics are used to evaluate the performance of the autotuning controller under different conditions. The time response of the autotuning controller is compared to that of Biggest Log Modulus Tuning (BLT) method with a few distillation column models proposed in the literature.     

Direct passivity of a class of MIMO non-linear systems using adaptive feedback

In this paper, an adaptive controller with adaptive laws specially designed is proposed to solve the problem of making a multi-input multi-output (MIMO) non-linear system, with explicit linear parametric uncertainty, equivalent to a passive system. These results are an extension of those obtained by the authors for the SISO case. Some stability issues associated to the resultant closed-loop passive system are also discussed. The results obtained are applied to models of dynamical MIMO systems, to illustrate the controller design methodology.     

Output feedback control with disturbance rejection of a class of nonlinear MIMO systems

Output feedback control with disturbance rejection is developed for a class of nonlinear multi-input-multi-output (MIMO) systems. The availability of state variables and the bound of disturbances are not required to be known in advance. In the design of an adaptive observer, a robust adaptive nonlinear state feedback controller using the estimated states is proposed. The control methodology is robust to bounded disturbances that are both constant and time-varying, with effective performance. The adaptive laws are derived based on the Lyapunov synthesis method; therefore closed-loop asymptotic stability is also guaranteed. Moreover, chattering can be reduced by the proposed design approach. Simulation results are included to illustrate the effectiveness of the proposed controller. The text was submitted by the authors in English.     

A measurement-based approach for designing reduced-order controllers with guaranteed bounded error

The objective of this paper is to present a measurement-based control-design approach for single-input single-output linear systems with guaranteed bounded error. A wide range of control-design approaches available in the literature are based on parametric models. These models can be obtained analytically using physical laws or via system identification using a set of measured data. However, due to the complex properties of real systems, an identified model is only an approximation of the plant based on simplifying assumptions. Thus, the controller designed based on a simplified model can seriously degrade the closed-loop performance of the system. In this paper, an alternative approach is proposed to develop fixed-order controllers based on measured data without the need for model identification. The proposed control technique is based on computing a suitable set of fixed-order controller parameters for which the closed-loop frequency response fits a desired frequency response that meets the desired closed-loop performance specifications. The control-design problem is formulated as a nonlinear programming problem using the concept of bounded error. The main advantages of our proposed approach are: (1) it guarantees that the error between the computed and the desired frequency responses is less than a small value; (2) the difficulty of finding the globally optimal solution in the error minimisation problem is avoided; (3) the controller can be designed without the use of any analytical model to avoid errors associated with the identification process; and (4) low-order controllers can be designed by selecting a fixed low-order controller structure. To experimentally validate and illustrate the efficacy of the proposed approach, proportional-integral measurement-based controllers are designed for a DC (direct current) servomotor.     

Direct adaptive interval type-2 fuzzy control of multivariable nonlinear systems

A fuzzy logic controller equipped with a training algorithm is developed such that the H^∞ tracking performance should be satisfied for a model-free nonlinear multiple-input multiple-output (MIMO) system, with external disturbances. Due to universal approximation theorem, fuzzy control provides nonlinear controller, i.e., fuzzy logic controllers, to perform the unknown nonlinear control actions and the tracking error, because of the matching error and external disturbance is attenuated to arbitrary desired level by using H^∞ tracking design technique. In this paper, a new direct adaptive interval type-2 fuzzy controller is developed to handle the training data corrupted by noise or rule uncertainties for nonlinear MIMO systems involving external disturbances. Therefore, linguistic fuzzy control rules can be directly incorporated into the controller and combine the H^∞ attenuation technique. Simulation results show that the interval type-2 fuzzy logic system can handle unpredicted internal disturbance, data uncertainties, very well, but the adaptive type-1 fuzzy controller must spend more control effort in order to deal with noisy training data. Furthermore, the adaptive interval type-2 fuzzy controller can perform successful control and guarantee the global stability of the resulting closed-loop system and the tracking performance can be achieved.     

A model-free design of reduced-order controllers and application to a DC servomotor

This paper presents a new model-free technique to design fixed-structure controllers for linear unknown systems. In the current control design approaches, measured data are used to first identify a model of the plant, then a controller is designed based on the identified model. Due to errors associated with the identification process, degradation in the controller performance is expected. Hence, we use the measured data to directly design the controller without the need for model identification. Our objective here is to design measurement-based controllers for stable and unstable systems, even when the closed-loop architecture is unknown. This proposed method can be very useful for many industrial applications. The proposed control methodology is a reference model design approach which aims at finding suitable parameter values of a fixed-order controller so that the closed-loop frequency response matches a desired frequency response. This reference model design problem is formulated as a nonlinear programming problem using the concept of bounded error, which can then be solved to find suitable values of the controller parameters. In addition to the well-known advantages of data-based control methods, the main features of our proposed approach are: (1) the error is guaranteed to be bounded, (2) it enables us to avoid issues related to the use of minimization methods, (3) it can be applied to stable and unstable plants and does not require any knowledge about the closed-loop architecture, and (4) the controller structure can be selected a priori, which means that low-order controllers can be designed. The proposed technique is experimentally validated through a real position control problem of a DC servomotor, where the results demonstrate the efficacy of the proposed method.     

Minimum entropy-based performance assessment of feedback control loops subjected to non-Gaussian disturbances

Control performance assessment (CPA) is a useful tool to establish the quality of industrial feedback control loops. While many current CPA techniques are developed solely for the controlled systems under the assumption of the Gaussian disturbance, the conventional minimum variance control (MVC) approach would not be applied when the disturbance distribution is non-Gaussian. In this paper, based on the information theory and the minimum entropy criterion, a more general CPA index for the feedback control loop subjected to unknown disturbance distribution is investigated. The fundamentals of MVC are first reexamined, and then an innovative performance index is given by incorporating the entropy. The feedback control algorithm based on minimum entropy, called MEC (minimum entropy control), is derived. MEC based CPA for the controlled system requires effective and systematic identification of the associated system models based on the closed-loop data. In this work, a new methodology based on the entropy criterion instead of the mean square error criterion is presented to estimate disturbances for the purpose of evaluating the performance of the control systems. To demonstrate the effective MEC based CPA method, both numerical and industrial examples are applied and compared with the MVC based CPA method.     

Data-driven diagnosis of sensor precision degradation in the presence of control

This paper considers the precision degradation type of sensor faults within control loops. In a closed loop, sensor faults propagate through controller to manipulated variables and disturb the other process variables, which obscures the source of sensor faults but receives less attention in existing methods of data-driven sensor fault diagnosis. With the assumption that only closed-loop data in normal condition are available, difficulty arises due to the facts that little a priori knowledge is known about closed-loop sensor fault propagation and the open-loop process model may not be identifiable. The proposed method in this paper constructs residual that is regarded as including two parts: the first part is the current sensor faults whose fault direction is known to be the identity matrix; and for the purpose of diagnosing the first part, the second part is considered as the disturbance which is affected by noises and past sensor faults due to unknown fault propagation. The disturbance variance is minimized in residual generator design to improve fault sensitivity. And the corresponding disturbance covariance is estimated and then utilized in residual evaluation. The proposed method in this paper is motivated by a pioneer work on closed-loop sensor fault diagnosis which performs principal component analysis in the feedback-invariant subspace of the closed-loop process outputs. But it is revealed by the proposed method that the feedback-invariant signal is affected by past sensor faults, leading to performance degradation of the pioneer work. The improvement of the proposed approach is due to analysis of residual dynamics and explicit handling of the disturbance in residual evaluation, which is not considered in the pioneer work. A simulated 4 × 4 dynamic process and a simulated two-product distillation column are studied to verify the effectiveness of the proposed approach compared to the existing principal component analysis method in feedback-invariant subspace.     

A closed-loop data based test for robust performance improvement in iterative identification and control redesigns

In robust iterative identification and control redesign techniques, a stabilizing controller connected in a closed loop is normally replaced by an alternative attractive stabilizing controller to improve robustness and performance of the closed-loop system. In this paper, novel test methods are proposed to check whether a new stabilizing controller improves performance or not when the existing controller is replaced by this new controller in the closed loop. The proposed tests are based on closed-loop data and no plant model, and can be used for both the SISO and MIMO linear time-invariant systems. For the proposed tests, the plant dynamics is assumed to be unknown whereas the existing and new controller transfer function matrices are known to the designer. These assumptions are common in iterative identification and control redesign techniques. The performance improvement test methods proposed in this paper build on the experimental set-up proposed in Dehghani, Lecchini, Lanzon, and Anderson (2009) which was used to only check whether controllers ensure internal stability of a feedback interconnection or not. In this paper, new test methods are proposed to ascertain robust performance improvement that cannot be obtained from test results of Dehghani et al. (2009). A numerical example is illustrated to show effectiveness of the proposed test methods.     

Development of a fractional order based MIMO controller for high dynamic engine testbeds

Testbed are used to tune and assess automotive engines. As more High Dynamic (HD) scenarios need to be simulated, the testbeds require Multi Input Multi Output (MIMO) and robust control systems. A cooperation involving a major testbed manufacturer and two university laboratories was therefore set up. This paper presents the Control-System Design (CSD) methodology developed from system identification to the design and assessment of the MIMO robust controller for a HD testbed coupled with a spark-ignition engine. It is specially highlighted how the entire process has been automated and simplified and how the fractional order based MIMO CRONE CSD has been parameterized to obtain the best performance. Experimental results show that the proposed fractional order based MIMO control system is able to improve robustness and decoupling.     

An adaptive fuzzy design for fault-tolerant control of MIMO nonlinear uncertain systems

This paper presents a novel control method for accommodating actuator faults in a class of multiple-input multiple-output (MIMO) nonlinear uncertain systems.The designed control scheme can tolerate both the time-varying lock-in-place and loss of effectiveness actuator faults.In each subsystem of the considered MIMO system,the controller is obtained from a backstepping procedure;an adaptive fuzzy approximator with minimal learning parameterization is employed to approximate the package of unknown nonlinear functions in each design step.Additional control effort is taken to deal with the approximation error and external disturbance together.It is proven that the closed-loop stability and desired tracking performance can be guaranteed by the proposed control scheme.An example is used to show the effectiveness of the designed controller.     

Tuning SISO offset-free Model Predictive Control based on ARX models

In this paper, we present a tuning methodology for a simple offset-free SISO Model Predictive Controller (MPC) based on autoregressive models with exogenous inputs (ARX models). ARX models simplify system identification as they can be identified from data using convex optimization. Furthermore, the proposed controller is simple to tune as it has only one free tuning parameter. These two features are advantageous in predictive process control as they simplify industrial commissioning of MPC. Disturbance rejection and offset-free control is important in industrial process control. To achieve offset-free control in face of unknown disturbances or model-plant mismatch, integrators must be introduced in either the estimator or the regulator. Traditionally, offset-free control is achieved using Brownian disturbance models in the estimator. In this paper we achieve offset-free control by extending the noise model with a filter containing an integrator. This filter is a first order ARMA model. By simulation and analysis, we argue that it is independent of the parameterization of the underlying linear plant; while the tuning of traditional disturbance models is system dependent. Using this insight, we present MPC for SISO systems based on ARX models combined with the first order filter. We derive expressions for the closed-loop variance of the unconstrained MPC based on a state space representation in innovation form and use these expressions to develop a tuning procedure for the regulator. We establish formal equivalence between GPC and state space based off-set free MPC. By simulation we demonstrate this procedure for a third order system. The offset-free ARX MPC demonstrates satisfactory set point tracking and rejection of an unmeasured step disturbance for a simulated furnace with a long time delay.     

A novel neural approximate inverse control for unknown nonlinear discrete dynamical systems.

A novel neural approximate inverse control is proposed for general unknown single-input-single-output (SISO) and multi-input-multi-output (MIMO) nonlinear discrete dynamical systems. Based on an innovative input/output (I/O) approximation of neural network nonlinear models, the neural inverse control law can be derived directly and its implementation for an unknown process is straightforward. Only a general identification technique is involved in both model development and control design without extra training (online or offline) for the neural nonlinear inverse controller. With less approximation made on controller development, the control will be more robust to large variations in the operating region. The robustness of the stability and the performance of a closed-loop system can be rigorously established even if the nonlinear plant is of not well defined relative degree. Extensive simulations demonstrate the performance of the proposed neural inverse control.     

SISO approaches for linear programming based methods for tuning decentralized PID controllers

Two tuning techniques are proposed to design decentralized PID controllers for weakly coupled and general MIMO systems, respectively. Each SISO loop is designed separately, and the controller parameters are obtained as a solution of a linear programming optimization problem with constraints on the process stability margins. Despite the SISO approach, loop interactions are accounted for either by Gershgorin bands (non-iterative method) or an equivalent open-loop process (iterative method). The tuning results and performance from both methods are illustrated in four simulations of linear processes, and a laboratory-scale application in a Peltier process. Four applications contemplate closed-loop performance comparisons between the proposed techniques and techniques from the literature. One application illustrates the feasibility of the proposed iterative method, based on EOPs, in tuning decentralized PIDs for a 5 × 5 system. Moreover, an analysis of the effect of model uncertainty in the phase and gain margins of the closed-loop process is performed.     

Practical application of model identification based on ARX models with transfer functions

A novel model identification methodology for ARX models based on transfer functions has been proposed. The identification approach converts transfer functions to ARX models with no approximation, except zero-order hold. Model parameters of the transfer functions are estimated directly. Model identification for process controls, especially MPCs, is of great importance for achieving the highest performance from them. However, step testing for model identification is a time-consuming task. Model identification techniques are necessary to save time for step tests. Therefore, a closed-loop identification method of multivariable systems is useful and helpful for time-saving. Herein, the proposed method, with control by model predictive controllers, is suited for a closed-loop identification technique and is applied in an industrial chemical plant.