Nonlinear Model Predictive Control Design Research Articles

Modeling and nonlinear predictive control of solar thermal systems in district heating

This study presents data-driven modeling and nonlinear model predictive control of solar thermal plants in district heating, for the purpose of operation optimization. The study considers the efficient operation of a solar thermal plant in Hillerød, Denmark. A dynamic model is estimated as a system of stochastic differential equations using grey-box modeling and real-world data. The presented nonlinear model predictive controller design is based on repeated trajectory linearization and the dynamic model. Several objective designs are considered, e.g., maximizing energy or temperature. The study provides simulations for analyzing the model fitness and controller performances. The model is shown to fit the daytime operation of the plant. The designed controllers are shown to improve efficiency, increasing the transported energy up to 28%.

Design of Multi-Input Multi-Output Non-linear Model Predictive Control for Main Steam Temperature of Super Critical Boiler

Flexible operation of coal-fired power plants is becoming increasingly necessary for successful integration of large-scale renewable power generation into the power grid. The maximum ramp rate and the number of load cycles are generally limited by the thermal stress experienced by the boiler pressure parts, turbine metallurgy and creep and fatigue of critical thick-walled components Main steam temperature is a critical operating parameter that must be controlled within acceptable limits for safe operation. Main steam temperature deviation beyond acceptable limit has impact on boiler pressure parts and turbine material of construction due to creep and fatigue effect. Base load operating units do not require steep ramp rate and hence recommended ramping rates are kept low within the safe operating zone in comparison to the flexible operation of the units with wide range load change width. Thermal stresses are caused by the temperature changes inside the thick-walled components and turbine steam admission parameters. Hence, the quality of main steam temperature control plays a vital role in flexible operation of the coal fired units. Conventional cascaded PID temperature control loop architecture performs well at steady state condition within a limited variation of load change at low ramp rate but it acts slowly and performs poorly at transient operating conditions of flexible operation of the boiler turbine with wide range load variation and load cycle with high ramp rate and remains far from rated conditions. In this paper, a Multi-Input Multi-Output (MIMO) Non-linear Model Predictive Control (MPC) design for regulation of the main steam temperature of a Once-Through supercritical Boiler is proposed. The controller is based on a non-linear dynamic model which incorporates dynamics of the variables of interest. It has the capability to operate effectively across a wide load range while maintaining main steam temperature within acceptable limits. A notable advancement in this design of MPC is the incorporation of coal flow demand and feedwater flow demand as additional control inputs alongside primary and secondary spray flows. In simulation test cases, the MPC controller demonstrates satisfactory performance and computational efficiency.

An advanced observer-based nonlinear model predictive controller design for distribution networks in bushfire prone areas

An advanced observer-based nonlinear model predictive controller design for distribution networks in bushfire prone areas

A Nonlinear Discrete-Time Backstepping Model Predictive Controller Design for Active Arc Suppression Coils in Compensated Power Systems to Mitigate Powerline Bushfire Hazards

A Nonlinear Discrete-Time Backstepping Model Predictive Controller Design for Active Arc Suppression Coils in Compensated Power Systems to Mitigate Powerline Bushfire Hazards

Generalized robust MPC with zone-tracking

We propose a robust nonlinear model predictive control design with generalized zone tracking (ZMPC) in this work. The proposed ZMPC has guaranteed convergence into the target zone in the presence of bounded disturbance. The proposed approach achieves this by modifying the actual target zone such that the effect of disturbances is rejected. A control invariant set (CIS) inside the modified target zone is used as the terminal set, which ensures the closed-loop stability of the proposed controller. Closed-loop stability analysis is presented. Simulation studies based on a continuous stirred tank reactor (CSTR) are performed to validate the effectiveness of the proposed ZMPC.

Least Square Support Vector Machines Laguerre Hammerstein Model Identification and Non-linear Model Predictive Controller Design for pH Neutralization Process

The ability to describe the nonlinear process dynamics is an essential feature of the Hammerstein model that paved more research and application studies in system identification and control. Using the Hammerstein model, this study shows an alternative approach to identify and control the highly nonlinear pH neutralization process. This Hammerstein model called Laguerre Least Square Support Vector Machines (LLSSVM) models the static nonlinearity with LSSVM and the linear part with Laguerre filter. The identified LLSSVM Hammerstein model performance evaluation with Mean Squared Error (MSE) and Variance Accounted For (VAF) is better than the Linear Laguerre model. We apply the identified LLSSVM Hammerstein model to implement a Nonlinear Model Predictive Controller (NMPC) to control the pH neutralization process. Then evaluated NMPC performance in terms of Integral Squared Error (ISE), Integral Absolute Error (IAE), and Total Variation (TV) and Control Effort (CE) parameters to verify its effectiveness in set-point tracking and disturbance rejection problems. The comparison of the NMPC with the Linear Laguerre Model-based Predictive Controller (LMPC) shows better performance of the NMPC than the LMPC. Results show that the LLSSVM Hammerstein model replicates the pH neutralization process well than the Linear Laguerre model. Also, the identified LLSSVM Hammerstein model provides an efficient NMPC than the LMPC for the pH neutralization process.

Power Losses Aware Nonlinear Model Predictive Control Design for Active Cell Balancing

Power Losses Aware Nonlinear Model Predictive Control Design for Active Cell Balancing

A machine learning approach for clinker quality prediction and nonlinear model predictive control design for a rotary cement kiln

AbstractCement manufacturing is energy‐intensive (5Gj/t) and comprises a significant portion of the energy footprint of concrete systems. Incorporating modern monitoring, simulation and control systems will allow lower energy use, lower environmental impact, and lower costs of this widely used construction material. One of the goals of the CESMII roadmap project on the Smart Manufacturing of Cement included developing an analytical process model for clinker quality that includes the chemistry of the kiln feed and accounts for critical process variables. This predictive model will be used in nonlinear model predictive control system designed to significantly reduce process energy use while maintaining or improving product quality. In the cement manufacturing plant used in this study, the kiln feed (meal) is tested every 12 h and used to estimate the mineral composition of the cement kiln output (clinker) using the stoichiometry‐based Bogue's model and the expertise of the plant operators. During kiln operation, kiln output (clinker) is sampled and tested every 2 h to measure its chemical and mineral composition. The predicted and measured values of the clinker composition are used by the plant operators to adjust the kiln input stream and the production process characteristics to maintain stable operation and uniform product quality. However, the time delay between prediction and testing, along with inaccuracies inherent in the Bogue's model have made any process changes designed to minimize energy use problematic, especially in‐light of potential clinker quality issues that process changes often pose. A new analytical model that integrates quality information and process operation information has been developed from data collected from 2 years of production from an operating cement facility. To make the model fuel‐type‐independent, consumed heat energy was computed in the model instead of fuel type and amount. A Feedforward Network was trained and tailored from collected data. Many data‐based simulations were conducted to quantitatively evaluate the proposed model and the 5‐fold cross‐validation procedure was used to test the models. The resulting predictive model was shown to have a low root mean square error (MSE) with respect to the estimated clinker mineral composition compared to that using the industry standard “Bogue’ model”. The end goal of this work was to develop a single machine learning tool that allows the use of quality control data and process control variables to improve energy efficiency of the process in a continuous fashion. The proposed nonlinear model predictive control system (NMPC) can generate predicted kiln production characteristics based on manipulated variables in manner that accurately follows the target product quality values. Simulation results also show that the proposed model produced accurate predictions of kiln outputs that fell within the required constraints, while manipulating control variables within typical operational ranges.

Higher Order Modeling of Reactor Regulating System and Nonlinear Neural Model Predictive Controller Design for a Nuclear Power Generating Station

In the existing instrumentation and control system of an operating Pressurized Heavy Water Reactor (PHWR) based nuclear power plant, conventional controllers are used to control the reactor power. A new idea of Nonlinear Neural Model Predictive Controller (NNMPC) is introduced in this research work. The new 17th order nonlinear higher order model of Reactor Regulating System (RRS) is developed under different plant operating modes and various parametric conditions in Single Input Multi Output (SIMO) configuration with special emphasis on Helium Control Valve Dynamics (HCVD) and Coupled Nonlinear Iodine and Xenon Dynamics (CNIXD). The SIMO RRS model is developed based on first principle. The 17th order model is reduced to 9th order lower dynamic model using Balanced Truncation Method (BTM). The Reduced Order SIMO RRS (RO-SIMO-RRS) model is programmed, simulated and validated in SIMULINK environment. The plant Neural SIMO RRS (N-SIMO-RRS) model is developed using innovative data generated from RO-SIMO-RRS simulations. The plant neural N-SIMO-RRS model is optimized using Levenberg-Marquardt Algorithm (LMA). Using the identified N-SIMO-RRS model, the Nonlinear Neural Model Predictive Controller (NNMPC) is designed, trained, verified, validated, and finally optimized using the backtracking technique in the SIMULINK environment. The optimized results are obtained from designed closed loop RRS and found within the acceptable design limits. The performance of the proposed closed loop RRS is also tested in reference tracking mode with excellent fast tractability near the optimal target demanded power level.

A nonlinear model predictive controller design for residual current compensation inverters in rapid earth fault current limiters to mitigate powerline bushfires

This paper presents a nonlinear model predictive control scheme for residual current compensation inverters in rapid earth fault current limiters to inject appropriate current to the neutral so that the fault current is compensated in distribution networks. The proposed nonlinear model predictive controller is designed to limit the fault current within a level that powerline bushfires do not ignite due to single line-to-ground faults on power distribution systems in bushfire prone areas. The nonlinear model predictive controller is designed for a T-type residual current compensation inverter in rapid earth fault current limiters based on its dynamical model where the control objective is to inject current for compensating the fault current. The control law for the residual current compensation inverter is obtained by solving an optimal control problem while using the concept of the receding horizon control scheme. The performance of the controller is evaluated through standard software-based computer and processor-in-loop simulations where results are benchmarked against backstepping and sliding mode controllers in terms of compensating both faulty phase voltage and fault current.

Nonlinear disturbance observer-based adaptive nonlinear model predictive control design for a class of nonlinear MIMO system

Model predictive control with less prior knowledge of system uncertainty and external disturbance is a long-standing theoretical and practical problem. In this paper, a solution is presented by proposing a disturbance observer-based adaptive nonlinear model predictive control scheme for a class of nonlinear MIMO systems. Our scheme requires the state and parameterdependent state-space model to linearise the nonlinear system along the prediction horizon. To cope with the unknown system uncertainty, the multiple estimation model and the concept of second-level adaptation [Pandey, V. K., Kar, I., & Mahanta, C. (2014). Multiple models and second level adaptation for a class of nonlinear systems with nonlinear parameterisation. In Industrial and Information Systems (ICIIS), 2014 9th International Conference on (pp. 1–6). IEEE.] technique for the nonlinear system is used. To ensure the boundedness of the estimated parameter, a projection-based adaptive law [Hovakimyan, N., & Cao, C. (2010). L1 adaptive control theory: Guaranteed robustness with fast adaptation. SIAM.] is used. Using a twin-rotor MIMO system (TRMS), the effectiveness of the proposed control algorithm has been verified. Simulation and real-time results show that the proposed control algorithm performs better than the existing control algorithm in the presence of unknown external disturbance and parameter uncertainties.

Practical Nonlinear Model Predictive Controller Design for Trajectory Tracking of Unmanned Vehicles

The trajectory tracking issue of unmanned vehicles has attracted much attention recently, with the rapid development and implementation of sensing, communication, and computing technologies. This paper proposes a nonlinear model predictive controller (NMPC) for the trajectory tracking application of an unmanned vehicle (UV). First, a two-degree-of-freedom (2-DOF) kinematics model of this UV is used to derive the desirable controller with two control variables as forward velocity and yaw angle. Next, the one-step Euler method is employed to establish the nonlinear prediction model, then a nonlinear optimization objective function is formulated to minimize the tracking errors of forward velocity and yaw angle from a preset time-varying reference road. Finally, the effectiveness of the proposed NMPC scheme is assessed under two different driving scenarios via MATLAB simulations. The simulation results confirm that the proposed NMPC scheme reveals better control accuracy and computational efficiency than the standard MPC controller under two different prescribed roads. Moreover, an outdoor field test is conducted to verify the performance of the proposed NMPC scheme, and the results show that the proposed NMPC can be applied to the real vehicle and can improve the tracking accuracy and the driving stability of trajectory tracking.

Extended Kalman filter state estimation-based nonlinear explicit model predictive control design for blood glucose regulation of type 1 diabetic patient.

The computational burden of iterative online optimization-based model predictive control (MPC) process is solved by adapting off-line optimization-based nonlinear explicit model predictive control (NEMPC). In this paper, the application of NEMPC is verified to regulate blood glucose level in type 1 diabetes mellitus (T1DM) patients. The objective of glucose regulation is to avoid hyperglycemia (> 180 mg/dl) and hypoglycemia (< 50 mg/dl) by maintaining glucose level in the range of 70 to 180 mg/dl. It helps to avoid time complexity of iterative process during solution of optimization stage in MPC. In the nonlinear T1DM model, only the state dynamic of sugar is measurable with low complexity and high cost among other states of the model. Therefore, an extended Kalman filter (EKF) is used developed to estimate unavailable states. The information of the estimated states are used to develop the proposed control approach for the T1DM patients. The simulation results of the NEMPC along with EKF-based state estimator for T1DM model shows the regulation of blood glucose-level (BGL) within 70 to 180 mg/dl within 120 min. The robustness of the proposed scheme is also verified under the change in parameters and food disturbance. The control variability grid analysis (CVGA) of NEMPC for 50 numbers of virtual T1DM patients under random parametric changes and meal disturbances shows the avoidance of hypoglycemia and hyperglycemia in type 1 diabetic patients. The proposed control method is simple, robust and efficient to regulate glucose level in T1DM patients. Extended Kalman filter state estimator based nonlinear explicit model predictive control for blood glucose regulation in Type 1 diabetic patients.

Robust Nonlinear Model Predictive Control for Ship Dynamic Positioning Using Laguerre Function

This paper is devoted to the issue of computationally efficient and robust nonlinear model predictive control (NMPC) for ship dynamic positioning (DP) systems subjected to input constraints and unknown environmental disturbances. The Laguerre functions, typically applied to the linear systems, are introduced to the constrained NMPC design of the nonlinear DP system to reduce the computational burden. The unscented Kalman filter is adopted to estimate the unknown disturbances and states; thus, the disturbance estimates are utilized as the cancellation signal to achieve robust offset-free control. Simulations of the proposed Laguerre function-based NMPC scheme are implemented and compared with the performance of typical Laguerre function-based linear model predictive control (LMPC) for the DP system. Simulation results well demonstrate the effectiveness, robustness and superiority of the proposed controller.

A Nonlinear Model Predictive Control Design for Autonomous Multivehicle Merging into Platoons

Integrated control for automated vehicles in platoons with nonlinear coupled dynamics is developed in this article. A nonlinear MPC approach is used to address the multi-input multi-output (MIMO) nature of the problem, the nonlinear vehicle dynamics, and the platoon constraints. The control actions are determined by using model-based prediction in conjunction with constrained optimization. Two distinct scenarios are then simulated. The first scenario consists of the multivehicle merging into an existing platoon in a controlled environment in the absence of noise, whereas the effects of external disturbances, modeling errors, and measurement noise are simulated in the second scenario. An extended Kalman filter (EKF) is utilized to estimate the system states under the sensor and process noise effectively. The simulation results show that the proposed approach is a suitable tool to handle the nonlinearities in the vehicle dynamics, the complication of the multivehicle merging scenario, and the presence of modeling uncertainties and measurement noise.

Nonlinear Model Predictive Velocity Control of a VTOL Tiltwing UAV

This letter presents the modeling, system identification and nonlinear model predictive control (NMPC) design for longitudinal, full envelope velocity control of a small tiltwing hybrid unmanned aerial vehicle (H-UAV). A first-principles based dynamics model is derived and identified from flight data. It captures important aerodynamic effects including propeller-wing interaction and stalled airfoils, but is still simple enough for on-board online trajectory optimization. Based on this model, a high-level NMPC is formulated which optimizes throttle, tilt-rate and pitch-angle setpoints in order to track longitudinal velocity trajectories. We propose and investigate different references suitable to regularize the optimization problem, including both offline generated trims as well as preceding NMPC solutions. In simulation, we compare the NMPC with a frequently reported dynamic inversion approach for H-UAV velocity control. Finally, the NMPC is validated in flight experiments through a series of transition maneuvers, demonstrating good tracking capabilities in the full flight envelope.

Stabilizing a multicopter using an NMPC design with a relaxed terminal region

Abstract This paper highlights the benefits of a feedback linearization local controller and the associated terminal bound constraints (box-type inequalities) in an NMPC (Nonlinear Model Predictive Control) design for a multicopter system. We replace the standard invariant construction for the terminal region of the NMPC design with two sets: i) a δ-invariant set (with δ the sampling time) which constrains the trajectories to re-enter it periodically, at pre-defined moments of time; ii) a constraint admissible safe set in which the trajectories lie in the remaining time instants. We show that this alternative construction verifies the recursive feasibility and asymptotic stability. Moreover, the additional degrees of freedom and simpler construction show advantages over similar NMPC designs with standard ellipsoidal terminal region.

Throttle Control using NMPC with Soft Intake Temperature Constraint for Knock Mitigation

Abstract Knocking is an unwanted behavior that is affected by the intake manifold temperature. This paper demonstrates through simulation how nonlinear Model Predictive Control design could be used as a reference governor for the control of the throttle position, with a soft constraint on intake manifold temperature. The implementation is able to suppress the peak temperature during an acceleration by slowing down the pressure build-up. Because of the usually slow dynamics of the temperature sensors, the paper proposes an Extended Kalman Filter implementation that uses a transient detection to decide whether to rely on the sensor feedback or the model.

Comparison and Benchmarking of NMPC for Swing-Up and Side-Stepping of an Inverted Pendulum with Underlying Velocity Control

Abstract This paper presents the design and investigation of a nonlinear model predictive controller (NMPC) for an inverted pendulum with velocity input. The controller is implemented on a test-rig using the GRAMPC-Toolbox. It is shown that swing-up/ stabilisation and side-stepping can be achieved in a single controller using a suitable cost functional as well as prediction horizon. The impact of different NMPC design parameters on the achievable performance and stability properties is investigated and discussed. Finally, a comparative analysis with an alternative nonlinear control – consisting of energy-based swing-up and a tracking controller based on extended linearisation techniques and state-dependent Riccati equations (SDRE) – is carried out. The individual strength or weakness is discussed based on experimental results at a test rig.

An improved two‐loop model predictive control design for nonlinear robust reference tracking with practical advantages

SummaryIn this paper, the nonlinear robust reference tracking problem is considered and an Improved Two‐Loop Nonlinear Model Predictive Control (ITL‐NMPC) design is proposed for a pre‐controlled system with bounded uncertainties subject to input and state constraints. In the industry, this scheme leads the lower design cost and fewer implementation risks since (i) it allows the existing controller to remain unchanged without any manipulation, (ii) it does not need the open‐loop model of the pre‐controlled system, and (iii) it does not require the terminal cost and constraint definition. For the proposed ITL‐NMPC, a practical parameter tuning algorithm is introduced and its robust exponential stability, as well as recursive feasibility, are guaranteed. Simulation results are used to better illustrate the effectiveness of the proposed approach and show that the proposed method not only improves the control performance of the pre‐controlled system but also reduces the design cost while satisfying the constraints.