Performance Of Model Predictive Control Research Articles

Integrating Vehicle Positioning and Path Tracking Practices for an Autonomous Vehicle Prototype in Campus Environment

This paper presents the implementation of an autonomous electric vehicle (EV) project in the National Taiwan University of Science and Technology (NTUST) campus in Taiwan. The aim of this work was to integrate two important practices of realizing an autonomous vehicle in a campus environment, including vehicle positioning and path tracking. Such a project is helpful to the students to learn and practice key technologies of autonomous vehicles conveniently. Therefore, a laboratory-made EV was equipped with real-time kinematic GPS (RTK-GPS) to provide centimeter position accuracy. Furthermore, the model predictive control (MPC) was proposed to perform the path tracking capability. Nevertheless, the RTK-GPS exhibited some robust positioning concerns in practical application, such as a low update rate, signal obstruction, signal drift, and network instability. To solve this problem, a multisensory fusion approach using an unscented Kalman filter (UKF) was utilized to improve the vehicle positioning performance by further considering an inertial measurement unit (IMU) and wheel odometry. On the other hand, the model predictive control (MPC) is usually used to control autonomous EVs. However, the determination of MPC parameters is a challenging task. Hence, reinforcement learning (RL) was utilized to generalize the pre-trained datum value for the determination of MPC parameters in practice. To evaluate the performance of the RL-based MPC, software simulations using MATLAB and a laboratory-made, full-scale electric vehicle were arranged for experiments and validation. In a 199.27 m campus loop path, the estimated travel distance error was 0.82% in terms of UKF. The MPC parameters generated by RL also achieved a better tracking performance with 0.227 m RMSE in path tracking experiments, and they also achieved a better tracking performance when compared to that of human-tuned MPC parameters.

Two-tier search space optimisation technique for tuning of explicit plant-model mismatch in model predictive controller for industrial cement kiln process

Optimal control of cement kiln is demanding to ensure cement quality and minimal energy usage in cement industries. Plant-model mismatch (PMM) in the prediction model predominantly determines the Model Predictive Controller (MPC) performance. The proposed work aims to determine the optimal PMM parameters that can improve the MPC performance under various scenarios of cement kiln operations. Many parameters in a MIMO transfer function model of cement kiln make it a higher-dimensional problem. Gain and time-constant of the individual First Order Plus Time Delay Model models are considered as tunable PMM parameters. A novel two-tier optimisation algorithm has been proposed to optimise the search space and reduce PMM tuning complexity. Tier-1 uses Ant Colony Optimisation (ACO) to identify the PMM parameters using combinatorial optimisation, and Tier-2 employs a Genetic algorithm (GA) to tune the identified PMM parameters. Five control scenarios encountered during cement kiln operations, including tracking and rejection of Pulse and Gaussian disturbances, have been considered in this study. Experimental results illustrate a reduction of 32.5% of PMM parameters with the use of Tier-1. GA-tuned PMM parameters improve MPC’s transient behaviour at a reduced energy loss across all the control scenarios.

An Improved Finite-Control-Set Model Predictive Current Control for IPMSM under Model Parameter Mismatches

The control performance of the finite control set model predictive current control (FCS-MPCC) for the interior permanent magnet synchronous machine (IPMSM) depends on the accuracy of the mathematical model. A novel robust model predictive current control method based on error compensation is proposed in order to reduce the parameter sensitivity and improve the current control robustness. In this method, the equivalent parameters are obtained from the known voltage and current information at the past time and the error between the predicted current and the actual current at the present time, which is utilized in the two-step prediction process to compensate the parameter mismatch error. Finally, the optimal voltage vector is selected by the cost function. The proposed method is compared with the traditional model predictive current control method through experiments. The experimental results show the effectiveness of the proposed method.

Artificial neural network based model predictive control: Implementing achievable set‐points

AbstractThis paper addresses the problem of determining achievable set‐points for artificial neural network (ANN)‐based model predictive control (MPC) designs. In particular, this work considers a case where a first‐principles model may not be readily available for a nonlinear process, while sufficient closed‐loop data containing possibly correlated outputs is available, such that an ANN‐based model that captures the nonlinear dynamics reasonably well can be identified. The paper addresses implementation aspects with such an ANN‐based MPC design—specifically that of ensuring that achievable set‐points are prescribed to the MPC. The key idea is to perform principal component analysis (PCA) on the training data in order to recognize existing collinearity and determine the upper confidence limit of squared prediction error (SPE) statistic. An optimization problem subject to the SPE constraint is then defined to calculate the achievable set‐points, that can in turn be provided to an MPC design. The efficacy of the proposed approach is illustrated via implementations on a chemical reactor example. The results reveal the superior tracking performance of MPC using the achievable set‐points over the case where arbitrarily prescribed set‐points are used in the MPC implementations.

Symposium Title: Construction and Validation of an Event-Related Potential Platform

A model predictive control (MPC) system based on latent variables (LV) model generated by using partial least squares (PLS) method is developed. The difference in the performance of MPCs that use recursively updated LV models based on autoregressive time series modeling (with exogenous inputs - ARX) and PLS is studied. The effect of signal noise on MPC performance is also investigated for both types of models. MPC performance is evaluated by regulating the blood glucose concentration (BGC) of people with Type 1 diabetes mellitus (T1DM) in simulation studies. Signal noise in glucose concentration sensor data, delays caused by insulin absorption and action, and disturbances caused by consumption of meals make the regulation of BGC difficult. The proposed controller is evaluated with 10 in-silico adult subjects of the UVa/Padova simulator with different levels of signal noise. The results illustrate the effectiveness of the MPC based on LV model. The average time for BGC in the safe range (70-180 mg/dL) for the LV-based MPC is 83.23% compared to 79.68% for the MPC based on ARX model when intravenous BGC values are used. The average time in safe range decreases to 76.04% and 71.92%, respectively, when using the generic CGM sensor of the simulator. It is reduced further to 71.93% and 67.20% when additional noise is added to CGM readings.

Model predictive control for energy-efficient optimization of radiant ceiling cooling systems

State-of-the-art model predictive control (MPC) applications have been performed in various heating and cooling systems of buildings, such as fan coil unit systems and radiant floor heating systems. However, there is also a significant potential for improved zone air temperature control for better thermal comfort and efficient energy savings in increasingly prosperous radiant ceiling cooling systems. In this research, the physics-based model was developed by applying the building envelope configuration and material property information. The reduced-order model of the original radiant ceiling cooling system model was then simplified using the balanced truncation method for reducing computational cost and maintaining a comparative model accuracy. The model predictive control of radiant ceiling cooling systems was proposed for zone air temperature tracking, allowing the system to be more robust and adaptive to external thermal disturbances such as solar radiation and ambient temperature. The superior performance of model predictive control in terms of accurate zone air temperature tracking and energy efficiency was evaluated by a simulation compared to PID control and conventional bang-bang control in both continuous and intermittent operation. The proposed model predictive control can achieve 21%–27% and 6% energy saving efficiency, compared with PID control and conventional bang-bang control, respectively. And there is rarely any overshoot or steady-state error presence for the zone air temperature, which demonstrated the significant potential of the robust model predictive control for better thermal comfort and efficient energy savings in growing prosperous radiant ceiling cooling systems.

Bayesian optimization with reference models: A case study in MPC for HVAC central plants

We present a framework for exploiting reference models in Bayesian optimization (BO). Our approach is motivated by a model predictive control (MPC) tuning application for central heating, ventilation, and air conditioning (HVAC) plants. Evaluating the closed-loop performance of MPC by trial-and-error is time-consuming (e.g., a closed-loop simulation can involve solving thousands of optimization problems). The BO algorithm can accelerate this process by treating the functional relationship between the closed-loop performance of MPC and its tuning parameters (e.g., constraint back off terms and objective weights) as a black-box model and by systematically navigating the parameter space to maximize MPC performance. Traditional BO algorithms have been recently developed to tune controllers but such frameworks tend not to use pre-existing (prior) system information. In this work, we propose to incorporate such information in the form of reference models and we show that such models can be constructed in creative ways. Specifically, we propose to construct a reference model by evaluating the closed-loop performance of a low-complexity MPC controller. We show that the use of a reference model changes the goal of BO from learning the objective function to learning the residual function (error between the reference and the objective function), which is a much easier task. Specifically, we show that the use of a reference model can help BO to more judiciously sample the parameter estimate and more rapidly discover regions where the solution exists. This feature significantly reduces the number of function evaluations and can help avoid getting stuck in local minima. The effectiveness of our BO framework is demonstrated using a central HVAC plant study with realistic data. The reference model is built by training a kriging model based on data collected for 21 low-fidelity, closed-loop MPC simulations. Using this reference model, we show that our BO method can find the optimal constraint back-off terms within 3 high-fidelity, closed-loop simulations (total computation time of 20 h). In contrast, a traditional BO approach without a reference model requires 14 high-fidelity, closed simulations (total time of 28 h). Our approach thus reduces the computational time by 28%.

Safe Reinforcement Learning Using Robust MPC

Reinforcement Learning (RL) has recently impressed the world with stunning results in various applications. While the potential of RL is now well-established, many critical aspects still need to be tackled, including safety and stability issues. These issues, while partially neglected by the RL community, are central to the control community which has been widely investigating them. Model Predictive Control (MPC) is one of the most successful control techniques because, among others, of its ability to provide such guarantees even for uncertain constrained systems. Since MPC is an optimization-based technique, optimality has also often been claimed. Unfortunately, the performance of MPC is highly dependent on the accuracy of the model used for predictions. In this paper, we propose to combine RL and MPC in order to exploit the advantages of both and, therefore, obtain a controller which is optimal and safe. We illustrate the results with a numerical example in simulations.

Binary search tree-based explicit MPC controller design with Kalman filter for vehicular adaptive cruise system

The adaptive cruise control (ACC) system has received significant attention due to traffic safety improvement, traffic throughput increment, and energy conservation. Model Predictive Control (MPC) has been successfully applied in the control of multi-objective vehicular ACC. However, as a state-feedback policy, MPC requires full state measurement. Meanwhile, the real-time performance of MPC is intractable. This paper proposes to estimate the state value and disturbance value with an extended state Kalman filter to deal with measurement uncertainty. The Kalman filter is based on an augmented state-space model which takes the disturbance term as a new state. To improve real-time performance, this paper suggests employing an explicit MPC (EMPC) based on binary search tree to move the online computational burden of MPC to offline computation by multi-parametric quadratic programming (MPQP). An improved algorithm to solve the MPQP problem offline is proposed, which is initialized discarding the requirement of parameters range, while previous methods need. In the simulated measurement process, the extended state Kalman filter can effectively reduce noise and accurately estimate the value of state and disturbance in the car-following model. Simulations in different scenarios are performed to test the effectiveness of the proposed ACC controller. Results show that the proposed EMPC for the ACC system can improve the real-time performance of the MPC with little loss of performance. On average, the EMPC via binary search is 95.8 times faster than the MPC with the same parameters as EMPC for the studied ACC system. And it has better overall performance compared with the ACC with collision avoidance (CA-ACC) method.

Comparative Assessment of Alternative Mpc Strategies Using Real Meteorological Data and Their Enhancement for Optimal Utilization of Flexibility-Resources in Buildings

Model predictive control (MPC) method shows superiority in enhancing system performance. But its actual performance in operation is hampered by forecast uncertainties. Different methods have been proposed to mitigate the impacts of these uncertainties, such as shrinking horizon MPC (SHMPC) and stochastic MPC (SMPC). However, the year-round performance of these methods has rarely been investigated, and there is little knowledge on their relative performance, particularly in optimal utilization of flexibility-resources in buildings. In this study, the year-round performance of conventional MPC (CMPC), SHMPC and SMPC strategies when used to optimize utilization of flexibility-resources in buildings are compared using real-time optimal control (RTC) as the benchmark, and their enhancement is ultimately proposed. Forecast uncertainties are quantified based on real meteorological data. Different optimization horizon start times and shrinking intervals are tested. Results show that there is no one control strategy which is superior to the other strategies under all operating conditions. The SMPC strategy has a higher probability of achieving daily cost saving than CMPC and SHMPC strategies, but still has higher daily costs than the RTC strategy in the winter. Hybrid control strategies with proper control schemes implemented under different operating conditions are therefore recommended.

Development of a model predictive controller for an active torsional vibration damper to suppress torsional vibrations in vehicle powertrains

The pressure of exhaust emission regulations on automotive manufacturers to reduce environmental pollution and fuel consumption of internal combustion engines (ICEs) have stimulated the works on the downsizing, downspeeding, and turbo supercharging concepts which result in boosted engine torsional vibrations. Despite significant momentum in the implementation of those concepts in modern ICEs in recent decades, similar progress has not taken place in parallel at torsional vibration isolation systems. To this end, this article centers on the development and implementation of a model predictive controller (MPC) on a novel active torsional vibration damper (ATVD) in which inertia, stiffness rate, and damping rate parameters can be varied to minimize torsional vibration transmission to the vehicle powertrain. Dynamic response of the ATVD is examined using an MPC inside a closed-loop control architecture with predicted variables. The MPC structure, state-space plant model, and physical constraint definitions are composed to be utilized in prediction models at various engine operating points. The MPC performance is evaluated in a co-simulation environment using Simcenter Amesim, NX Motion, and Matlab Simulink software, and are compared with that of the fuzzy logic controller (FLC). The simulation results clearly indicate that the MPC applied to the ATVD system has certain advantages over the FLC and is able to provide satisfactory isolation of the powertrain from engine-borne torsional vibrations while satisfying the physical constraints.

ANN model adaptation algorithm based on extended Kalman filter applied to pH control using MPC

The performance of model predictive controllers (MPCs) strongly depends on the precision of the prediction model. Nonlinear systems, such as neutralization reactors, provide special challenges to MPC design. Linear prediction models may be inadequate to describe the process at all operating points. One alternative is the use of artificial neural networks (ANNs) as prediction models. ANNs are nonlinear structures that can be trained to reproduce the process behavior. Inside MPC schemes, ANNs can rapidly predict the process response to a control action. The time-consuming step for ANN training is to obtain a representative overall data set from experiments or simulation data from the studied process. In the present work, we propose to obtain this data set from computational simulations using a first principles model. However, mismatches were found between rigorous simulation and actual pH process responses. Those deviations were naturally transferred to the internal neural model, as a consequence, actual control problems were identified. Avoiding high costs of performing actual experimental runs for ANN and MPC design, we used a real-time adaptation algorithm, based on extended Kalman filter (EKF), that acts to correct the ANN prediction while process is running. The adaptive model ANN-based MPC was able to maintain the actual controlled process, in all operating conditions tested. The sum of square error of pH was reduced in 64.3%, compared to the ANN-based MPC without model adaptation. Using a Kalman filter to adapt the internal model has significantly improved the MPC performance, reducing oscillations and maintaining the controlled variable in the setpoint, even in servo regulatory situations of industrial practice. In addition, the proposed scheme has great potential for controlling highly nonlinear processes.

Advanced forecasting and disturbance modelling for model predictive control of smart energy systems

We describe a method for embedding advanced weather disturbance models in model predictive control (MPC) of energy consumption and climate management in buildings. The performance of certainty-equivalent controllers such as conventional MPC for smart energy systems depends critically on accurate disturbance forecasts. Commonly, meteorological forecasts are used to supply weather predictions. However, these are generally not well suited for short-term forecasts. We show that an advanced physical and statistical description of the disturbances can provide useful short-term disturbance forecasts. We investigate the case of controlling the indoor air temperature of a simulated building using stochastic differential equations (SDEs) and certainty-equivalent MPC using the novel short-term forecasting method. A Lamperti transformation of the data and the models is an important contribution in making this SDE-based approach work. Simulation-based studies suggest that significant improvements are available for the performance of certainty-equivalent MPC based on short-term forecasts generated by the advanced disturbance model: Electricity savings of 5%–10% while at the same time improving the indoor climate by reducing comfort violations by up to over 90%.

Model Predictive Control with Adaptive Building Model for Heating Using the Hybrid Air-Conditioning System in a Railway Station

A model predictive control (MPC) system with an adaptive building model based on thermal-electrical analogy for the hybrid air conditioning system using the radiant floor and all-air system for heating is proposed in this paper to solve the heating supply control difficulties of the railway station on Tibetan Plateau. The MPC controller applies an off-line method of updating the building model to improve the accuracy of predicting indoor conditions. The control performance of the adaptive MPC is compared with the proportional-integral-derivative (PID) control, as well as an MPC without adaptive model through simulation constructed based on a TRNSYS-MATLAB co-simulation testbed. The results show that the implementation of the adaptive MPC can improve indoor thermal comfort and reduce 22.2% energy consumption compared to the PID control. Compared to the MPC without adaptive model, the adaptive MPC achieves fewer violations of constraints and reduces energy consumption by 11.5% through periodic model updating. This study focuses on the design of a control system to maintain indoor thermal comfort and improve system efficiency. The proposed method could also be applied in other public buildings.

Direct Harmonic Current Control Scheme for Dual Three-Phase PMSM Drive System

The performance of model predictive control mainly depends on the accuracy of model and parameters, such as the back electromotive force (EMF) harmonics in dual three-phase permanent magnet synchronous motors (PMSMs). However, the back EMF harmonics would vary with the operation conditions. Thus, the parameter mismatches in the harmonic subspace would be inevitable. In this article, a direct harmonic current control scheme is proposed to provide further harmonic current suppression under parameter mismatches in the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">xy</i> subspace. First, deadbeat control concept is applied to calculate the reference voltage in the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">αβ</i> subspace. This reference voltage vector is utilized to generate a group of control sets with different voltage vectors in the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">xy</i> subspace. Then, a slide mode control scheme is provided to deal with the inaccurate parameters in the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">xy</i> subspace. The reference voltage vector in the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">xy</i> subspace is obtained with this slide mode control scheme without the remaining inductance parameters. Third, a two-step modulation method and cost function are discussed to further suppress the harmonic currents. The control sets generated by deadbeat control are optimized with the cost function. Moreover, a switching pattern with fixed switching frequency is proposed in this section. Finally, experimental results verify that proposed control scheme could further suppress the harmonic currents.

Model Predictive Control of Nonlinear System Based on GA-RBP Neural Network and Improved Gradient Descent Method

A model predictive control (MPC) method based on recursive backpropagation (RBP) neural network and genetic algorithm (GA) is proposed for a class of nonlinear systems with time delays and uncertainties. In the offline modeling stage, a multistep-ahead predictor with GA-RBP neural network is designed, where GA-BP neural network is used as a one-step prediction model and GA is employed to train the initial weights and bias of the BP neural network. The incorporation of GA into RBP can reduce the possibility of the BP neural network falling into a local optimum instead of reaching global optimization. In the online optimizing stage, a multistep-ahead GA-RBP neural network predictor and an improved gradient descent method (IGDM) are proposed to efficiently solve the online optimization problem of nonlinear MPC by minimizing a modified quadratic criterion. The designed MPC strategy can avoid information loss while linearizing the controlled system and computing the Hessian matrix and its inverse matrix. Experimental results show that the proposed approach can reduce the computational burden and improve the performance of MPC (i.e., the maximum overshoots, calculation time, rise time, and RMSE tracking error value) for the solution of nonlinear controlled systems.

Investigation of the Performance of Model Predictive Control for Induction Motor Drives

The current work presents speed, torque and flux control of an induction motor (IM) drive, founded on model predictive control (MPC). Via the MPC techniques, the motor electromagnetic torque and flux linkage are controlled as an internal loop. However, the speed is controlled as the external loop. The internal control loop is founded on finite control set FCS-MPC, and the external control founded on the torque PI controller. The performance of the MPC is tested with various conditions of the drive operation, and the outcomes approve the excellent steady-state and dynamic operation of the system in a wide range of speeds and with torque disturbance.

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.

Model Predictive Control for a Linear Parameter Varying Model of an UAV

This paper presents a Model Predictive Control (MPC) based autopilot for a fixed-wing Unmanned Aircraft Vehicle (UAV) for meteorological data sampling tasks, named Aerosonde. Aerosonde missions are featured by predetermined operating conditions, allowing the design of ad-hoc controllers for each control task by using the future knowledge of the reference signals driving the aircraft during operations. To develop the controller, the nonlinear dynamics of the vehicle has been described by a Linear Parameter-Varying (LPV) model identified from the plant data by using a subspace identification technique. The LPV model is used to design a MPC to drive the UAV. Two different Linear Parameter-Varying MPC (MPCLPV) algorithms have been proposed by introducing the previewing technique in the controller due to the a priori knowledge of full reference signals. In the design of the inner Attitude Controller (AC), a future LPV scheduling parameters estimation policy has been introduced (PF −MPCLPV) for improving the control results of the standard Previewing MPCLPV (P-MPCLPV). Furthermore, an anticipative switching approach (PS −MPCS) has been considered for the altitude External Controller (EC) to improve the control performances of the standard previewing switching MPC (P-MPCS). Both PF −MPCLPV and PS −MPCS algorithms have been compared to the P-MPCLPV and P-MPCS baseline algorithms, showing the effectiveness of proposed methods.

Prioritize effluent quality, operational costs or global warming? – Using predictive control of wastewater aeration for flexible management of objectives in WRRFs

This study presents a general model predictive control (MPC) algorithm for optimizing wastewater aeration in Water Resource Recovery Facilities (WRRF) under different management objectives. The flexibility of the MPC is demonstrated by controlling a WRRF under four management objectives, aiming at minimizing: (A) effluent concentrations, (B) electricity consumption, (C) total operations costs (sum electricity costs and discharge effluent tax) or (D) global warming potential (direct and indirect nitrous oxide emissions, and indirect from electricity production) . The MPC is tested with data from the alternating WRRF in Nørre Snede (Denmark) and from the Danish electricity grid. Results showed how the four control objectives resulted in important differences in aeration patterns and in the concentration dynamics over a day. Controls B and C showed similarities when looking at total costs, while similarities in global warming potential for controls A and D suggest that improving effluent quality also reduced greenhouse gasses emissions. The MPC flexibility in handling different objectives is shown by using a combined objective function, optimizing both cost and greenhouse emissions. This shows the trade-off between the two objectives, enabling the calculation of marginal costs and thus allowing WRRF operators to carefully evaluate prioritization of management objectives. The long-term MPC performance is evaluated over 51 days covering seasonal and inter-weekly variations. On a daily basis, control A was 9–30% cheaper on average compared to controls A, D and to the current rule-based control. Similarly, control D resulted on average in 35–43% lower greenhouse gasses daily emission compared to the other controls. Difference between control performance increased for days with greater inter-diurnal variations in electricity price or greenhouse emissions from electricity production, i.e. when MPC has greater possibilities for exploiting input variations. The flexibility of the proposed MPC can easily accommodate for additional control objectives, allowing WRRF operators to quickly adapt the plant operation to new management objectives and to face new performance requirements.