Model Predictive Control Solution Research Articles

Real-Time Co-optimization of Gear Shifting and Engine Torque for Predictive Cruise Control of Heavy-Duty Trucks

Fuel consumption is one of the main concerns for heavy-duty trucks. Predictive cruise control (PCC) provides an intriguing opportunity to reduce fuel consumption by using the upcoming road information. In this study, a real-time implementable PCC, which simultaneously optimizes engine torque and gear shifting, is proposed for heavy-duty trucks. To minimize fuel consumption, the problem of the PCC is formulated as a nonlinear model predictive control (MPC), in which the upcoming road elevation information is used. Finding the solution of the nonlinear MPC is time consuming; thus, a real-time implementable solver is developed based on Pontryagin’s maximum principle and indirect shooting method. Dynamic programming (DP) algorithm, as a global optimization algorithm, is used as a performance benchmark for the proposed solver. Simulation, hardware-in-the-loop and real-truck experiments are conducted to verify the performance of the proposed controller. The results demonstrate that the MPC-based solution performs nearly as well as the DP-based solution, with less than 1% deviation for testing roads. Moreover, the proposed co-optimization controller is implementable in a real-truck, and the proposed MPC-based PCC algorithm achieves a fuel-saving rate of 7.9% without compromising the truck’s travel time.

Explicit flatness-based MPC design for indoor nano-quadcopter position tracking

Due to the nonlinearities and operational constraints of quadcopters, Model Predictive Control (MPC) encounters the requirement of high computational power. This problem may prove impractical, especially for hardware-limited setups. By removing the need for online solvers, Explicit MPC (ExMPC) stands out as a strong candidate. Yet, the formulation was usually hindered by the system's nonlinearity and dimensionality. In this paper, we propose an ExMPC solution for quadcopter position stabilisation. With the former issue, the system is exactly linearised into a concatenation of three double integrators. For the latter, with a suitable characterisation of the new convoluted constraints, the stabilising ExMPC can be computed for each double integrator separately. The controller is validated via simulations and experiments on a nanodrone platform. The proposed scheme provides similar performance and theoretical guarantees to the up-to-date nonlinear MPC solutions but with notably less computational effort, allowing scalability in a centralised manner.

Stochastic Control of Battery Energy Storage System with Hybrid Dynamics

This paper addresses the control of load demand and power in a battery energy storage system (BESS) with Boolean-type constraints. It employs model predictive control (MPC) tailored for such systems. However, conventional MPC encounters computational challenges in practical applications, including battery storage control, and requires dedicated, mostly licensed solvers. To mitigate this, a solver-free yet efficient, suboptimal method is proposed. This approach involves generating randomized control sequences and assessing their feasibility to ensure adherence to constraints. The sequence with the best performance index is then selected, prioritizing feasibility and safety over optimality. Although this chosen sequence may not match the exact MPC solution in terms of optimality, it guarantees safe operation. The optimal control problem for the BESS is outlined, encompassing constraints on the state of charge, power limits, and charge/discharge modes. Three distinct scenarios evaluate the proposed method. The first prioritizes minimizing computational time, yielding a feasible solution significantly faster than the optimal approach. The second scenario strikes a balance between computational efficiency and suboptimality. The third scenario aims to minimize suboptimality while accepting longer computation times. This method’s adaptability to the user’s requirements in various scenarios and solver-free evaluation underscores its potential advantages in environments marked by stringent computational demands, a characteristic often found in BESS control applications.

Data-Driven Self-Triggered Control via Trajectory Prediction

Self-triggered control, a well-documented technique for reducing the communication overhead while ensuring desired system performance, is gaining increasing popularity. However, a majority of existing self-triggered control methods require explicit system models. An end-to-end control paradigm known as data-driven control designs control laws directly from data and offers a competing alternative to the routine system identification-then-control strategy. In this context, the present paper puts forth data-driven self-triggered control schemes for unknown linear systems using input-output data collected offline. Specifically, a data-driven model predictive control (MPC) scheme is proposed, which computes a sequence of control inputs while generating a predicted system trajectory. In addition, a data-driven self-triggering mechanism is designed, which determines the next triggering time using the solution of the data-driven MPC and the newly collected measurements. Finally, both feasibility and stability are established for the proposed self-triggered controller, which are validated using a numerical example.

Rotary Kiln Temperature Control Under Multiple Operating Conditions: an Error-Triggered Adaptive Model Predictive Control Solution

The temperature of rotary kiln, as one of the essential equipment in zinc smelting process, determines the product quality and resource utilization. However, since rotary kiln is a large-scale and highly coupled system, there are plenty of variables affecting the rotary kiln temperature, bringing too much redundant information to describe rotary kiln dynamics. In addition, due to the variations in raw materials, production load, and market demand, there exist various operation conditions, making it difficult to achieve stability control of the rotary kiln temperature with traditional control methods. To solve these problems, an error-triggered adaptive model predictive control (ET-AMPC) is proposed in this article. Specifically, since rotary kiln temperature is hard to regulate due to redundancy among variables and strong nonlinearity, an orthogonal maximum mutual information coefficient feature selection (OMICFS) method is first proposed to determine vital variables affecting temperature most. Then, aiming at the problem of changing operating conditions of rotary kilns, an ET-AMPC method is proposed, which can precisely adapt to different operating conditions and achieve stability control. Finally, experiments on a numerical simulation case and an industrial rotary kiln show the strength and reliability of the proposed method, which reduces 10%–20% trajectory tracking error in the period of operating condition changing and improves the control accuracy effectively.

Novel model predictive control-based motion cueing algorithm for compensating centrifugal acceleration in KUKA robocoaster-based driving simulators.

The washout motion cueing algorithm (MCA) is a critical element in driving simulators, designed to faithfully reproduce precise motion cues while minimizing false cues during simulation processes, particularly deceptive translational and rotational cues. To enhance motion sensation accuracy and optimize the use of available workspace, model predictive control (MPC) has been employed to develop innovative motion cueing algorithms. While most MCAs have been tailored for the Steward motion platform, there has been a recent adoption of the motion platform based on KUKA Robocoaster as an economical option for driving simulators. However, leveraging the full potential of the KUKA Robocoaster requires trajectory conversion of the motion base. Thus, this research proposes a novel MCA specifically designed for the KUKA Robocoaster-based motion platform, utilizing large planar circular motion to simulate lateral movement for drivers. Nonetheless, circular motion introduces disruptive centrifugal forces, which can be mitigated through proper pitch-tilted angles. The novel MPC generates simulated motion that accurately follows the lateral specific force target and effectively maintains the roll angular velocity below its threshold value. Additionally, it compensates for disturbing centrifugal acceleration by implementing pitch rotational motion, ensuring the pitch angular velocity remains below its threshold. Simulation tasks conducted on the motion platform, focusing solely on lateral acceleration, demonstrate the successful elimination of false motion cues in both the roll/sway and pitch/surge channels. The proposed innovative MPC solution offers an original approach to motion cueing algorithms in KUKA Robocoaster-based driving simulators. It enables the exploitation of the KUKA Robocoaster platform's capabilities while delivering accurate and immersive motion cues to drivers during simulation experiences.

Lattice piecewise affine approximation of explicit nonlinear model predictive control with application to trajectory tracking of mobile robot

AbstractTo promote the widespread use of mobile robots in diverse fields, the performance of trajectory tracking must be ensured. To address the constraints and nonlinear features associated with mobile robot systems, nonlinear model predictive control (MPC) is applied to realize trajectory tracking of mobile robots. Specifically, to alleviate the online computational complexity of nonlinear MPC, this paper devises a lattice piecewise affine (PWA) approximation method that can approximate both the nonlinear system and control law of explicit nonlinear MPC. The kinematic model of the mobile robot is successively linearized along the trajectory to obtain a linear time‐varying description of the system, which is then expressed using a lattice PWA model. Subsequently, the nonlinear MPC problem can be transformed into a series of linear MPC problems. Furthermore, to reduce the complexity of online calculation of multiple linear MPC problems, the optimal solution of the linear MPCs is approximated by using the lattice PWA models. That is, for different sampling states, the optimal control inputs are obtained offline, and lattice PWA approximations are constructed for the state control pairs. Simulations are performed to evaluate the performance of the method in comparison with the state‐of‐the‐art methods, and the results show that the method has a higher online computing speed and can decrease the offline computing time without significantly increasing the tracking error.

Automatic decomposition of large-scale industrial processes for distributed MPC on the Shell–Yokogawa Platform for Advanced Control and Estimation (PACE)

The kernel of industrial advanced process control (APC) lies in the formulation and solution of model predictive control (MPC) problems, which specify the controller moves according to the solution of an optimal control problem at each sampling time. A significant challenge is the online computation for large-scale industrial systems. As the state-of-the-art APC technology, the Shell–Yokogawa Platform for Advanced Control and Estimation (PACE) has adopted a systematic framework of handling dynamic optimization of large-scale systems, where an automatic decomposition procedure generates subsystems for distributed MPC. The decomposition is implemented on network representations of the MPC models that capture interactions among process variables, with community detection used to maximize the statistical significance of the subnetworks with preferred internal interconnections. This paper introduces the fundamentals of such a decomposition approach and this functionality in PACE, followed by a case study on a crude distillation process to showcase its industrial application.

Deep learning-based model predictive control for real-time supply chain optimization

This paper presents a deep learning-based model predictive control (MPC) method for operational supply chain optimization in real time. The method follows an offline-online procedure. In the offline phase, the state-space model of a supply chain system is developed and the MPC problem for supply chain operation is formulated. Then, the MPC problem is solved for a set of initial states to obtain the corresponding optimal inputs. A deep neural network (DNN) is built and trained by using the optimal state-input pairs as training data to approximate the optimal MPC law. In the online phase, the DNN controller is employed to provide real-time decisions. In this paper, the MPC problem for supply chain operation is formulated as a mixed-integer linear program. A deep learning-based MPC method is proposed to accommodate time delays in the system. Moreover, a heuristic method is proposed for feasibility recovery with the binary decision variables taken into account. The training set for the DNN controller contains two subsets, one formed from MPC solutions corresponding to random initial states, and the other formed from optimal state-input pairs in closed-loop simulations. The deep learning-based MPC is validated via two case studies through closed-loop simulation. The first case study involves a linear MPC, and the second case study involves a more complicated mixed-integer linear MPC. Results show that deep learning-based MPC can achieve a high accuracy in approximating the MPC decisions and a significant reduction in the online computation time. Compared with MPC, the average performance loss of using deep learning-based MPC in the two cases is 0.43% and 1.8%, respectively.

Predictive Position Control With System Constraints for PMSM Drives Based on Geometric Optimization

The system constraints (current, speed and voltage limitations) are essential for the safety control of predictive position control (PPC) method. However, online solution of model predictive control (MPC) with complex system constraints is still a challenge. In this paper, a novel discrete-time model predictive position control (DMPPC) strategy for surface permanent magnet synchronous motor (SPMSM) drive is proposed, the current, speed and position are regulated simultaneously. The optimization model of the position control system considering system constraints is formulated, the current, speed and voltage constraints are analyzed and transformed into the incremental voltage constraints. To reduce the calculation burden, a simplified method based on the geometric boundaries and cost function is proposed to solve the optimization problem, complex iterative calculations are avoided, the system constraints are well limited and less calculation time can be achieved. Finally, the proposed DMPPC method is experimentally verified and compared with a traditional iterative method and a cascade predictive position control (CPPC) method.

Practical deadbeat MPC design via controller matching with applications in power electronics

Several applications, including power electronics and electrical machines, require a fast system response, which is typically achieved via deadbeat control. Hence, there has been an interest in developing model predictive control (MPC) algorithms with deadbeat control properties, i.e., finite-time convergence to a set-point, for power electronics applications. In this paper, we design a practical deadbeat MPC via controller matching. We make use of an existing result for tuning the weight matrices of the MPC cost function such that the corresponding unconstrained MPC solution matches a desired deadbeat controller. This approach allows for a positive definite input weight matrix and provides stability and recursive feasibility guarantees for the resulting MPC controller. We additionally propose a vertex relaxation of the matching problem, which reduces conservatism, and a method for enlarging the terminal set of the deadbeat MPC controller. Three benchmark examples from the power electronics field are used to show the effectiveness of the proposed MPC design.

Data-driven modeling and stability control for industrial zinc roaster and its edge controller implementation

As large-scale industrial equipment, the operation stability control of the zinc roaster can improve the roasting efficiency and ensure industrial safety. In the industrial field, the roaster temperature is generally controlled manually, but automatic control is an important way to obtain real-time, accuracy, and safety of operation performance. However, existing control methods highly depend on manual experience and knowledge, which decreases their robustness and accuracy. In addition, the complex control algorithm can hardly meet the real-time requirement on the premise of pursuing accuracy. In order to address these puzzles, a data-driven explicit model predictive control solution is proposed in this paper. Specifically, the canonical correlation analysis method is introduced to extract the key controllable variables from the complex and coupled observer variables of the industrial field roaster. Then, the subspace identification method is proposed to obtain the system model with a balance between model complexity and fitting accuracy. Finally, an explicit model predictive control is introduced to simplify the calculation process of online control and simultaneously ensure the real-time stability control of the roaster. The hardware platform deployment experiment is presented to verify the feasibility and real-time performance of the proposed control scheme.

Enhancing sustainability of acid gas treatment in a Waste-to-Energy plant via Model Predictive Control

The municipal solid waste fed to waste-to-energy (WtE) plants produces acid flue gas with a wide and volatile range of composition, a scenario which implies significant process disturbances for traditional control schemes. In this paper, a two-stage dry sorbent system in an Italian treatment plant is used as a case study. The focus was on the first stage of abatement, where calcium hydroxide is injected into a reactor to reduce the hydrogen chloride (HCl) content in the acid flue gas. A state-space model, identified and tested in a previous work, was here implemented in a model predictive control (MPC) structure. In particular, four different MPC solutions were derived and tested on routine data in order to increase the process performance. Three suitable key performance indicators were used to assess the quantitative comparison between the proposed advanced control approaches and the simulated architecture of the one implemented in the WtE plant. The analysis evidenced the benefits obtained by MPC structures with respect to the current sub-optimal control architecture. Controller tuning and the possibility to include the online HCl concentration in the model have been also tested to highlight the best solution. Overall, the advanced controllers allowed one to achieve a solid profit-safety trade-off, by strictly tracking set-point on outlet HCl concentration and, at the same time, by requiring minimal sorbent doses and then minimal solid residues, with limited stress on the actuation system.

Optimization of the model predictive control meta-parameters through reinforcement learning

Model predictive control (MPC) is increasingly being considered for control of fast systems and embedded applications. However, MPC has some significant challenges for such systems, such as its high computational complexity. Further, the MPC parameters must be tuned, which is largely a trial-and-error process that affects the control performance, the robustness, and the computational complexity of the controller to a high degree. This paper presents a multivariate optimization method based on reinforcement learning (RL) that automatically tunes the control algorithm’s parameters from data to achieve optimal closed-loop performance. The main contribution of our method is the inclusion of state-dependent optimization of the meta-parameters of MPC, i.e. parameters that are non-differentiable wrt. the MPC solution. Our control algorithm is based on an event-triggered MPC, where we learn when the MPC should be re-computed, and a dual-mode MPC and linear state feedback control law applied in between MPC computations. We formulate a novel mixture-distribution RL policy determining the meta-parameters of our control algorithm and show that with joint optimization we achieve improvements that do not present themselves with univariate optimization of the same parameters. We demonstrate our framework on the inverted pendulum control task, reducing the total computation time of the control system by 36% while also improving the control performance by 18.4%.

Field test of Model Predictive Control in residential buildings for utility cost savings

Air conditioners in residential buildings often rely on local feedback control to regulate the indoor temperature, where the unit is cycled on and off by comparing the actual temperature with the temperature set-point. Model Predictive Control (MPC) is a technique that makes use of building models, disturbance forecasts, and optimization algorithms to enhance building performance. MPC has demonstrated its potential in reducing building energy consumption and operating costs; however, it has seldom been applied in residential buildings because of the high implementation costs, complicated hardware configuration, and insufficient data. In this study, we developed and tested a MPC controller in a real apartment aimed at reducing the operating costs based on the local Time-of-Use (ToU) utility structure. We developed a feasible and easy-to-use hardware configuration as well as a cloud-based software deployment. The MPC controllers were implemented and evaluated through one-month field testing in a bedroom and living room of an apartment in a residential building. The field test showed that the MPC controller saved 22.1% for the bedroom and 26.8% cooling costs for the living room, compared to conventional rule-based control (RBC). We further confirmed the robustness of the MPC controller as the field test showed that the MPC controller is able to outperform the conventional RBC controller, even if the model is not accurate. Our work provides a practical MPC solution that can unlock the load flexibility potential of residential buildings, which creates a win–win solution for the households and the grid: saving utility costs for households and helping the grid to manage the balance between supply and demand.

Finite-time ESO-based cascade-free FCS-MPC for NNPC converter

This article addresses a novel finite control-set model predictive control solution for nested neutral point-clamped converter. More specifically, it is formed by incorporating a finite-time extended state observer design into a cascade-free finite control-set model predictive control architecture. In this architecture, a finite-time extended state observer is developed to estimate the total disturbances, and an integral error term and a dynamic reference design point of view are embedded into the proposed design so as to improve the performance. The main features of this proposal are: first of all, the detailed knowledge of the physical structure of the controlled plant is not required; second, a cascade-free structure is achieved in finite control-set model predictive control solution without weighting factors and steady-state error; and third, the proposed methodology can operate with different systems not just power converters, while keeping the fast transient response. In contrast to existing finite control-set model predictive control approaches, it can be found that our modification not only can track fast to their references but also can have superior robustness performance. Finally, the proposed solution is verified by comprehensive results that prove the theoretical researches for nested neutral point-clamped converter, while meeting the harmonic standards.

Efficient Uncertainty Mitigation in Automated Vehicles: Combining MPC with Model Reference Adaptive Control

Automated vehicles must be equipped with the ability to plan and execute trajectories in the presence of uncertainties for safe and effective navigation in both on-and of-road environments. Model predictive control (MPC) is a powerful and popular optimal control solution for both planning and control tasks, but even robust MPC solutions still suffer from decreased performance and the curse of dimensionality in the optimization problem when subject to model errors. We propose an adaptive control scheme that combines a fast, nominal MPC with our previously developed Model Reference Adaptive Control strategy in a cascaded architecture. The effectiveness of the resulting framework is demonstrated via robust and computationally efficient trajectory tracking under severe uncertainties. This study includes detailed tuning considerations and numerical evaluation with different fidelity vehicle models.

Robust Learning-Based Predictive Control for Discrete-Time Nonlinear Systems With Unknown Dynamics and State Constraints

Robust model predictive control (MPC) is a well-known control technique for model-based control with constraints and uncertainties. In classic robust tube-based MPC approaches, an open-loop control sequence is computed via periodically solving an online nominal MPC problem, which requires prior model information and frequent access to onboard computational resources. In this paper, we propose an efficient robust MPC solution based on receding horizon reinforcement learning, called r-LPC, for unknown nonlinear systems with state constraints and disturbances. The proposed r-LPC utilizes a Koopman operator-based prediction model obtained off-line from pre-collected input-output datasets. Unlike classic tube-based MPC, in each prediction time interval of r-LPC, we use an actor-critic structure to learn a near-optimal feedback control policy rather than a control sequence. The resulting closed-loop control policy can be learned off-line and deployed online or learned online in an asynchronous way. In the latter case, online learning can be activated whenever necessary; for instance, the safety constraint is violated with the deployed policy. The closed-loop recursive feasibility, robustness, and asymptotic stability are proven under function approximation errors of the actor-critic networks. Simulation and experimental results on two nonlinear systems with unknown dynamics and disturbances have demonstrated that our approach has better or comparable performance when compared with tube-based MPC and LQR, and outperforms a recently developed actor-critic learning approach.

Semi-Explicit Model Predictive Control of Quasi Linear Parameter Varying Systems

Explicit linear model predictive control (MPC) is a proven method for constrained optimal control of fast, linear time invariant (LTI) dynamic systems. However, an extension to quasi-linear parameter varying (Q-LPV) systems requires overcoming significant challenges, since neither the explicit MPC law is piecewise linear in state nor are the critical regions polytopic. In this work, we propose a semi-explicit solution to a sub-optimal MPC solution for a class of Q-LPV systems, which are obtained as multiple linear model approximations to nonlinear systems. The sub-optimal MPC for Q-LPV systems, which has been shown to be stabilizing in an earlier work, requires an online solution of a quadratic program (QP). Casting the QP into a multiparametric form leads to a new class of multiparametric QP (mpQP), termed herein as generalized mpQP (GmpQP). Information about the critical regions and the MPC law are obtained offline using a semi-explicit solution of the GmpQP based on an implicit enumeration of the active sets. Three algorithms are compared for the online evaluation of the control law. Offline and online complexity of the proposed method are presented for an example, including comparison of computational speeds with well-known implicit QP solvers.

Recurrent Model Predictive Control: Learning an Explicit Recurrent Controller for Nonlinear Systems

This paper proposes an offline control algorithm, called Recurrent Model Predictive Control (RMPC), to solve large-scale nonlinear finite-horizon optimal control problems. It can be regarded as an explicit solver of traditional Model Predictive Control (MPC) algorithms, which can adaptively select appropriate model prediction horizon according to current computing resources, so as to improve the policy performance. Our algorithm employs a recurrent function to approximate the optimal policy, which maps the system states and reference values directly to the control inputs. The output of the learned policy network after N recurrent cycles corresponds to the nearly optimal solution of N-step MPC. A policy optimization objective is designed by decomposing the MPC cost function according to the Bellman's principle of optimality. The optimal recurrent policy can be obtained by directly minimizing the designed objective function, which is applicable for general nonlinear and non input-affine systems. Both simulation-based and real-robot path-tracking tasks are utilized to demonstrate the effectiveness of the proposed method.