Plant-model Mismatch Research Articles

Model Predictive Control of an Industrial Distillation Column Based on a Hybrid Model: Adapting the Domain of Validity

In any model predictive control (MPC) implementation, the key factor is the quality of the employed system model in order to guarantee constraint satisfaction and to optimize the performance of the controlled system. However, it is difficult in practice to model all the phenomena of the true system which leads to plant-model mismatch. We propose to augment a simple first principles based model with a machine learning model to capture the plant dynamics which are not represented in the semi-rigorous model. The use of data-based models however can be problematic outside the region where the model was trained. In this work, we estimate the domain of validity of the data-based model using a one-class support vector machine (SVM) which is trained on a low-dimensional projection of the available training data. During the application of the controller, data of newly visited regions is collected and the domain of validity is adapted based on checking a performance criterion. The hybrid model incorporates a weighted contribution of the data-based model based on its predicted validity. We demonstrate the versatility and the benefits of the proposed adaptive MPC based on a hybrid model (AHMPC) approach via an industrial distillation column case study.

Stochastic Hybrid Model Predictive Control: Application to Parallel Hybrid Electric Vehicles

Hybrid electric vehicles (HEVs) are attracting attention for their high fuel efficiency and low emissions compared to diesel-powered vehicles. The fuel efficiency of the HEV is highly dependent on the optimal power split ratio. The problem of finding the optimal power split ratio trajectory is difficult to solve with linear and/or deterministic controllers because it has nonlinear and stochastic characteristics. In this study, stochastic hybrid model predictive control (SHMPC) was applied to the HEV system. Piecewise affine (PWA) modeling of HEV systems was performed to model nonlinear systems with smaller model-plant mismatch compared to linear models. Furthermore, to account for the driver's stochastic behavior, a scenario-based stochastic model predictive control (SMPC) approach was employed. Controllers of scenario-based linear SMPC and scenario-based SHMPC are built. The controllers were tested in MATLAB/Simulink HEVP2 Reference Application simulation environment.

Tube-based distributionally robust model predictive control for nonlinear process systems via linearization

Model predictive control (MPC) is an effective approach to control multivariable dynamic systems with constraints. Most real dynamic models are however affected by plant-model mismatch and process uncertainties, which can lead to closed-loop performance deterioration and constraint violations. Methods such as stochastic MPC (SMPC) have been proposed to alleviate these problems; however, the resulting closed-loop state trajectory might still significantly violate the prescribed constraints if the real system deviates from the assumed disturbance distributions made during the controller design. In this work we propose a novel data-driven distributionally robust MPC scheme for nonlinear systems. Unlike SMPC, which requires the exact knowledge of the disturbance distribution, our scheme decides the control action with respect to the worst distribution from a distribution ambiguity set. This ambiguity set is defined as a Wasserstein ball centered at the empirical distribution. Due to the potential model errors that cause off-sets, the scheme is also extended by leveraging an offset-free method. The favorable results of this control scheme are demonstrated and empirically verified with a nonlinear mass spring system and a nonlinear CSTR case study.

Online Feedback Optimization of Compressor Stations with Model Adaptation using Gaussian Process Regression

Online Feedback Optimization is a method used to steer the operation of a process plant to its optimal operating point without explicitly solving a nonlinear constrained optimization problem. This is achieved by leveraging a linear plant model and feedback from measurements. However the presence of plant-model mismatch leads to suboptimal results when using this approach. Learning the plant-model mismatch enables Online Feedback Optimization to overcome this shortcoming. In this work we present a novel application of Online Feedback Optimization with online model adaptation using Gaussian process regression. We demonstrate our approach with a realistic load sharing problem in a compressor station with parametric and structural plant-model mismatch. We assume imperfect knowledge of the compressor maps and design an Online Feedback Optimization controller that minimizes the compressor station power consumption. In the evaluated scenario, imperfect knowledge of the plant leads to a 5% increase in power consumption compared to the case with perfect knowledge. We demonstrate that Online Feedback Optimization with model adaptation reduces this increase to only 0.8%, closely approximating the case of perfect knowledge of the plant, regardless of the type of mismatch.

Output-Feedback Multi-Loop Positioning Technique via Dual Motor Synchronization Approach for Elevator System Applications

This paper devises an output-feedback multi-loop positioning technique adopting the speed observer and multi-motor synchronizer, targeting the dual (master and slave) motor elevator system applications, providing the three contributions. First, the order-reduction observer continuously extracts the speed information from the motor position measurement, independent of the system model information. Second, the order-reduction stabilizer accomplishes the speed synchronization tasks for both the master and slave motors. Third, the resultant feedback system guarantees to exponentially recover the desired first-order transfer function from the reference to the actual motor position despite the model-plant mismatches. The prototype elevator system adopting the dual motor experimentally validates the practical advantages of the proposed technique.

서보 시스템 응용을 위한 능동형 영-극점 상쇄 속도 추종 기술

This study presents a novel speed-tracking controller by considering not only model-plant mismatches but also load variations. The proposed solution has a simple conventional proportional–integral (PI) controller structure, including a specially structured feedback gain with respect to active damping and cut-off frequency, invoking an order reduction to 1 despite inclusion of the additional integral action. A prototype 400 W brushless DC motor dynamo system was constructed to verify the effectiveness of the proposed solution compared with the conventional PI controller equipped with a well-tuned feedback gain.

Development of offset-free Koopman Lyapunov-based model predictive control and mathematical analysis for zero steady-state offset condition considering influence of Lyapunov constraints on equilibrium point

Koopman operator theory enables a global linear representation of a given nonlinear dynamical system. However, since an approximation to the Koopman operator cannot fully represent a nonlinear dynamical system, plant-model mismatch inherently exists and negatively influences the performance of control systems. To this end, we present a new approach called offset-free Koopman Lyapunov-based model predictive control (KLMPC) that augments disturbance dynamics to a Koopman-based model to consider the plant-model mismatch in the optimal control problem. The zero steady-state offset condition of the developed framework is also mathematically examined by rigorously investigating the influence of Lyapunov constraints on the equilibrium point of the offset-free KLMPC system.

Current-Sensorless Energy-Shaping Output Voltage-Tracking Control for dc/dc Boost Converters With Damping Adaptation Mechanism

This article exhibits an output voltage-derivative observer-based output voltage-tracking technique for dc/dc boost converters without current feedback, taking the model-plant mismatches (caused by parameter and load variations) and model nonlinearity into consideration. In contrast to extant passivity-based approaches, the proposed solution includes observers to estimate the output voltage derivative and does not require exact model information, which offers a few features: converter parameter information-free output voltage-derivative observers including the modified disturbance observation algorithm for improving the high-frequency disturbance rejection capability as a replacement of the estimation error integral actions, and the observer-based output voltage and its derivative error stabilizer with a damping adaptation mechanism assigning the desired energy function to the closed-loop system. Experimental verification is provided to demonstrate the practical advantages of the proposed solution using a 3-kW bidirectional converter.

Batch-to-Batch Iterative Learning Control of a Fed-Batch Fermentation Process

In this work, Iterative Learning Control on a fed-batch fermentation process using linearised models has been studied. The repetitive nature of batch processes enables ILC to obtain information from a previous batch in order to improve the performance of the current batch such that the product quality converges asymptotically to the desired trajectory The basic batch to batch ILC law presents the control action of a current batch as a summation of the control action from the previous batch and the deviation of the output trajectory from the desired reference trajectory incorporation with a learning rate. In a bid to address the issue of the process non-linearity, the control policy and the output trajectory were linearised around their respective nominal trajectories. The linearised models were then identified using Multi Linear Regression (MLR), Principal Component Analysis (PCR) and Partial Least Squares (PLS). In order to curb the effects of plant-model mismatches and process variations, the linearised models were reidentified after each batch operation. This was done by selecting the immediate previous batch as the nominal batch and then adding the recently obtained process data into the historical data batch on completion of the current batch run. The weighting matrices in the objective function were carefully selected taking into consideration that they have a major influence on the robust performance of the process. In using PLS and PCR models the issue of process collinearity was effectively addressed. The proposed batch to batch ILC strategy was applied to a simulated fed-batch fermentation process for the production of secreted protein. The results of the optimal control policy were comparable to that obtained in using full mechanistic model. ILC, a simple but yet an effective optimal control strategy has demonstrated to be a viable option in complex processes such as batch processes where mechanistic models are difficult to develop. Keywords: Iterative Learning Control, batch process, fed-batch fermentation, batch to batch ILC, control policy. DOI: 10.7176/CMR/14-3-02 Publication date: August 31 st 2022

Generalized Parameter Estimation Method for Model-Based Real‑Time Optimization

• Generalized parameter estimation is proposed to handle structural mismatches. • Synergy between model parameters and gradient modifiers is visualized. • Convergence of the proposed algorithm is discussed. • Simulations show the proposed method is relatively noise-insensitive. Real-time optimization is the technology to find the optimal setpoint of a plant under uncertainty. Iterative two-step approach with alternating parameter estimation and optimization is popular and intuitive in practice. However, this approach does not guarantee convergence if structural plant-model mismatches exist. Using the modifier adaptation principle, we improve the iterative two-step approach by the proposed generalized parameter estimation method. The flexibility and estimation capability of the generalized parameters enable optimality in the presence of structural plant-model mismatches. The synergy between model parameters and modifiers is visualized and demonstrated by three examples. The convergence of the proposed algorithm and its relation with existing work are analyzed theoretically. Simulation shows that the proposed method converges to a plant optimum in the presence of structural plant-model mismatch in a relatively noise-insensitive way, and the model parameters are properly adapted during the iteration.

Performance-Boosting Attitude Control for 2-DOF Helicopter Applications via Surface Stabilization Approach

This study solves the attitude stabilization problem of 2-degree-of-freedom (2-DOF) helicopters by robustly assigning the variable-performance to the closed-loop system in the presence of the model-plant mismatches and load variations. The proposed approach reformulates the original problem to a surface stabilization one which yields three contributions: a) the proposed attitude velocity observer forms a conventional Luenberger-type observer incorporating the parameter-independence and estimation gains specifically designed for causing the pole-zero cancellation, b) the pole-zero cancellation velocity control loop makes it possible to accomplish the surface stabilization task with the first-order closed-loop order, and c) the closed-loop analysis results demonstrate the attractive properties of the exponential performance recovery and convergence. The effectiveness of the proposed technique is verified using the experimental platform provided by the Quanser AERO.

An implementable zone NMPC applied to an ESP-lifted oil well system: Handling the lack of measurements with nonlinear state estimator coupling

This paper addresses the first application of a nonlinear model predictive control (NMPC) scheme, coupled with an extended Kalman filter (EKF), for oil production processes with electric submersible pump (ESP) installations. The resulting nonlinear program of the proposed NMPC is most computationally tractable by the use of zone control scheme to deal with the downthrust and upthrust operational envelope-type ESP time-varying constraints, making it implementable in practice. The coupling of EKF seeks to solve the challenger problem of lack of measurements in ESP-lifted oil wells, besides is strategically used to compute downthrust and upthrust ESP head bounds from the estimated average flow rate in the production column. The implementable zone NMPC+EKF scheme is also flexible to incorporate optimizing targets in its formulation aiming at economic performance improvements. The effectiveness of the proposal is carried out in noisy plant-model mismatch scenarios for fairly different operating condition tracking, including cases of rejection of significant disturbances on manifold pressure. Analysis on the inclusion (or not) of optimizing target on the choke valve opening also demonstrates the economic gains in terms of ESP power savings, in addition, the computational effort evaluation corroborates with the feasibility of the controller in real-time implementation purposes.

A Note on the Robustness of the Disturbance Observer-Based Robust Control Systems

Abstract This brief shows that the design constraints on the plant-model mismatch and the bandwidth of the disturbance observer (DOb) become more severe when the robust controller is implemented using computers. This brief also shows that continuous-time analysis methods fall-short in explaining the fundamental design constraints of the DOb-based robust digital control systems, therefore leading to unexpected stability and performance problems in practice.

Tube-based iterative-learning-model predictive control for batch processes using pre-clustered just-in-time learning methodology

Iterative-learning-model predictive control (ILMPC) has been considered a potential control strategy for batch processes. ILMPC can converge to the desired reference trajectory with high precision along cycles and reject real-time disturbances within cycles. However, as a model-based control method, the control performance of the ILMPC algorithm deteriorates when it suffers the problem of model-plant mismatches. Therefore, simultaneously guaranteeing system convergence along the cycle-axis and robust stability on the time-axis is a challenging task in the framework designing of ILMPC control systems. To this end, we present a type of tube-based ILMPC strategy based on an empirical model for nonlinear batch processes. First, to describe the dynamic behavior of nonlinear batch processes as much as possible with the goal of low computational cost and high modeling accuracy, a pre-clustered just-in-time learning (JITL) model focused on operation data is developed. Then, an ancillary MPC controller is combined with the ILMPC algorithm to form a tube scheme to relieve the impact of model error. In addition, we construct an inverse model system (IMS) to systematically determine the first cycle control input trajectory of the proposed tube-based ILMPC algorithm. As a result, they simultaneously ensure the system convergence along the cycle-axis and robust stability on the time-axis. Still, they can improve convergence speed and tracking performance. Finally, comparative simulations demonstrate the superiority of the proposed control algorithm.

On improving the efficiency of modifier adaptation via directional information

In real-time optimization, the solution quality depends on the model ability to predict the plant Karush–Kuhn–Tucker (KKT) conditions. In the case of non-parametric plant-model mismatch, one can add input-affine modifiers to the model cost and constraints as is done in modifier adaptation (MA). These modifiers require estimating the plant cost and constraint gradients. This paper discusses two ways of reducing the number of input directions, thereby improving the efficiency of MA in practice. The first approach capitalizes on the knowledge of the active set to reduce the number of KKT conditions. The second approach determines the dominant gradients using sensitivity analysis. This way, MA reaches near plant optimality efficiently by adapting the first-order modifiers only along the dominant input directions. These approaches allow generating several alternative MA schemes, which are analyzed in terms of the number of degrees of freedom and compared in a simulated study of the Williams–Otto plant.

An operating economics-driven perspective on monitoring and maintenance in multiple operating regimes: Application to monitor fouling in heat exchangers

Process monitoring is required to ensure consistent product quality and safe operation. Equipment degradation leads to changes in the process model causing plant-model mismatch, e.g., fouling in heat exchangers. This is particularly important for slow drifting industrial processes, where monitoring just the process variables is insufficient, as controllers continuously seek to track key process variables to ensure that they adhere to strict design conditions, despite increased operating costs to compensate for the model degradation. An objective of this work is to develop a straightforward operating economics-driven monitoring algorithm to track process drifts and equipment degradation in multiple operating regimes by monitoring deviations in model parameters along with the states. A 2014 estimate put the economic cost of fouling in heat exchangers for US industries at $14 billion per year. To mitigate this expenditure, and highlight the importance of this work, illustrative examples involving both simulated synthetic data and experimental data from a double-pipe heat exchanger are used. Traditional state estimation methods are integrated with cost contours based on operating economics to accurately track equipment degradation by monitoring deviations in model parameters, even when drastic changes in input conditions are present. Tracking process drifts and equipment degradation while evaluating the economic impact helps determine the urgency of cleaning and maintenance that is required.

Learning of model-plant mismatch map via neural network modeling and its application to offset-free model predictive control

We propose an improved offset-free model predictive control (MPC) framework, which learns and utilizes the intrinsic model-plant mismatch map, to effectively exploit the advantages of model-based and data-driven control strategies and overcome the limitation of each approach. In this study, the model-plant mismatch map on steady-state manifold is approximated via artificial neural network (ANN) modeling based on steady-state data from the process. Though the learned model-plant mismatch map can provide the information at the equilibrium point (i.e., setpoint), it cannot provide model-plant mismatch information during transient state. To handle this, we additionally apply a supplementary disturbance variable which is updated from a revised disturbance estimator considering the disturbance value obtained from the learned model-plant mismatch map. Then, the learned and supplementary disturbance variables are applied to the target problem and finite-horizon optimal control problem of the offset-free MPC framework. By this, the control system can utilize both the learned model-plant mismatch information and the stabilizing property of the nominal disturbance estimator. The closed-loop simulation results demonstrate that the proposed offset-free MPC scheme utilizing the model-plant mismatch map learned via ANN modeling efficiently improves the closed-loop reference tracking performance of the control system. Additionally, the zero-offset tracking condition of the developed framework is mathematically examined.

Real-Time Optimization of Wastewater Treatment Plants via Constraint Adaptation

An important requirement of wastewater treatment plants (WWTPs) is compliance with the local regulations on effluent discharge, which are going to become more stringent in the future. The operation of WWTPs exhibits a trade-off between operational cost and effluent quality, which provides a scope for optimization. Process optimization is usually done by optimizing a model of the process. However, due to inevitable plant–model mismatch, the computed optimal solution is usually not optimal for the plant. This study represents the first attempt to handle plant–model mismatch via constraint adaptation (CA) for the real-time optimization of WWTPs. In this simulation study, the “plant” is a model adopted from the BSM1 benchmark, while a reduced-order “model” is used for making predictions and computing the optimal inputs. A first implementation uses steady-state measurements of the plant constraints to adjust the model in the optimization framework. A fast CA technique is also proposed, which adjusts the model using transient measurements. It is observed that, even in the presence of significant plant–model mismatch, the two proposed techniques are able to meet the active plant constraints. These techniques are found to reduce the pumping and aeration energy by 20%, as compared to that adopted in BSM1.

Modified smith predictor for slug control with large valve stroke time in unstable systems

Slugging as a flow assurance challenge is an upsetting condition to the oil and gas industry due to the instabilities it poses on the system. The negative repercussions associated with slug flow stems from the inlet through to the topside facilities where processing is done. Active control has been established as one of the best techniques to eradicate slug and its accompanying challenges, however the controller robustness and some setbacks make improvement a necessity. Again, the robustness of the controller has been in question.Due to the potential of active control, several other researchers have delved into it. Many outcomes from pilot scale experiments (usually 2–4 inch valves), that shows promising and improved benefits fail to replicate when emulated on real offshore facilities (over 8 inch valve diameters). This is because of the difference in the valve stroke time (time taken for a valve to move from fully open to fully close or vice versa). Comparatively, larger diameter valves are designed to have larger stroke time than smaller diameter.In this paper, an advancement and extension of an active slug control strategy that uses measurement signals from the topside of the riser, will be used to deal with systems with time-delay as a result of large valve stroke time. The Smith predictor model was specially modified not just to deal with time-delay but also to deal with variable time-delay in both stable and unstable systems. Thus, a design of a modified smith predictor where the modification mitigates the direct estimation of the time delay itself. This is supposedly due to the internal structure of the proposed modification which, accounts for plant-model mismatch and makes small changes to the control input based on a reference controller.

Implementable MPC-based surge avoidance nonlinear control strategies for non-ideally modeled natural gas compression systems

The surge avoidance control plays a pivotal role in a centrifugal compression process to maintain safety and high efficiency. In the literature, MPC-like schemes have shown promise for use in such tasks given that they can systematically deal with several process constraints. However, to obtain a good performance in the compression process with a significant deviation of gas ideality, the model used in MPC formulations has to be able to predict the process behavior correctly. This paper proposes surge avoidance feasible optimization-based MPC schemes for non-ideally modeled natural gas compression systems. Its pivotal contributions are: (i) extension of the isothermal and ideal gas thermodynamic behaviors commonly adopted in models of surge prevention MPC schemes to a non-isothermal flow and non-ideally behaved gas-like more realistic compression system; (ii) formulation of a proposed nonlinear model-based MPC control law with surge protection being managed by slacked nonlinear constraints; (iii) synthesis of an adaptive infinite horizon MPC-based surge avoidance scheme that relies upon the successive linearization of the proposed rigorous model for the compression system. From simulations carried out with a plant-model mismatch oriented by distinct equations of state, results obtained from the proposed rigorous model-based surge avoidance NMPC strategy are favorably compared to those obtained with the simplified model widely used in the literature. Finally, the proposed adaptive MPC-based surge prevention scheme showed convergence towards the corresponding NMPC with a drastically reduced computational cost.