Plant-model Mismatch Research Articles

Channel oriented approach for multivariable model updating using historical data

The model-plant mismatch (MPM) can be responsible for poor control performance. This can be solved by locating which channels (i.e., pars of MVs-CVs) are suffering the highest MPM, and then, proceed with the model updating using the same historical data used for the assessment and diagnosis steps. This paper proposes a method for updating models based on the nominal error: a benchmark that quantifies the model discrepancy by comparing the measured output of a system with its corresponding nominal output, i.e., the output of the closed-loop with no MPM or unmeasured disturbances. The main advantages of the method are to avoid usual multivariable model identification and use simpler SISO structures, thus reducing the workload of the model maintenance. The effectiveness of the method is illustrated using the quadruple-tank process with a nonminimum phase operating point to explore multivariable characteristics of the final updated model. All the required methodologies for assessment, diagnosis, and model maintenance are also presented in the paper and can be applied in the same historical data. No additional plant perturbations are required to improve the model. Although it is not limited to Model Predictive Control (MPC), the proposed methodology can be successfully applied to MPC assessment, diagnosis, and model maintenance.

A framework of hybrid model development with identification of plant‐model mismatch

AbstractHybrid modeling has attracted increasing attention in order to take advantage of the additional data to improve process understanding. Current practice often adopts mechanistic models to predict process behaviors. These mechanistic models are based on physical understandings and experimental studies, but they sometimes lead to plant‐model mismatch (PMM) as they may be inaccurate to fully describe real processes. Black‐box models can serve as an alternative, but they often suffer from poor generalization and interpretability. To combine the two techniques, hybrid models are developed to make use of process data while maintaining a degree of physical understanding. In this work, we implement a framework of identification of PMM using partial correlation coefficient and mutual information, followed by introducing and comparing serial, parallel, and combined structures of hybrid models. The framework is applied and tested with a simulated reactor model and two pharmaceutical unit operation case studies.

Disturbance Observer-Based Offset-Free Global Tracking Control for Input-Constrained LTI Systems with DC/DC Buck Converter Applications

This paper presents an offset-free global tracking control algorithm for the input-constrained plants modeled as controllable and open-loop strictly stable linear time invariant (LTI) systems. The contribution of this study is two-fold: First, a global tracking control law is devised in such a way that it not only leads to offset-free reference tracking but also handles the input constraints using the invariance property of a projection operator embedded in the proposed disturbance observer (DOB). Second, the offset-free tracking property is guaranteed against uncertainties caused by plant-model mismatch using the DOB’s integral action for the state estimation error. Simulation results are given in order to demonstrate the effectiveness of the proposed method by applying it to a DC/DC buck converter.

Constrained iterative learning control of batch transesterification process under uncertainty

Biodiesel are fatty acid methyl esters (FAME), which can be produced by the transesterification reaction of vegetable oils with methanol. A batch transesterification process is often associated with model uncertainties and unmeasured disturbances, which may create a detrimental effect on the batch end FAME yield due to plant-model mismatch. Therefore, batch-to-batch iterative learning control (ILC) is necessary to track the desired reference FAME profile under such process variations. This work demonstrates a constrained quadratic programming problem (QPP) based batch-to-batch ILC framework for optimizing the endpoint FAME concentration by controlling the hot water flow profile passing through the reactor jacket under uncertainty. Parametric uncertainties are modeled separately in two case studies, which involve different batch transesterification models differing in the state variables. Case study 1 considers uncertainty in the apparent activation energy and brings out a comparative study between a QPP based ILC and a heuristics based approach. The comparison is shown based on the tracking performance of the ILC in terms of reduction in the batch end tracking error and total root mean square error of the same. Batch-to-batch ILC is superior as it produces faster convergence of the tracking error by saving 6 batches as compared to the heuristics approach. Case study 2 involves the implementation of constrained QPP based ILC algorithm on a proposed 54-state detailed batch transesterification model of canola oil, where uncertainty is modeled as the change in the input triglyceride composition from the base case. The desired reference FAME concentration profile is tracked in 9 batches for fixed uncertainty whereas it takes 15 batches to achieve the stochastic convergence under stochastic disturbance.

Real-time optimization of wind farms using modifier adaptation and machine learning

Abstract. Coordinated wind farm control takes the interaction between turbines into account and improves the performance of the overall wind farm. Accurate surrogate models are the key to model-based wind farm control. In this article a modifier adaptation approach is proposed to improve surrogate models. The approach exploits plant measurements to estimate and correct the mismatch between the surrogate model and the actual plant. Gaussian process regression, which is a probabilistic nonparametric modeling technique, is used in the identification of the plant–model mismatch. The efficacy of the approach is illustrated in several numerical case studies. Moreover, challenges in applying the approach to a real wind farm with a truly dynamic environment are discussed.

Artificial pancreas under stable pulsatile MPC: Improving the closed-loop performance

This work presents a pulsatile Zone Model Predictive Control (pZMPC) for the control of blood glucose concentration (BGC) in patients with Type 1 Diabetes Mellitus (T1DM). The main novelties of the algorithm – in contrast to other existing strategies – are: (i) it controls the patient glycemia by injecting short duration insulin boluses for both, the basal and bolus infusions, in an unified manner, (ii) it performs the predictions and estimations (critical to anticipate both, hypo and hyperglycemia) based on a physiological individualized long-term model, (iii) it employs disturbance observers to compensate plant-model mismatches, (iv) it ensures, under standard assumptions, closed-loop stability, and (v) it can be used – under minor modifications – as an optimal basal–bolus calculator to emulate conventional therapies. Because of the latter characteristic, a significantly better performance is achieved, not only in terms of classical indexes (time in the normoglycemia zone, avoidance of hypoglycemia in the short term, avoidance of hyperglycemia in the long term) but also in terms of its applicability (use of the pump or injections). Such a performance is tested in a cohort of in-silico patients from the FDA-accepted UVA/Padova simulation platform, considering the most challenging scenarios.

NMPC-based control scheme for a semi-batch reactor under parameter uncertainty

Exothermic reactions are often performed in SBR because the generated reaction heat can be more easily kept under control in such construction. However, an unsuitable control system can lead to the development of thermal runaway, which may cause lethal damage. NMPC with implemented thermal runaway criteria is a promising tool to operate SBRs. However, engineers should always consider plant-model mismatch because uncertain predictions can cause undesirable scenarios. A novel control framework is proposed to operate SBRs and consists of NMPC with the implemented runaway criterion, extended Kalman filter and parameter identification algorithm. Both Multi-Stage NMPC and NMPC with the worst-case scenario are investigated and tested in terms of ability to handle parameter uncertainty. The former is 38 times slower than the latter with no noticeable increase in reactor performance. NMPC initialized based on the worst-case scenario with updating uncertain kinetic parameters results in a promising control structure for SBRs.

A new control strategy for a higher order proton exchange membrane fuel cell system

In this paper, a new cascade control strategy is proposed for a higher order Proton Exchange Membrane (PEM) Fuel Cell system for improving the performance on the basis of stack voltage. In the proposed strategy, stack voltage is considered as the primary objective and maintaining oxygen excess ratio value as a secondary aim, by manipulating the air compressor voltage. A higher-order PEMFC model is reduced to lower order integer and fractional models using varied model reduction techniques, which are then used to realize the primary as well as secondary controllers. Both integer and fractional order PID controllers are designed for the reduced order models and then implemented for the higher order system. The control performance is evaluated for disturbance rejection, system model mismatch and better controlled output for continuous random disturbance on the basis of Integral Absolute Error and controller effort. The outcome of the proposed control strategy is advantageous in terms of disturbance rejection, robustness, parameter uncertainty and reduction of plant-model mismatch.

A model mismatch assessment method of MPC by decussation

For the model plant mismatch (MPM) assessment of MPC systems, a correlation analysis method between the input and the disturbance (CAID) is proposed and is combined with model quality index (MQI) for its application in multivariable system. By deducing the input–output correlation coefficient variation law of adding independent variables in a function, the paper defines the CAID index of assessing the MPM. To realize the exact location of sub-model mismatch in multivariable system, the synthetical disturbance variable is constructed through principle component analysis (PCA), then it is used to define the synthetical CAID index of multivariable MPC system, and finally the decussation method combining synthetical CAID and MQI is presented. The proposed method is validated in Wood-Berry distillation process and an industrial air separate process.

Homothetic tube-based robust offset-free economic Model Predictive Control

This paper proposes a novel economic Model Predictive Control algorithm aiming at achieving optimal steady-state performance despite the presence of plant-model mismatch or unmeasured nonzero mean disturbances. According to the offset-free formulation, the system’s state is augmented with disturbances and transformed into a new coordinate framework. Based on the new variables, the proposed controller integrates a moving horizon estimator to determine a solution of the nominal system surrounded by a set of potential states compatible with past input and output measurements. The worst cost within a single homothetic tube around the nominal solution is chosen as the economic objective function which is minimized to provide a tightened upper bound for the accumulated real cost within the prediction horizon window. Thanks to the combined use of the nominal system and homothetic tube, the designed optimization problem is recursively feasible and less conservative economic performance bounds are achieved. The proposed controller is demonstrated on a two-tanks system.

Real-time optimization via modifier adaptation of closed-loop processes using transient measurements

Real-time optimization (RTO) has the ability to boost the performance of a process whilst satisfying the constraints by using process measurements, driving the operating conditions towards optimality. Modifier adaptation (MA) is a methodology of RTO which can find the optimal operating point of a process even in the presence of plant-model mismatch. This work presents an extension to MA through the combination of two established frameworks, allowing for the optimization of a controlled process using transient measurements whilst using a steady-state open-loop model. In addition, an approach for model-based gradient estimation, despite the mismatch between the degrees of freedom of the closed-loop plant and the available open loop model is suggested that does not necessitate amending the model. The proposed scheme is illustrated on a case study of a CSTR and a distillation column, detailing how the gradient can be estimated.

Observer-Based Incremental Predictive Control of Networked Multi-Agent Systems With Random Delays and Packet Dropouts

This brief addresses the cooperative output tracking control problem for a linear heterogeneous networked multi-agent system with random network-induced delays and packet dropouts in the feedback channel of each agent, which consists of one leader agent and multiple following agents. To compensate for adverse effects of those random communication constraints, an incremental networked predictive control scheme based on state observers is proposed. A necessary and sufficient condition is derived for the stability of the resulting closed-loop system, which is independent of random communication constraints. Experimental results on a networked multi-motor control test rig show the effectiveness and applicability of the proposed scheme, including a feature that zero steady-state output tracking errors can be achieved even for the case with plant-model mismatch.

Experimental Verification of Robust PID Controller Under Feedforward Framework for a Nonminimum Phase DC–DC Boost Converter

This article addresses the disturbance rejection problem of a nonminimum phase dc-dc boost converter operating in the continuous conduction mode (CCM) using a novel robust proportional-integral-derivative (PID) controller design method. The proposed idea is to design the controller using the equivalent feedforward formulation of the modified direct synthesis (MDS) approach. The advantages of the proposed MDS design are: 1) systematic incorporation of disturbance dynamics and the converter dynamics explicitly in the controller design to reduce the complex tuning effort of the controller parameters; 2) allowing the converter to operate close to the performance limit set by the zero in the right half-plane (RHP); 3) the closed-loop performance specifications can be incorporated into the desired loop response using only single tuning parameter based on Bode's gain crossover frequency inequality; 4) attenuates the loop gain to improve the disturbance rejection; and 5) realization of controller requires only output voltage as a feedback signal. The strength of the proposed MDS method is compared with the internal model control (IMC) method in both simulations and experiments. Based on these responses, the proposed PID ensures robust performance to the model-plant mismatch and allows the output voltage to quickly recover back to the operating voltage in the presence of external disturbances with less inductor current.

Active damping injection controller for web longitude and tensions of nonlinear roll-to-roll systems

This study presents an advanced algorithm for controlling the web longitude and tension of nonlinear roll-to-roll systems in the form of a cascade structure. Parameter variation and disturbance attenuation problems are addressed systematically. The features of this article are divided into two parts. First, active damping terms are injected to stabilize the system nonlinear dynamics so that the first-order closed-loop transfer functions are obtained for each loop via pole-zero cancelation. Second, disturbance observers are introduced to ensure the performance recovery property by attenuating the disturbances from the model-plant mismatches. The closed-loop system is numerically emulated using MATLAB/Simulink to show the effectiveness of the proposed technique.

Stochastic data-driven model predictive control using gaussian processes

Nonlinear model predictive control (NMPC) is one of the few control methods that can handle multivariable nonlinear control systems with constraints. Gaussian processes (GPs) present a powerful tool to identify the required plant model and quantify the residual uncertainty of the plant-model mismatch. It is crucial to consider this uncertainty, since it may lead to worse control performance and constraint violations. In this paper we propose a new method to design a GP-based NMPC algorithm for finite horizon control problems. The method generates Monte Carlo samples of the GP offline for constraint tightening using back-offs. The tightened constraints then guarantee the satisfaction of chance constraints online. Advantages of our proposed approach over existing methods include fast online evaluation, consideration of closed-loop behaviour, and the possibility to alleviate conservativeness by considering both online learning and state dependency of the uncertainty. The algorithm is verified on a challenging semi-batch bioprocess case study.

Distributed output feedback control for multi-unit system with delayed multirate measurements

The aim of this work is to analyze output feedback distributed control framework based on model predictive control (MPC) for multi-unit systems with multirate and delayed measurements. Primary controlled variable(s) is sampled infrequently, and the measurement is available after a delay. The distributed, unit-specific estimators and controllers communicate through selective information transfer based on process knowledge. The distributed state estimator is designed based on sampled state augmentation method to efficiently compute improved state estimates on arrival of the delayed infrequent measurements. The multirate estimators are appropriately modified to incorporate the disturbance model to handle model-plant mismatch (MPM). The proposed implementation is analyzed using two case studies. A linearized, reactor-separator system is used to demonstrate that multirate estimation is required for offset-free tracking. A more complex variant of the reactor-separator system with recycle demonstrates the ability of nonlinear distributed estimator-MPC framework to incorporate infrequent and delayed primary measurements.

Hierarchical model predictive control of Venlo-type greenhouse climate for improving energy efficiency and reducing operating cost

In this paper, a hierarchical control strategy for Venlo-type greenhouse climate control under South Africa climate is proposed to improve energy efficiency and reduce operating cost. The proposed hierarchical control architecture includes two layers. The upper layer is to generate set points by solving different optimization problems. Three different strategies with different optimization objectives are studied. The meteorological data of a typical winter day is used. Strategy 1 is to minimize the energy consumption. Strategy 2 is to minimize the energy cost under the time-of-use (TOU) tariff. Strategy 3 is to minimize the total cost of energy consumption, ventilation and carbon dioxide (CO2) supply. The lower layer is to track the trajectories obtained from the upper layer. A closed-loop model predictive control (MPC) strategy is introduced to address model plant mismatch and reject system disturbances. Two performance indices, relative average deviation (RAD) and maximum relative deviation (MRD), are introduced to compare the tracking performance of the proposed MPC and an open loop control under three different levels of system disturbances (2%, 5%, 10%). Simulation results show that the proposed strategy can effectively reduce the operating cost while keeping the temperature, relative humidity and CO2 concentration within required ranges. Compared with Strategy 1 and Strategy 2, the total cost of Strategy 3 is reduced by 72.07% and 71.41% respectively. Moreover, the proposed MPC has better tracking performance than the open loop control. Therefore, the proposed hierarchical MPC strategy could be an effective way to improve greenhouse energy efficiency and achieve sustainable cleaner production.

Developing and validating a dynamic model of water production by direct-contact membrane distillation.

We consider the development and fitting of a dynamic model for desalinated water production by a direct-contact membrane distillation (DCMD) unit. Two types of dynamic-model structures, namely, lumped parameter and spatial, were evaluated. Both the models were validated using experimental response data generated by step testing the inlet hot stream temperature of a DCMD pilot plant. Both the model structures failed to follow the dynamic response adequately. However, a modification of the model by adding a heat loss term resulted in enhanced predictions for both model structures. The overall relative error in the model-plant mismatch was approximately 3%. This is reasonable considering the random uncertainties associated with the plant operation. This observation also improves our understanding of the importance of using better correlations for heat-transfer coefficients, to develop a more reliable and accurate predictive model for a wide range of operating conditions.

A Retrofit Hierarchical Architecture for Real-Time Optimization and Control Integration

To achieve the optimal operation of chemical processes in the presence of disturbances and uncertainty, a retrofit hierarchical architecture (HA) integrating real-time optimization (RTO) and control was proposed. The proposed architecture features two main components. The first is a fast extremum-seeking control (ESC) approach using transient measurements that is employed in the upper RTO layer. The fast ESC approach can effectively suppress the impact of plant-model mismatch and steady-state wait time. The second is a global self-optimizing control (SOC) scheme that is introduced to integrate the RTO and control layers. The proposed SOC scheme minimizes the global average loss based on the approximation of necessary conditions of optimality (NCO) over the entire operating region. A least-squares regression technique was adopted to select the controlled variables (CVs) as linear combinations of measurements. The proposed method does not require the second order derivative information, therefore, it is numerically more reliable and robust. An exothermic reaction process is presented to illustrate the effectiveness of the proposed method.

Offset-free MPC strategy for nonzero regulation of linear impulsive systems

In various biomedical applications, drug administration treatment can be modeled as an impulsive control system. Despite the development of different control strategies for impulsive systems, the elimination of the offset generated by a plant-model mismatch has not yet been researched. In biomedical systems, this mismatch is a consequence of physiological changes and can result in inaccurate treatment of patients. Therefore, control techniques that accomplish the objectives by compensating the effect of variations are required. The present paper proposes and substantiates a novel offset-free model predictive control (MPC) strategy for impulsive systems. To that aim, an impulsive disturbance model is introduced, and an observer design is developed that includes new observability criteria for estimating the disturbance and the state. Further, it is demonstrated that the proposed control strategy achieves zero offset tracking from an analysis of the observer and the controller at steady state. Additionally, the controller incorporates a recent MPC formulation to steer the state to an equilibrium set using artificial/intermediary variables to achieve nonzero regulation. Finally, these results are evaluated and illustrated using a dynamical model for type 1 diabetic patients.