Implicit Model Predictive Control Research Articles

DC-Link Utilization Enhanced Implicit Model Predictive Control for Dual Three-Phase PMSMs

DC-Link Utilization Enhanced Implicit Model Predictive Control for Dual Three-Phase PMSMs

A PLC-Embedded Implementation of a Modified Takagi–Sugeno–Kang-Based MPC to Control a Pressure Swing Adsorption Process

The paper presents a case study that applies a model predictive control (MPC) approach in a Micro850 programmable logic controller (PLC) to a laboratory pressure swing adsorption (PSA) process used for separating gas mixtures of CO2 and CH4. PLC is an industrial hardware characterized by its robustness to hazardous environments and limited computational capacities, which poses computational challenges for MPC implementation. This paper’s main contribution is the application of the modified Takagi–Sugeno–Kang-based MPC (MTSK-MPC) algorithm to this PSA unit, which provides features to investigate and implement feasible MPC designs in PLCs. The investigation consists of a sensitivity analysis of how some design parameters influence the PLC memory and the MPC implementation and a comparative evaluation of the computational processing from different MPC algorithms and simulations. The comparison comprises software-in-the-loop simulations with three algorithms in the PC: an implicit MPC, an explicit MPC, and the MTSK-MPC. Additionally, it includes a hardware-in-the-loop simulation with the implemented MTSK-MPC in Micro850. The results show that the MPC algorithms achieve close performance, tracking setpoint changes and rejecting output disturbances, with the MTSK-MPC presenting the lower processing time among the MPCs in the PC. The study concludes that the implementation of MTSK-MPC in the Micro850 is feasible.

Composing MPC With LQR and Neural Network for Amortized Efficiency and Stable Control

Model predictive control (MPC) is a powerful control method that handles dynamical systems with constraints. However, solving MPC iteratively in real time, i.e., implicit MPC, remains a computational challenge. To address this, common solutions include explicit MPC and function approximation. Both methods, whenever applicable, may improve the computational efficiency of the implicit MPC by several orders of magnitude. Nevertheless, explicit MPC often requires expensive pre-computation and does not easily apply to higher-dimensional problems. Meanwhile, function approximation, although scales better with dimension, still requires pre-training on a large dataset and generally cannot guarantee to find an accurate surrogate policy, the failure of which often leads to closed-loop instability. To address these issues, we propose a triple-mode hybrid control scheme, named Memory-Augmented MPC, by combining a linear quadratic regulator, a neural network, and an MPC. From its standard form, we derive two variants of such hybrid control scheme: one customized for chaotic systems and the other for slow systems. The proposed scheme does not require pre-computation and is capable of improving the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">amortized</i> running time of the composed MPC with a well-trained neural network. In addition, the scheme maintains closed-loop stability with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">any</i> neural networks of proper input and output dimensions, alleviating the need for certifying optimality of the neural network in safety-critical applications. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This article was motivated by the need to reduce the amortized cost of MPC in repetitive industrial robotic applications, where long-term operational cost is important and safety is critical. Examples of such applications include factory robotic arm manipulation and fixed-route quadcopter payload transport. Unlike explicit MPC or function approximation, our approach does not require any pre-computation or pre-training. Rather, it attains task proficiency over time by learning a surrogate neural network on the spot and by gradually replacing the costly MPC with the more efficient surrogate model so long as safety permits. Consequently, the proposed scheme incurs a learning cost during the initial phase of the deployment but usually becomes more adept on the task afterwards, leading to amortized efficiency.

Approximated MPC for embedded hardware: Recursive random shooting approach

Advanced, optimization-based control methods are implemented at each level of industrial production. Although the model predictive control (MPC) represents a state-of-the-art control strategy maximizing profit, and, simultaneously, minimizing the energy losses, its industrial implementation is limited by the requirements on the software and hardware resources. This paper proposes an approximated MPC for such cases when the implementation of implicit MPC has a prohibitive effort on industrial hardware and its explicit counterpart is limited by its memory footprint requirements. The recursive random shooting-based approach is introduced to eliminate the conventional optimization and minimize the memory requirements, meanwhile guarantying the asymptotic stability subject to the physical constraints on control inputs and system states. The benefits of the proposed method are significantly reduced computational complexity by 93%, and decreased energy consumption by 93%, compared to non-recursive random shooting, while the performance loss is approximately 8%.

State-Constrained Sub-Optimal Tracking Controller for Continuous-Time Linear Time-Invariant (CT-LTI) Systems and Its Application for DC Motor Servo Systems

In this paper, we propose an analytic solution of state-constrained optimal tracking control problems for continuous-time linear time-invariant (CT-LTI) systems that are based on model-based prediction, the quadratic penalty function, and the variational approach. Model-based prediction is a concept taken from model-predictive control (MPC) and this is essential to change the direction of calculation for the solution from backward to forward. The quadratic penalty function plays an important role in deriving the analytic solution since it can transform the problem into a form that does not have inequality constraints. For computational convenience, we also propose a sub-optimal controller derived from the steady-state approximation of the analytic solution and show that the proposed controller satisfies the Lyapunov stability. The main advantage of the proposed controller is that it can be implemented in real time with a lower computational load compared to the implicit MPC. Finally, the simulation results for a DC motor servo system are shown and compared with the results of the direct multi-shooting method and the implicit MPC to verify the effectiveness of the proposed controller.

Approximate Explicit Model Predictive Control via Piecewise Nonlinear System Identification

This article presents an identification methodology to capture general relationships, with application to piecewise nonlinear approximations of model predictive control for constrained (non)linear systems. The mathematical formulation takes, at each iteration, the form of a constrained linear (or quadratic) optimization problem that is mathematically feasible as well as numerically tractable. The efficiency of the devised methodology is demonstrated via two industrial applications. Results suggest the possibility to achieve high approximate precision with limited number of regions, leading to a significant reduction in computation time when compared to the state-of-the-art implicit model predictive control solvers.

Exact Complexity Certification of Active-Set Methods for Quadratic Programming

Active-set methods are recognized to often outperform other methods in terms of speed and solution accuracy when solving small-size quadratic programming (QP) problems, making them very attractive in embedded linear model predictive control (MPC) applications. A drawback of active-set methods is the lack of tight bounds on the worst-case number of iterations, a fundamental requirement for their implementation in a real-time system. Extensive simulation campaigns provide an indication of the expected worst-case computation load, but not a complete guarantee. This paper solves such a certification problem by proposing an algorithm to compute the exact bound on the maximum number of iterations and floating point operations required by a state-of-the-art dual active-set QP solver. The algorithm is applicable to a given QP problem whose linear term of the cost function and right-hand side of the constraints depend linearly on a vector of parameters, as in the case of linear MPC. In addition, a new solver is presented that combines explicit and implicit MPC ideas, guaranteeing improvements of the worst-case computation time. The ability of the approach to exactly quantify memory and worst-case computation requirements is tested on a few MPC examples, also highlighting when online optimization should be preferred to explicit MPC.

An efficient Model Predictive Control-based motion cueing algorithm for the driving simulator

Recently, a new technique using a MPC (Model Predictive Control)-based motion cueing algorithm has been successfully applied in driving simulation. However, the feasibility and the stability condition of MPC, a crucial criterion for high-performance simulators, has barely been addressed except in our previous works and in Dagdelen et al. (Model-based predictive motion cueing strategy for vehicle driving simulators. Contr Eng Pract 2009; 17: 995–1003). In this paper, it is shown that based on an implicit MPC algorithm using qpOASES, the authors’ proposed feasibility and stability condition not only guarantees the feasibility and stability of the MPC-based motion cueing algorithm, but also controls washout motion, taking into account the driver’s perception threshold, thus resulting in a more robust and flexible motion cueing algorithm and a better motion feeling than that for the conventional motion cueing algorithms.

Efficient Implicit Model-Predictive Control of a Three-Phase Inverter With an Output LC Filter

Three-phase inverters with an output LC filter are commonly used to provide sinusoidal voltages with low-harmonic distortion. Constraint on peak filter current is often desirable to protect the components from potential damage. In case of constraints, implicit and explicit model-predictive control (MPC) are some of the feasible controller options. The conventional implicit MPC requires a large number of computations, whereas explicit MPC cannot directly incorporate real-time changes in model parameters, while still being computationally expensive than some of the other control schemes, e.g., hysteresis, dead beat control, etc. In this paper, we propose a new approach to solve the optimization problem in implicit MPC that has a computational complexity approximately five times less than that of explicit MPC. We have been able to achieve lower computational requirements by exploiting the inverter model and the structure of constraints.

Implicit Model Predictive Control of a Full Bridge DC–DC Converter

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> This paper presents a model predictive control (MPC)-based approach for a full bridge dc–dc converter of a fuel cell power system. The objective of the proposed control algorithm is to regulate the output voltage without violating the peak current constraint. We first develop a large signal dynamic model for the full bridge dc–dc converter. The peak current protection requirement is then formulated as a mixed input and state constraint for the MPC scheme. We next introduce the integrated perturbation analysis and sequential quadratic programming (InPA-SQP) method to solve the constrained optimal control problem with sub-millisecond level sampling time. The InPA-SQP solver can meet the computational efficiency demand, thereby enabling implementation of an implicit MPC for power electronics system with fast dynamics. The effectiveness of the proposed control algorithm in the peak current protection and the output voltage regulation has been verified with experimental results. </para>