Shrinking Horizon Model Predictive Control Research Articles

Minimizing total annualized cost per tonne of feed processed of a semicontinuous distillation process utilizing data-driven model predictive control

Semicontinuous distillation is a separation technique used to purify multicomponent mixtures with low to medium throughput. This research addresses the problem of designing a Data-driven Model Predictive Control (MPC) approach that enables minimizing the Total Annualized Cost (TAC) of the semicontinuous process per tonne of feed processed while maintaining the required product purity. In lieu of typically unavailable first principles models, the manuscript demonstrates the implementation of data-driven technique using data collected from an Aspen Plus Dynamics simulation as a test bed. A subspace model identification technique is adapted to develop a multi-model framework to capture the dynamic behavior of the process and then utilized within a Shrinking Horizon MPC (SHMPC) scheme, to achieve the required objective. The simulation results demonstrate a lowering of the TAC/tonne of feed by 11.4% compared to the traditional PI setup used in the previous studies.

A Warm-Start Strategy in Interior Point Methods for Shrinking Horizon Model Predictive Control With Variable Discretization Step

For optimal control problems with random external disturbances, offline algorithms may not perform well because the state cannot be predicted. To solve the problems online, the model predictive control is frequently used, where a series of subproblems with different initial conditions are solved. These convex subproblems could be solved by using interior point methods after discrete approximations. To obtain a solution as accurately as possible under limited computing resources, the variable discretization step is usually considered. To improve efficiency, warm-start methods are considered, which utilize the similarity of subproblem structures. Specifically, the information obtained by solving earlier subproblems is used to solve subsequent subproblems. However, the discretization steps and the sampling numbers of subproblems may be different, and the initial states vary greatly, resulting in poor performance of existing warm-start strategies for interior point methods. In this paper, we present a new warm-start strategy for interior-point methods. In the strategy, a convex combination of components of the earlier optimal solution is used to construct an interpolation point, and we use the convex combination of the modified interpolation point and the cold-start point to obtain a warm-start point. We prove that the worst-case iteration complexity of our strategy is better than that of the cold-start. In the numerical experiment of fuel-optimal planetary powered-descent guidance problems, our strategy reduces the number of iterations of second-order cone programming by about <inline-formula><tex-math notation="LaTeX">$80\%$</tex-math></inline-formula> with the number of samples available in practical applications.

Energy-efficient predictive control for trams incorporating disjunctive time constraints from traffic lights

Tram operations are often blocked by traffic lights, leading to frequent decelerations and re-accelerations that increase operational energy consumption. This paper focuses on tram energy-efficient control problem incorporating time constraints from traffic lights that have multiple feasible green time windows (GTWs). We formulate the problem as a mixed-integer nonlinear program (MINLP), where binary variables are assigned to model disjunctive time constraints of the GTWs. To address computational challenge of solving the MINLP, we reformulate it as a tractable nonlinear program (NLP). Specifically, an equivalent NLP is first presented by replacing the integrality constraint with nonlinear constraints, and then the nonlinear constraints are relaxed and penalized into cost functions. To recover a solution of the MINLP, we propose a computationally efficient sequential quadratic programming algorithm in a shrinking horizon model predictive control framework, which updates the penalty parameter and quadratic programming subproblems in parallel. The solution obtained from the subproblem is feasible in each iteration, and convergence of the feasibility iterations can be enforced by the updated penalty. The performance of the proposed approach is investigated on different scenarios using real-life tram data. Results show that the method is able to generate energy-efficient driving trajectories in a dynamic environment, while crossing traffic lights in effective GTWs without unnecessary decelerations and re-accelerations.

Cooperative game-based multi-objective optimization of cargo transportation with floating partial space elevator

This paper develops a dual-phase control strategy based on the piecewise cooperative game method to balance the multiple competing objectives for cargo transportation by a partial space elevator in terms of orbital state stability and cargo transport efficiency and ensure final state stability. The cargo transportation is performed in the libration-free mode to facilitate the control implementation, where all libration motions are kept at zero. The new control strategy is split into phases I and II. Phase I focuses on cargo transportation and covers most cargo transfer distances. Multiple competing control objectives in this phase are balanced by the newly proposed piecewise cooperative game method. Once the remaining distance meets the preset threshold, the transportation enters phase II, which focuses on bringing the state of the partial space elevator to a stable equilibrium state. A shrinking horizon model predictive control method is used to ensure the state converges to the equilibrium point by the end of transportation. The simulation results reveal that the newly proposed dual-phase control scheme effectively balances multiple competing control objectives in the cargo transfer period. Moreover, by introducing phase II, the system can achieve a stable equilibrium state by the end of the transfer period.

Time-distributed optimization for shrinking horizon MPC

This paper proposes a strategy for implementing shrinking horizon Model Predictive Control (MPC) using a limited number of optimization iterations at each timestep. Offline and online certification methods are presented for determining a time-varying bound on the number of optimization iterations that ensures the closed-loop system satisfies a specified terminal constraint. An axisymmetric spacecraft spin stabilization example is reported to demonstrate the certification procedure.

A Novel Framework for Trajectory Planning and Safe Navigation of Satellite Swarms

This paper proposes a new framework for near-optimal, collision-free navigation of a swarm of identical satellites from an initial formation to a desired final formation. The framework combines a centralized optimization problem for location assignment with collision avoidance constraints, a decentralized fuel-optimal trajectory planner, a decentralized Artificial Potential Field (APF)-based real-time controller to ensure robustness, and a Shrinking Horizon Model Predictive Control logic to prevent deadlocks and livelocks and to improve robustness. To ensure high performance and low fuel cost, a novel optimization problem is formulated to tune the APF parameters based on mission requirements. The proposed framework provides a balance between optimality and scalability while keeping computational requirements low. The effectiveness of the frame work is demonstrated using numerical simulations.

Libration-free cargo transfer of floating space elevator

This paper studies the libration-free cargo transfer control of a partial space elevator where the main satellite may change its orbital state in the transfer period. The orbital motion of the main satellite in the climber transfer period is first studied. Then, a reduced-order libration-free dynamics of the partial space elevator is derived. Accordingly, a novel libration-free switching control strategy is proposed to stabilize cargo transportation with two alternating controllers. The Controller I controls the cargo speed in the libration-free mode by a shrinking horizon model predictive control based on the reduced-order libration-free dynamic mode of the partial space elevator. It leads to high computational efficiency in control. Once the libration is induced by the cargo transfer, the control turns off the Controller I and activates the Controller II to suppress the libration to zero within one time step of the Controller I by a novel prescribed-time control law based on the fixed-time control scheme. The stability of the control is proved in the Lyapunov framework. The validity and effectiveness of the proposed control strategy are demonstrated by computation simulation. Simulation results reveal that the proposed control strategy is effective in keeping stable cargo transportation while ensuring the equilibrium state at the end of transportation.

A Shrinking Horizon Model Predictive Controller for Daily Scheduling of Home Energy Management Systems

In this paper, the model predictive control (MPC) strategy is utilized in smart homes to handle the optimal operation of controllable electrical loads of residential end-users. In the proposed model, active consumers reduce their daily electricity bills by installing photovoltaic (PV) panels and battery electrical energy storage (BEES) units. The optimal control strategy will be determined by the home energy management system (HEMS), benefiting from the meteorological and electricity market data stream during the operation horizon. In this case, the optimal scheduling of home appliances is managed using the shrinking horizon MPC (SH-MPC) and the main objective is to minimize the electricity cost. To this end, the HEMS is augmented by the SH-MPC, while maintaining the desired operation time slots of controllable loads for each day. The HEMS is cast as a standard mixed-integer linear programming (MILP) model that is incorporated into the SH-MPC framework. The functionality of the proposed method is investigated under different scenarios applied to a benchmark system while both time-of-use (TOU) and real-time pricing (RTP) mechanisms have been adopted in this study. The problem is solved using six case studies. In this regard, the impact of the TOU tariff was assessed in Scenarios 1&#x2013;3 while Scenarios 4&#x2013;6 evaluate the problem with the RTP mechanism. By adopting the TOU tariff and without any load shifting program, the cost is <inline-formula> <tex-math notation="LaTeX">$\$ $ </tex-math></inline-formula>1.2274 while by using the load shifting program without the PV and BEES system, the cost would reduce to <inline-formula> <tex-math notation="LaTeX">$\$ $ </tex-math></inline-formula>0.8709. Furthermore, by using the SH-MPC model, PV system and the BEES system, the cost would reduce to <inline-formula> <tex-math notation="LaTeX">$\$ $ </tex-math></inline-formula>-0.282713 with the TOU tariff. This issue shows that the prosumer would be able to make a profit. By adopting the RTP tariff and without any load shifting program, the cost would be <inline-formula> <tex-math notation="LaTeX">$\$ $ </tex-math></inline-formula>1.22093 without any PV and BEES systems. By using the SH-MPC model, the cost would reduce to <inline-formula> <tex-math notation="LaTeX">$\$ $ </tex-math></inline-formula>1.08383. Besides, by adopting the SH-MPC, and the PV and BEES systems, the cost would reduce to <inline-formula> <tex-math notation="LaTeX">$\$ $ </tex-math></inline-formula>0.05251 with the RTP tariff, showing the significant role of load shifting programs, local power generation, and storage systems.

Approximating optimal control by shrinking horizon model predictive control for spacecraft rendezvous and docking

The paper considers shrinking horizon model predictive control (MPC) as an approximation to the optimal finite horizon control. Recent theoretical results bounding the error of such an approximation in terms of the discretization time-step and accuracy of the preview are discussed, and illustrated/confirmed through a computational case study of spacecraft rendezvous and docking. In addition, we consider the effects of inexactness in solving the optimization problem in the shrinking horizon MPC and examine properties and benefits of the implementation based on a gradient descent method with warm-starting and a varying number of iterations per time step.

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 little is known about their relative performance, particularly in utilization of building flexibility-resources. 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 with PV power generation and battery storage systems 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.

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.

Energy-efficient receding horizon trajectory planning of high-speed trains using real-time traffic information

Optimal trajectory planning of high-speed trains (HSTs) aims to obtain such speed curves that guarantee safety, punctuality, comfort and energy-saving of the train. In this paper, a new shrinking horizon model predictive control (MPC) algorithm is proposed to plan the optimal trajectories of HSTs using real-time traffic information. The nonlinear longitudinal dynamics of HSTs are used to predict the future behaviors of the train and describe variable slopes and variable speed limitations based on real-time traffic information. Then optimal trajectory planning of HSTs is formulated as the shrinking horizon optimal control problem with the consideration of safety, punctuality, comfort and energy consumption. According to the real-time position and running time of the train, the shrinking horizon is updated to ensure the recursive feasibility of the optimization problem. The optimal speed curve of the train is computed by online solving the optimization problem with the Radau Pseudo-spectral method (RPM). Simulation results demonstrate that the proposed method can satisfy the requirements of energy efficiency and punctuality of the train.

Shrinking Horizon Model Predictive Control Method for Helicopter–Ship Touchdown

A model predictive control (MPC) framework with a fixed maneuver horizon and shrinking prediction and control horizons is presented that, at each time step, minimizes the most accurate prediction of a complete cost for a discrete linear system, subject to constraints. Methods of weight selection to ensure strong convexity of the cost, which makes the quadratic programming problem associated with MPC numerically more tractable, are discussed. A continuous-time flexible-blade helicopter dynamic model is discretized, and the resulting model is used to demonstrate this control design method in ship landing and touchdown maneuvers. Inequality constraints, ship-induced turbulence, and parametric uncertainty are gradually included in the design and analysis. Several case studies are used to illustrate the effectiveness of this control method in landings on ships that experience quiescent and nonquiescent motions.

Shrinking Horizon Model Predictive Control With Signal Temporal Logic Constraints Under Stochastic Disturbances

We present shrinking horizon model predictive control for discrete-time linear systems under stochastic disturbances with constraints encoded as signal temporal logic (STL) specification. The control objective is to satisfy a given STL specification with high probability against stochastic uncertainties while maximizing the robust satisfaction of an STL specification with minimum control effort. We formulate a general solution, which does not require precise knowledge of probability distributions of (possibly dependent) stochastic disturbances; only the bounded support of the density functions and moment intervals are used. For the specific case of disturbances that are normally distributed, we optimize the controllers by utilizing knowledge of the probability distribution of the disturbance. We show that in both cases, the control law can be obtained by solving optimization problems with linear constraints at each step. We experimentally demonstrate effectiveness of this approach by synthesizing a controller for a heating, ventilation, and air conditioning system.

Real-time feasible multi-objective optimization based nonlinear model predictive control of particle size and shape in a batch crystallization process

This paper presents nonlinear model predictive control (NMPC) and nonlinear moving horizon estimation (MHE) formulations for controlling the crystal size and shape distribution in a batch crystallization process. MHE is used to estimate unknown states and parameters prior to solving the NMPC problem. Combining these two formulations for a batch process, we obtain an expanding horizon estimation problem and a shrinking horizon model predictive control problem. The batch process has been modeled as a system of differential algebraic equations (DAEs) derived using the population balance model (PBM) and the method of moments. Therefore, the MHE and NMPC formulations lead to DAE-constrained optimization problems that are solved by discretizing the system using Radau collocation on finite elements and optimizing the resulting algebraic nonlinear problem using Ipopt. The performance of the NMPC–MHE approach is analyzed in terms of setpoint change, system noise, and model/plant mismatch, and it is shown to provide better setpoint tracking than an open-loop optimal control strategy. Furthermore, the combined solution time for the MHE and the NMPC formulations is well within the sampling interval, allowing for real world application of the control strategy.

Subspace model identification and model predictive control based cost analysis of a semicontinuous distillation process

Semicontinuous distillation is a process intensification technique for purification of multicomponent mixtures. The system is control-driven and thus the control structure and its tuning parameters have crucial importance in the operation and the economics of the process. In this study, for the first time, a model predictive control (MPC) formulation is implemented on a semicontinuous process to evaluate the associated closed-loop cost. A cascade configuration of MPC and PI controllers is designed in which the setpoints of the PI controllers are determined via a shrinking-horizon MPC. The objective is to reduce the operating cost of a cycle while simultaneously maintaining the required product qualities. A subspace identification method is adopted to identify a linear, state-space model to be used in the MPC. The first-principals model of the process is then simulated in gPROMS. Simulation results demonstrate that the MPC has reduced the operational cost of a semicontinuous process by about 11%.

Tracking Control for Batch Processes through Integrating Batch-to-Batch Iterative Learning Control and within-Batch On-Line Control

An integrated strategy for product quality trajectory tracking control in batch processes is proposed by combing batch-to-batch iterative learning control (ILC) with on-line shrinking horizon model predictive control (SHMPC) within a batch. Under batch-to-batch ILC based on a linear time varying perturbation model, the performance of future batch runs can be enhanced, and the convergence of batch-wise tracking error is guaranteed. But ILC cannot affect the performance of current batch run, and the correction to control policy is not made until the next batch run. On the other hand, on-line SHMPC within a batch can reduce the effects of disturbances and improve the performance of the current batch run. By combing two methods for tracking trajectories, the integrated control strategy can complement both methods to obtain good performance because on-line SHMPC can respond to disturbances immediately and batch-to-batch ILC can correct bias left uncorrected by the on-line controller. The proposed strategy is illustrated on a simulated batch polymerization process. The results demonstrate that the performance of tracking product qualities can be improved quite well under the integrated control strategy than under the simple batch-to-batch ILC, especially when disturbances exist.

INTEGRATED BATCH-TO-BATCH ITERATIVE LEARNING CONTROL AND WITHIN BATCH CONTROL OF PRODUCT QUALITY FOR BATCH PROCESSES

An integrated strategy for the tracking control of product qualities in batch processes is proposed by combing batch-to-batch iterative learning control (ILC) with on-line shrinking horizon model predictive control (SHMPC) within a batch. ILC is used in batch-to-batch control and the convergence of batch-wise tracking error under ILC is guaranteed. On-line SHMPC within a batch can reduce the effects of disturbances immediately and improve the performance of the current batch run. The integrated control strategy can complement both strategies to obtain good performance of tracking trajectories. The proposed strategy is illustrated on a simulated batch polymerization process. The results demonstrate that the performance of tracking product qualities can be improved quite well under the integrated control strategy than under the simple batch-to-batch ILC, especially when disturbances exist.

Recursive data-based prediction and control of product quality for a PMMA batch process

In many batch processes, frequent process/feedstock disturbances and unavailability of direct on-line quality measurements make it very difficult to achieve tight control of product quality. Motivated by this, we present a simple data-based method in which measurements of other process variables are related to end product quality using a historical data base. The developed correlation model is used to make on-line predictions of end quality, which can serve as a basis for adjusting the batch condition/time so that desired product quality may be achieved. This strategy is applied to a methyl methacrylate (MMA) polymerization process. Important end quality variables, the weight average molecular weight and the polydispersity, are predicted recursively based on the measurements of reactor cooling rate. Subsequently, a shrinking-horizon model predictive control approach is used to manipulate the reaction temperature. The results in this study show promise for the proposed inferential control method.

Batch chemical process quality control applied to curing of composite materials

AbstractModel predictive control is used extensively to control continuous‐process systems. Application of a shrinking horizon model predictive control strategy is used to predict and control the end product quality of composite laminates produced by batch autoclave curing. The main contribution is the demonstration, using a laboratory‐scale autoclave, of the feasibility and advantages of a control strategy that adjusts the batch recipe on‐line to correct for unmeasured disturbance: entering the process. Readily available, on‐line secondary measurements are used in conjunction with the process model to predict (and hence control) quality‐related end product properties. On‐line monitoring is also used to monitor the process even after the possibility of on‐line correction has passed. The results show that this approach significantly reduces end product quality variance.