Plant-model Mismatch Research Articles

Output-Voltage-Tracking Control for Buck Converters Using Variable Convergence Rate Mechanism Without Current Feedback

This article aims to accomplish the output voltage tracking task for buck converters without current feedback, diminishing the performance degradation from model-plant mismatches and load variations. The following contributions overcome these difficulties: a) the combination of Luenberger and disturbance observer (DOB) techniques for a parameter-independent voltage-derivative observer; b) the pole-zero cancellation control incorporating the DOB and active-damping injection techniques; and c) the exponential convergence guarantee to the target tracking system subject to the variable convergence rate mechanism. Convincing experimental evidence confirms the effectiveness of proposed tracking control using a prototype 3 kW buck converter control system.

An event-triggered model predictive control with exponentially stable offset free for PWA systems with model-plant mismatch

A new event-triggered model predictive control (MPC) method is proposed for PWA systems with model-plant mismatch, such that, for a given asymptotically constant reference signal, exponential stability and unbiased tracking can be achieved. Firstly, for the PWA system, an observer is designed to estimate state and the model-plant mismatch. To guarantee the exponential stability, an event is introduced, and an event-triggered model predictive controller is designed as well. By introducing state error and estimate error, an augmented model is constructed. Then, using the model-dependent average dwell time (MDADT) method and Lyapunov stability theory, exponentially stable condition of the closed-loop system is derived, which is formulated by linear matrix inequalities (LMIs), and zero offset is also guaranteed under some mild assumptions. Moreover, the MDADT of each sub-system is given simultaneously. Finally, simulations have been taken to verify the effectiveness of the proposed method.

Explicit Nonlinear MPC for Fault Tolerance Using Interacting Multiple Models

This article presents a novel algorithm for adaptive explicit nonlinear model predictive control (eNMPC) with applications to fault tolerance. In order to account for plant-model mismatch, under which fault tolerance applies, the controller's explicit solution is designed with multiple dynamic models representing various operating modes as opposed to a single system model. Each model is weighted by a parameter variable to be evaluated online as mode probabilities produced by an interacting multiple model (IMM). Weighting each potential system model allows the controller to use a dynamic model that best matches the current operating mode, thus mitigating the degrading performance brought on by plant-model mismatch. The developed strategy is validated on attitude maneuvers for a nonlinear spacecraft system in the presence of disturbances and two actuator faults, which are indicative of the system mode. Average root mean squared values on the tracking error and control effort over Monte Carlo simulations are used to evaluate the effectiveness of the proposed techniques. Results indicate eNMPC benefits from access to weighted system models and manages similar levels of tracking error to standard spacecraft controllers at the same or minimal control effort.

Offset-free neural network-based nonlinear model predictive controller design using parameter adaptation

The performance of conventional nonlinear model predictive control $$\left( {{\text{NMPC}}} \right)$$ system relies heavily on the accuracy of the prediction model. In cases of significant plant-model mismatch, non-desirable responses may be observed in the controlled outputs. This paper proposes a parameter adaptation technique for tackling this problem. In the proposed approach, the output disturbance is selected as the adaptation parameter while the adaptation law is modelled as a function of the tracking error using a first-order difference equation. The adaptation law is integrated into a $$\mathrm{NMPC}$$ algorithm to achieve offset-free tracking. The effectiveness of the proposed scheme is demonstrated on two simulation case studies—a pH system and a continuously stirred tank reactor (CSTR); and an experimental cascaded two tank process. The simulation results obtained showed that the proposed scheme achieves zero offset in the face of significant plant-model mismatch arising from uncertainties in model parameters, unmeasured disturbances, and measurement noise and compared favourably with existing methods. The experimental results obtained during real-time implementation of the proposed control scheme corroborate this assertion and show its industrial applicability.

Sensitivity-Assisted multistage nonlinear model predictive control: Robustness, stability and computational efficiency

Key requirements for robust nonlinear model predictive control (NMPC) are stability, efficient performance under uncertainty, constraint satisfaction and computational efficiency. Multistage NMPC, based on a scenario tree formulation for the uncertainty, has been shown to satisfy the first three objectives under plant-model mismatch. However, a limiting factor in multistage NMPC, is the exponential scaling of the scenarios with respect to uncertain parameters and the length of the robust horizon. To address this issue, we present an approximate sensitivity-assisted multistage NMPC (samNMPC) scheme that reduces the problem size by dividing the scenario set into critical and noncritical scenarios, with the former composed of the worst-case realizations of the uncertain parameters. In this approach, the optimization is sought explicitly over the critical scenarios, while noncritical scenarios are included implicitly through nonlinear programming (NLP) sensitivity-based approximations in the objective function. A key advantage of the proposed approach is that the problem size is independent of the number of constraints and scales only linearly with the robust horizon. This allows faster computations with longer robust horizons that rigorously account for future uncertainty. In this paper, we explore the samNMPC approach and discuss its robust stability properties in context of the robust horizon. We demonstrate the applicability of the approach for the continuous stirred tank reactor (CSTR) and the quadtank case studies for tracking setpoints, and show that samNMPC compares favorably in performance and robustness to ideal multistage NMPC, but with a significant reduction in computational cost.

Model-plant mismatch detection for cross-directional processes

This paper presents a two-component framework to detect model-plant mismatch (MPM) in cross-directional (CD) processes on paper machines under model-predictive control. First, routine operating data is used for system identification in closed loop; second, a one-class support vector machine (SVM) is trained to predict MPM. The iterative identification method alternates between identifying the finite impulse response coefficients of the spatial and temporal models. It converges, and the parameter estimates are asymptotically consistent. Coefficient estimates drawn from normal operation are used to train a one-class SVM, which then detects model-plant mismatch in subsequent routine operation. This approach applies to routine operating data without requiring external excitations. It can also distinguish mismatches in the process model from changes in the noise model. Examples of CD processes on paper machines are provided to verify the effectiveness of both components.

Multirate moving horizon estimation combined with parameter subset selection

Due to the model-plant mismatch in practical applications of a nonlinear model, it is necessary to estimate both states and model parameters online. However, when the number of uncertain parameters is large, it is difficult to estimate all the parameters due to a lack of information in measurements. Under this condition, model prediction can be inaccurate although the current states are accurately estimated. To improve the accuracy of both state estimation and prediction, we propose a moving horizon estimation combined with a parameter subset selection scheme. In the proposed MHE framework, a subset of estimable parameters is selected within each horizon. Then, only the selected parameters are estimated along with the state variables. The proposed method is illustrated with the numerical example of a fed-batch bioreactor. The result shows that the proposed method improves the accuracy of model prediction, compared to the conventional MHE, while maintaining the state estimation performance.

Real-time optimization meets Bayesian optimization and derivative-free optimization: A tale of modifier adaptation

This paper investigates a new class of modifier-adaptation schemes to overcome plant-model mismatch in real-time optimization of uncertain processes. The main contribution lies in the integration of concepts from the fields of Bayesian optimization and derivative-free optimization. The proposed schemes embed a physical model and rely on trust-region ideas to minimize risk during the exploration, while employing Gaussian process regression to capture the plant-model mismatch in a non-parametric way and drive the exploration by means of acquisition functions. The benefits of using an acquisition function, knowing the process noise level, or specifying a nominal process model are analyzed on numerical case studies, including a semi-batch photobioreactor optimization problem with a dozen decision variables.

A robust modifier adaptation method via Hessian augmentation using model uncertainties

Typical model-based optimization approaches cannot handle plant-model mismatch, therefore the use of real-time optimization (RTO) schemes which take advantage of measurements from the plant is required. Modifier adaptation (MA) uses the measurements to add a bias to the model which iteratively matches the model with the local gradient estimates of the plant, leading to satisfaction of the Karush–Kuhn–Tucker (KKT) conditions of the plant upon convergence. Whilst feasibility of the convergence solution is guaranteed, there is no such promise of the feasibility of the iterates before convergence. Some methods have been proposed which can guarantee feasibility of the iterates, however all proposed methods suffer from being extremely conservative with long convergence times and are not readily applicable without global information of the plant. This article proposes an alternative approach which uses model uncertainties to avoid the use of unobtainable information whilst removing the overly conservative iterates of previous methods. This new approach is illustrated on the Williams-Otto CSTR, illustrating rapid convergence.

A New Adaptive Factor-Based Output Compensation Strategy for Offset Free Control of MLD–MPC with Model–Plant Mismatch

The mixed logical dynamical (MLD) model is a powerful framework of multimodel combinations for nonlinear systems control. Although superior control performance can be obtained by MLD-MPC, model–pla...

Online learning‐based model predictive control with Gaussian process models and stability guarantees

AbstractModel predictive control allows to provide high performance and safety guarantees in the form of constraint satisfaction. These properties, however, can be satisfied only if the underlying model, used for prediction, of the controlled process is sufficiently accurate. One way to address this challenge is by data‐driven and machine learning approaches, such as Gaussian processes, that allow to refine the model online during operation. We present a combination of an output feedback model predictive control scheme and a Gaussian process‐based prediction model that is capable of efficient online learning. To this end, the concept of evolving Gaussian processes is combined with recursive posterior prediction updates. The presented approach guarantees recursive constraint satisfaction and input‐to‐state stability with respect to the model–plant mismatch. Simulation studies underline that the Gaussian process prediction model can be successfully and efficiently learned online. The resulting computational load is significantly reduced via the combination of the recursive update procedure and by limiting the number of training data points while maintaining good performance.

An Adaptive Infinite Horizon Model Predictive Control Strategy Applied to an ESP-lifted Oil Well System

This work presents the benefits of using an adaptive model predictive control approach for controlling an ESP-lifted oil well system. The idea behind the proposed scheme is the successive linearization of the plant nonlinear model and incorporate it into an infinite-horizon MPC formulation, which handles feasibility issues by considering slacked terminal constraints. Also, suitable use of a zone control strategy to deal with time-varying ESP operating envelope constraints (downthrust and upthrust) becomes the approach implementable in practice. Nonlinear plant-model mismatch scenarios, including simulation of unmeasured disturbances and the tracking of ESP operation economic targets, show the effectiveness of the proposed controller concerning different operating conditions of the oil production process equipped with ESP.

State estimation and sensor location for Entrained-Flow Gasification Systems using Kalman Filter

This study presents the estimation of key unknown states for a pilot-scale gasifier using Kalman Filter (KF). The transient behaviour of a pilot-scale gasification unit is represented using a dynamic reduced order model. This model consists of 479 state variables including molar fractions for the species, temperature, and slag thickness across the gasifier. The quality of the state estimation provided by KF has been evaluated under multiple arrangements of the number and the location of the sensors available for the top section of the gasifier. Also, plant-model mismatch, additive uncertainty in the prior estimation, and load-following scenarios have been considered. The results show that KF is capable of estimating the unknown states for a large variety of changes in the gasifier’s inputs, even though online temperature sensors are only available in limited locations across the gasifier.

Glycemic Control Strategy Based on an Impulsive MPC With Safety Layer Coupling for IOB Limitation

Insulin stacking is one of the major concerns in intensive insulin therapy for type 1 diabetes. Despite the development of several control strategies for constraining the insulin-on-board (IOB), the benefits and drawbacks of this type of constraint under hypo- and hyperglycemia sensitivity scenarios have not been deeply analyzed for model-based controllers. Here, a safety layer based on IOB estimation is coupled with an impulsive offset-free zone model predictive control to tackle this problem. First, the resulting glycemic behavior of applying the safety layer under different scenarios of physiological variations are discussed. And then, simple rules for adapting the safety layer are developed. The envisioned strategy takes advantage of the plant-model mismatch estimation to determine when physiological variations in a subject are inducing hypoglycemia or hyperglycemia, and thus, the IOB safety layer can be tightened or released according to the sign of the estimated mismatch. The performance of the strategy was assessed in-silico on a cohort of 10 adult patients under challenging scenarios considering parameter variations of ±30%, a circadian insulin sensitivity, and sensor noise.

MPC model monitoring and diagnosis for non-square systems

Many industrial model predictive control applications, called non-square systems, have more variables to be controlled than manipulated variables available. At these cases, the control objectives are related to keep the controlled ones within a range, instead in reference value (setpoint). Assessing the model quality of these controllers is fundamental, however, most available MPC assessment methods are setpoint dependent, providing misleading results when these are unavailable. The methods proposed by Botelho et al. (2015, 2016a, 2016b) allow the model assessment of linear MPCs independently from the setpoints. Even though such methodologies have this advantage, there is not a procedure to assess this kind of controller. Therefore, this paper presents a guideline to apply Botelho et al. (2015, 2016a, 2016b) methods in non-square MPCs. The Shell Heavy Oil Process is used as a case study. The results demonstrate that the procedure is capable of estimate the effect of modeling problems and indicate the associated controlled variable, as well as whether the problem is due to a model-plant mismatch or unmeasured disturbance in non-square controllers.

Fast approximate learning-based multistage nonlinear model predictive control using Gaussian processes and deep neural networks

Scenario-based model predictive control (MPC) methods introduce recourse into optimal control and can thus reduce the conservativeness inherent to open-loop robust MPC. However, the uncertainty scenarios are often generated offline using worst-case uncertainty bounds quantified a priori, limiting the potential gains in control performance. This paper presents a learning-based multistage MPC (msMPC) for systems with hard-to-model dynamics and time-varying plant-model mismatch. Gaussian Processes (GP) are used to learn state- and input-dependent plant-model mismatch in real-time and accordingly adapt the scenario tree online. Due to the increased computational complexity associated with incorporating the GP predictions into the optimal control problem, the learning-based msMPC (LB-msMPC) law is approximated by a deep neural network (DNN) that is cheap-to-evaluate online and has a small memory footprint, which makes it suitable for embedded applications. In addition, we present a novel algorithm for training the DNN-based controller that uses a GP description of the plant-model mismatch to generate closed-loop simulation data, which ensures the LB-msMPC law is evaluated in regions of the state space most relevant to closed-loop operation. The proposed LB-msMPC strategy is demonstrated on a cold atmospheric plasma jet with applications in (bio)materials processing. The simulation results indicate the promise of the approximate LB-msMPC strategy for control of hard-to-model systems with fast dynamics on millisecond timescales.

Variable Cut-Off Frequency Observer-Based Positioning for Ball-Beam Systems Without Velocity and Current Feedback Considering Actuator Dynamics

This paper develops an observer-based positioning scheme for ball-beam systems considering actuator dynamics. The practical constraints are handled systematically, including the mechanical dynamical nonlinearities, mismatched load disturbances, and parameter uncertainties. This result provides contributions as follows. First, parameter-independent observers exponentially estimate the ball velocity, motor speed, and its acceleration to remove the velocity, motor speed, and current feedback. Second, the auto-tuner automatically adjusts the desired closed-loop input-output behaviors to update its cut-off frequency in the transient operations. Third, observer-based active damping injection reduces the closed-loop ball position and actuator speed dynamics to 1 by pole-zero cancellation. Finally, disturbance observers act as a dynamic compensator by estimating the disturbances from model-plant mismatches such as dynamic nonlinearities, mismatched load disturbances, and parameter variations. The experimental study verifies the applicability of the proposed technique using the Quanser Ball-Beam hardware driven by an SRV02 servomotor.

Error minimization based on multi-objective finite control set model predictive control for matrix converter in DFIG

Matrix Converter (MC) has many advantages such as capability of bi-directional energy conversion, no need for DC bus and high value filters. However, modulation methods are very difficult and require high computational effort. Therefore, Multi-objective Finite Control Set Model Predictive Control (MFCS-MPC) has been implemented to simplify the complexity of this topology. However, the weakness of this control method is using mathematical model and affected by parameter mismatches due to the external disturbances, frequency and temperature variations. In this study, past errors of rotor current are added to the cost function and the weighting factors are adjusted with the Fuzzy Decision Making (FDM) approach. Due to the combination of these two methods, a robust system is obtained that can operate even in model-plant mismatch. The proposed algorithm is implemented using the TMS320F28335 Digital Signal Processor (DSP), a 32-bit floating-point processor operating at 150 MHz. Results obtained from simulation and experimental setup are compared with the current literature studies and the performance of the proposed method is confirmed.

Dynamic modeling and offset-free predictive control of LNG tank

Due to tightened regulations on sulfur oxide (SOx) and nitrogen oxide (NOx) emissions, especially, in the ocean industry, liquefied natural gas (LNG) is becoming more important as an eco-friendly fuel source because of its extremely low SOx and NOx emissions. However, since LNG is usually stored at below its boiling temperature (-160°C) and slightly above the atmospheric pressure, the invasion of natural heat causing evaporation of LNG is inevitable even with proper insulation. This evaporated LNG called boil-off gas (BOG) accumulates inside the tank, and without proper venting, the pressure inside the tank will build up and eventually reach the maximum allowable working pressure (MAWP) of the storage tank. The violation of this threshold will lead to serious consequences. Therefore, safe control of storage tank pressure is critical to its safe operation. In this paper, we propose to use a model predictive control (MPC) system to regulate the LNG tank pressure. Firstly, a dynamic model of the LNG storage tank is developed using the film evaporation theory. Secondly, a reduced-order model is developed using the N4SID algorithm. Finally, the offset-free MPC system scheme is applied to control the tank pressure. For demonstrating the performance of the offset-free MPC system in unnatural circumstances, a fire around the tank is applied. The results show that the offset-free MPC system is able to regulate the pressure even when a fire accident occurs despite the plant-model mismatch in such conditions.

Offset-free IMC with generalized disturbance models

Integral action is an essential component for offset-free response in many feedback control systems. Standard internal model control design rules ensure an offset-free response for open-loop stable plants. In this paper a linear feedback control structure is proposed that comprises an observer using an augmented plant model, state estimate feedback and disturbance estimate feedback. This allows internal model control design principles to be applied to unstable and marginally stable plants. Conditions are given for both nominal internal stability and offset-free action even in the case of plant-model mismatch. The Youla parameterization is recovered as a limiting case with reduced-order observers. The design is illustrated on a large scale non-square model with marginally stable dynamics.