Model Predictive Control Tuning Research Articles

Spider Monkey Metaheuristic Tuning of Model Predictive Control with Perched Landing Stabilities for Novel Auxetic Landing Foot in Drones

The study focuses on improving drone landing gear dynamics through an innovative auxetic foot design, leveraging Spider Monkey Optimization for Model Predictive Control adjustment, facilitated by an Arduino-MATLAB interface. The auxetic foot design incorporates materials with a negative Poisson ratio, which allows the foot to expand and enhance energy absorption during landings. This design improves stability and safety during the perched landing process. The SMO-MPC approach is used to optimise the control of the perched landing gear. SMO, inspired by spider monkey search behaviour, optimises auxetic foot control input sequences with the limits of rotational displacement (theta = 30 deg to -30 deg) on the prediction horizon to improve landing gear performance. The real-time implementation of SMO-MPC is achieved through an Arduino-MATLAB interface on quadcopter drone. A comparative analysis is conducted to evaluate the benefits of SMO-MPC compared to conventional MPC methods. The results show that the SMO-MPC approach with auxetic foot design surpasses conventional MPC methods in terms of landing performance with 14.6 % improvement in damping force control and control of aerodynamic stability with pitch of 34.16 %, yaw of 16.87 %, and roll of 31.74 %.

What Is the Best Way to Optimally Parameterize the MPC Cost Function for Vehicle Guidance?

Model predictive control (MPC) is a promising approach to the lateral and longitudinal control of autonomous vehicles. However, the parameterization of the MPC with respect to high-level requirements such as passenger comfort, as well as lateral and longitudinal tracking, is challenging. Numerous tuning parameters and conflicting requirements need to be considered. In this paper, we formulate the MPC tuning task as a multi-objective optimization problem. Its solution is demanding for two reasons: First, MPC-parameterizations are evaluated in a computationally expensive simulation environment. As a result, the optimization algorithm needs to be as sample-efficient as possible. Second, for some poor parameterizations, the simulation cannot be completed; therefore, useful objective function values are not available (for instance, learning with crash constraints). In this work, we compare the sample efficiency of multi-objective particle swarm optimization (MOPSO), a genetic algorithm (NSGA-II), and multiple versions of Bayesian optimization (BO). We extend BO by introducing an adaptive batch size to limit the computational overhead. In addition, we devise a method to deal with crash constraints. The results show that BO works best for a small budget, NSGA-II is best for medium budgets, and none of the evaluated optimizers are superior to random search for large budgets. Both proposed BO extensions are, therefore, shown to be beneficial.

Optimal tuning of model predictive controllers for organic Rankine cycle systems recovering waste heat from heavy-duty vehicles

The organic Rankine cycle power system is an emerging technology, which is able to recover the waste heat from the diesel engine of heavy-duty trucks and thus increase the overall engine efficiency. One of the major technical challenges for the integration of the organic Rankine cycle unit on-board trucks are the broad and rapid fluctuations of the available waste heat, caused by the unsteady driving conditions of the truck. Model predictive control has shown to be a powerful tool to ensure safe operation and optimal performance of the organic Rankine cycle unit on-board trucks. This paper presents a novel systematic method for the tuning of model predictive controllers based on a multi-objective optimization routine using a fourth-order reduced linear model. The objectives of the optimization are the settling time due to a step change of the exhaust gas mass flow rate and the cumulative controller effort due to measurement noise. The results suggest that a trade-off exists between the two objectives. Among the controller design parameters, the input rate weight has the largest influence on the controller performance. Interestingly, the simplified optimization procedure based on the reduced-order linear model of the organic Rankine cycle unit can provide key information about the controller performance based on a more complex nonlinear model of the organic Rankine cycle unit when subjected to a realistic waste heat profile. The results indicate that the settling time due to a step change of the exhaust gas mass flow rate is a good indicator of the absolute mean square tracking error over the profile, and it should not exceed 15 s for an absolute mean square tracking error below 2 K. On the other hand, the cumulative controller effort due to measurement noise is strongly correlated to the cumulative controller effort over the profile, and it should stay below 0.5 %/s for a cumulative controller effort over the whole profile below 2 %/s. The presented method is a powerful tool to help the control designer to find the optimal design parameters of model predictive controllers in a systematic way, in contrast to the time-consuming, experience-based trial and error methods.

SMGO-[formula omitted]: Balancing caution and reward in global optimization with black-box constraints

In numerous applications across all science and engineering areas, there are optimization problems where both the objective function and the constraints have no closed-form expression or are too complex to be managed analytically, so that they can only be evaluated through experiments. To address such issues, we design a global optimization technique for problems with black-box objective and constraints. Assuming Lipschitz continuity of the cost and constraint functions, a Set Membership framework is adopted to build a surrogate model of the optimization program, that is used for exploitation and exploration routines. The resulting algorithm, named Set Membership Global Optimization with black-box constraints (SMGO-Δ), features one tunable risk parameter, which the user can intuitively adjust to trade-off safety, exploitation, and exploration. The theoretical properties of the algorithm are derived, and the optimization performance is compared with representative techniques from the literature in several benchmarks. An extension to uncertain cost/constraint function outcomes is presented, too, as well as computational aspects. Lastly, the approach is tested and compared with constrained Bayesian optimization in a case study pertaining to model predictive control tuning for a servomechanism with disturbances and plant uncertainties, addressing practically-motivated task-level constraints.

An efficient bounded-variable nonlinear least-squares algorithm for embedded MPC

This paper presents a novel approach to solve linear and nonlinear model predictive control (MPC) problems that requires small memory footprint and throughput and is particularly suitable when the model and/or controller parameters change at runtime. The contributions of the paper include: (i) a formulation of the nonlinear MPC problem as a bounded-variable nonlinear least-squares (BVNLS) problem, demonstrating that the use of an appropriate solver can outperform industry-standard solvers; (ii) an easily-implementable library-free BVNLS solver with a novel proof of global convergence; (iii) a matrix-free method for computing the products of vectors and Jacobians, required by BVNLS; (iv) an efficient method for updating sparse QR factors when using active-set methods to solve sparse BVNLS problems. Thanks to explicitly parameterizing the optimization algorithm in terms of the model and MPC tuning parameters, the resulting approach is inherently and immediately adaptive to any changes in the MPC formulation. The same algorithmic framework can cope with linear, nonlinear, and adaptive MPC variants based on a broad class of prediction models and sum-of-squares cost functions.

Reinforcement learning for online adaptation of model predictive controllers: Application to a selective catalytic reduction unit

This work presents a novel application of reinforcement learning (RL) for online dynamic tuning of model predictive controllers (MPC). Applying a state-action-reward-state-action (SARSA) algorithm for temporal difference learning with a control-specific reward function improves the error tracking performance of a standard MPC formulation. The proposed RL approach is also readily adaptable to other MPCs, or entirely different control approaches. Practical details for the implementation of the RL-MPC algorithm are also presented. The proposed algorithm is applied to a case study of controlling nitrogen oxide (NOx) emissions in an industrial selective catalytic reduction (SCR) unit, a control problem characterized by significant nonlinearity and time delay. Along with an RL-MPC formulation for NOx control, another MPC is proposed to mitigate ammonia slip and decrease ammonia consumption in the SCR. Results showing the efficacy of the RL-MPC for NOx control through learning and implementation on the nonlinear SCR dynamic model are presented.

Tuning of Model Predictive Controllers Based on Hybrid Optimization

A tuning procedure for a model predictive controller (MPC) is presented for multi-input multi-output systems. The approach consists of two steps based on a hybrid method: the goal attainment method and a variable neighborhood search. In the first step, the weights of the MPC objective function are obtained, minimizing the square error between the closed-loop response of the internal controller model and a predefined desired reference trajectory. In the second step, the integer variables of the problem (prediction and control horizons) are obtained, minimizing the square error between the closed-loop response and an optimal trajectory, aiming a controller with low computational cost and good performance. The proposed method was tested in two benchmark processes using different MPC formulations, showing satisfactory results.

Model Predictive Control-Based Reinforcement Learning Using Expected Sarsa

Recent studies have shown the potential of Reinforcement Learning (RL) algorithms in tuning the parameters of Model Predictive Controllers (MPC), including the weights of the cost function and unknown parameters of the MPC model. However, a framework for easy and straightforward implementation that allows training in just a few episodes and overcoming the need for imposing extra constraints as required by state-of-the-art methods, is still missing. In this study, we present two implementations to achieve these goals. In the first approach, a nonlinear MPC plays the role of a function approximator for an Expected Sarsa RL algorithm. In the second approach, only the MPC cost function is considered as the function approximator, while the unknown parameters of the MPC model are updated based on more classical system identification. In order to evaluate the performance of the proposed algorithms, first numerical simulations are performed on a coupled tanks system. Then, both algorithms are applied to the real system and their closed-loop performance and convergence speed are compared with each other. The results indicate that the proposed algorithms allow tuning of MPCs over very few episodes. Finally, also the disturbance rejection ability of the proposed methods is demonstrated.

Can Deep Models Help a Robot to Tune Its Controller? A Step Closer to Self-Tuning Model Predictive Controllers

Motivated by the difficulty roboticists experience while tuning model predictive controllers (MPCs), we present an automated weight set tuning framework in this work. The enticing feature of the proposed methodology is the active exploration approach that adopts the exploration–exploitation concept at its core. Essentially, it extends the trial-and-error method by benefiting from the retrospective knowledge gained in previous trials, thereby resulting in a faster tuning procedure. Moreover, the tuning framework adopts a deep neural network (DNN)-based robot model to conduct the trials during the simulation tuning phase. Thanks to its high fidelity dynamics representation, a seamless sim-to-real transition is demonstrated. We compare the proposed approach with the customary manual tuning procedure through a user study wherein the users inadvertently apply various tuning methodologies based on their progressive experience with the robot. The results manifest that the proposed methodology provides a safe and time-saving framework over the manual tuning of MPC by resulting in flight-worthy weights in less than half the time. Moreover, this is the first work that presents a complete tuning framework extending from robot modeling to directly obtaining the flight-worthy weight sets to the best of the authors’ knowledge.

An Improved Approach for Robust MPC Tuning Based on Machine Learning

A robust tuning method based on an artificial neural network for model predictive control (MPC) of industrial systems with parametric uncertainties is put forward in this work. Firstly, an efficient approach to characterize the mapping relationship between the controller parameters and the robust performance indices is established. As there are normally multiple conflicted robust performance indices to be considered in MPC tuning, the neural network is further used to fuse the indices to produce a simple label representing the acceptable level of the robust performance. Finally, an automated algorithm is proposed to tune the MPC parameters for the considered uncertain system to achieve the desired robust performance. In addition, the regulation of the pH value of the sewage treatment system is used to verify the effectiveness of the robust tuning algorithm which is described in this paper.

Pole‐zero assignment in model predictive control, using analytical tuning approach

AbstractThis paper proposes a new analytical tuning strategy for Model Predictive Control (MPC). In the proposed approach, MPC tuning problem is restated as a pole‐zero placement problem. New analytically tuning equations are given and a deep study on the places of poles and zeros of the closed‐loop system is performed. It is known that, appropriate zero placement can improve the robust stability of the closed‐loop system, so the proposed tuning strategy can be applicable. In MPC tuning strategies, analytical equations are very interesting and useful. To achieve analytical equations, First Order plus Dead Time models are used in this work. These models with adequate accuracy can describe many industrial processes. With simulation studies, the effectiveness of the proposed pole‐zero assignment strategy is indicated.

A Data-Driven Automatic Tuning Method for MPC under Uncertainty using Constrained Bayesian Optimization

Abstract The closed-loop performance of model predictive controllers (MPCs) is highly dependent on the choice of prediction models, controller formulation, and tuning parameters. However, prediction models are typically optimized for prediction accuracy, instead of performance, and MPC tuning is typically done manually to satisfy (probabilistic) constraints. In this work, we demonstrate a general approach for automating the tuning of MPC under uncertainty. In particular, we formulate the automated tuning problem as a constrained black-box optimization problem that can be tackled with derivative-free optimization. We rely on a constrained variant of Bayesian optimization to solve the MPC tuning problem that can directly handle noisy and expensive-to-evaluate functions. The benefits of the proposed automated tuning approach are demonstrated on a benchmark continuously stirred tank reactor case study.

Neural networks-based model predictive control for precision motion tracking of a micropositioning system

Micropositioning systems are widely employed in industrial applications. Nonminimum-phase (NMP) is a normal phenomenon in micropositioning system, which leads to a great challenge for control system design. Model predictive control (MPC) is effective in handling the NMP problem. However, the parameter tuning of MPC is quite complicated and time-consuming using traditional methods for motion tracking control implementation. In this paper, an efficient neural networks (NN) model is established to optimize the MPC controller parameters including the prediction horizon, control horizon, and weighting factor. With the developed NN model, the motion tracking process of the micropositioning system is more intelligent and adaptive. The effectiveness of the presented novel NN-MPC control strategy has been verified by conducting extensive simulation studies. Furthermore, the results demonstrate that the NN-MPC scheme has good robustness under model parameter variation and noise condition.

Tuning Guidelines for Model-Predictive Control

This paper reviews available tuning guidelines for model-predictive control (MPC) from theoretical and practical perspectives. Its primary focus is on the guidelines introduced since the publication of our previous review of MPC tuning guidelines in this same journal in 2010. Since then, new guidelines based on approaches such as pole placement and multiobjective optimization have been proposed, and more autotuning methods have been introduced. This review covers different implementations of MPC such as dynamic matrix control, generalized predictive control, and state-space-model predictive control that requires Kalman filter tuning. The closed-loop performances of a distillation column and the Shell fractionator under model-predictive controllers tuned using four different tuning guidelines are compared through numerical simulations.

Analytical Tuning Method of MPC Controllers for MIMO First-Order Plus Fractional Dead Time Systems

An analytical model predictive control (MPC) tuning method for multivariable first-order plus fractional dead time systems is presented in this paper. First, the decoupling condition of the closed-loop system is derived, based on which the considered multivariable MPC tuning problem is simplified to a pole placement problem. Given such a simplification, an analytical tuning method guaranteeing the closed-loop stability as well as pre-specified time-domain performance is developed. Finally, simulation examples are provided to show the effectiveness of the proposed method.

Comparison of model predictive controller and optimized min-max algorithm for turbofan engine fuel control

Min-max selector structure is traditionally used as the industrial control architecture of commercial turbofan engines. However, recent studies indicate that this structure with linear compensators suffers from lack of safety guarantee in fast demands. On the other hand, model predictive control (MPC) technique, which incorporates input/output constraints in its optimization process, has the potential to fulfill the control requirements of an aircraft engine. In this paper, a practical approach is performed for design and optimization of the turbofan engine controller through a comparative study where all control modes and requirements have been taken into account simultaneously. For this purpose, a thermodynamic nonlinear model is firstly developed for the turbofan engine. The linear regulators of minmax structure are then optimized via genetic algorithm (GA). The MPC technique is formulated based on the proper discrete-time linearized state-space models at desired operating points with real-time optimization, in which the MPC tuning horizons are obtained through GA optimization procedure. The both controllers are implemented on appropriate hardware taking the real-time aspects into account. Finally, a hardware in the loop (HIL) platform is developed for the turbofan engine electronic control unit (ECU) testing. The software and HIL simulation results confirm that MPC improves the response time of the system in comparison with min-max algorithm and guarantees the engine limit protection. This study demonstrates competitive advantages of MPC in terms of limit protection assurance and fast response, despite more computational burden.

Model Predictive Control Tuning by Inverse Matching for a Wave Energy Converter

This paper investigates the application of a method to find the cost function or the weight matrices to be used in model predictive control (MPC) such that the MPC has the same performance as a predesigned linear controller in state-feedback form when constraints are not active. This is potentially useful when a successful linear controller already exists and it is necessary to incorporate the constraint-handling capabilities of MPC. This is the case for a wave energy converter (WEC), where the maximum power transfer law is well-understood. In addition to solutions based on numerical optimization, a simple analytical solution is also derived for cases with a short prediction horizon. These methods are applied for the control of an empirically-based WEC model. The results show that the MPC can be successfully tuned to follow an existing linear control law and to comply with both input and state constraints, such as actuator force and actuator stroke.

Optimization of Robust Model Predictive Controllers for Second-Order Biological Processes Using Markov Chain Monte Carlo Techniques

For biological fermentation processes in vaccine manufacturing, the development of a robust controller is essential to manage uncertainty in the process model and external disturbances in the control setup. A possible control strategy for this purpose is to use model predictive control (MPC), which utilizes a process model to compute a sequence of control moves via a receding horizon approach. To determine each control move, an MPC controller solves an optimization problem which can be modified to a min–max problem in order to achieve robustness. Extensive work has been undertaken to develop and test the min–max approach to obtain robust MPC; however, there is a paucity of control literature that has focused on the offline optimization of MPC control parameters (e.g., MPC horizons, control weights) to achieve robustness. To address this issue, a model predictive controller for a second-order process model representing a microbial fermentation process is developed. Uncertainty is simulated by generating 500 mismatched process models based on observed experimental data. The developed MPC controller is then applied to these process models, resulting in 500 scenarios of plant and nominal model mismatch, from which the average control performance and variation in control performance are computed. Markov Chain Monte Carlo (MCMC) techniques are successfully used to find the optimal settings that maximize control performance and minimize variation in control performance in response to step changes in both the set-point and the input disturbance. This novel approach may serve as a foundation for future MPC tuning studies which seek to determine the optimal combination of MPC settings that result in robust control.

Model Predictive Control and energy optimisation in residential building with electric underfloor heating system

This work is concerned with modelling, Model Predictive Control (MPC) and on-line energy optimisation of a residential building in which an underfloor heating system based on electric heating foils is used. At first, the first-principle model is developed to determine air temperature inside the building. Low-order linear models for MPC are found. Tuning of MPC is discussed, both set-point change and disturbance compensation cases are discussed. Next, two control system structures are considered: MPC with a constant temperature set-point and MPC cooperating with a set-point optimiser which repeatedly calculates on-line the set-point in order to minimise the amount of energy used. Effectiveness of these structures is validated in simulations using a real scenario of outdoor temperature changes. In the first structure a natural method to reduce energy used is to slightly reduce the temperature set-point, e.g. reduction of the set-point from 21∘C to 18.5∘C leads to reducing the energy usage by approx. 1430 KWh during the heating season. Introduction of the set-point optimiser makes it possible to further reduce energy used by approx. 300 KWh annually. The presented solution is computationally efficient since in MPC and set-point optimisation the classical quadratic optimisation method is used on-line.

MPC Inspired Dynamical Output Feedback and Adaptive Feedforward Control Applied to Piezo-Actuated Positioning Systems

It has been shown that the closed-loop transfer function representation of the unconstrained model predictive control (MPC) for single input single output systems is similar to a two-degree-of-freedom controller, which is capable of improving the tracking performance of positioning systems. Conventionally, the optimal parameters of the above-mentioned transfer function are result of a quite complicated MPC tuning. This paper proposes a new approach to obtain the parameters directly instead, where the input/output constraints are not considered. The method combines conventional feedback and adaptive feedforward techniques to minimize the tracking error as well as mitigate the influence of the load disturbance. Experiments on an ultra precision positioning system actuated by piezoelectric actuator show that the proposed method achieves much better tracking performance over a well-tuned conventional MPC.