Evaluation of explicit model predictive temperature control for on-off air conditioner

This thesis is concerned with different topics in multi-parametric programming and explicit model predictive control, with particular emphasis on hybrid systems. The main goal is to extend the applicability of these concepts to a wider range of problems of practical interest, and to propose algorithmic solutions to challenging problems such as constrained dynamic programming of hybrid linear systems and nonlinear explicit model predictive control. The concepts of multi-parametric programming and explicit model predictive control are presented in detail, and it is shown how the solution to explicit model predictive control may be efficiently computed using a combination of multi-parametric programming and dynamic programming. A novel algorithm for constrained dynamic programming of mixed-integer linear problems is proposed and illustrated with a numerical example that arises in the context of inventory scheduling. Based on the developments on constrained dynamic programming of mixed-integer linear problems, an algorithm for explicit model predictive control of hybrid systems with linear cost function is presented. This method is further extended to the design of robust explicit controllers for hybrid linear systems for the case when uncertainty is present in the model. The final part of the thesis is concerned with developments in nonlinear explicit model predictive control. By using suitable model reduction techniques, the model captures the essential nonlinear dynamics of the system, while the achieved reduction in dimensionality allows the use of nonlinear multi-parametric programming methods.

Trajectory tracking is a basic function required for autonomous helicopters, but it also poses challenges to control design due to the complexity of helicopter dynamics. This article introduces an explicit model predictive control (MPC) to solve this problem, which inherits the advantages of non-linear MPC but eliminates time-consuming online optimization. The explicit solution to the non-linear MPC problem is derived using Taylor expansion and exploiting the helicopter model. With the explicit MPC solution, the control signals can be calculated instantaneously to respond to the fast dynamics of helicopters and suppress disturbances immediately. On the other hand, the online optimization process can be removed from the MPC framework, which can accelerate the software development and simplify onboard hardware. Due to these advantages of the proposed method, the overall control framework has a low complexity and high reliability, and it is easy to deploy on small-scale helicopters. The proposed explicit non-linear MPC has been successfully validated in simulations and in actual flight tests using a Trex-250 small-scale helicopter.

A novel traffic signal split approach based on Explicit Model Predictive Control

This work deals with the development of double closed loop control based on explicit model predictive control (MPC) for permanent magnet synchronous motor (PMSM) system with constraints. The aim of the proposed controller is to solve the constrained optimization problem for fast-sampling time PMSM system and improve the robustness of the system. The recreated mathematical model of PMSM is introduced at first. Then the proposed explicit MPC controller is designed based on the reformed model. The explicit controller is employed to control the mechanical speed and the q-axis current, and the proportional-integral (PI) control is employed to control d-axis current. The simulation results demonstrate that the proposed double closed loop control method is effective when the working condition of PMSM changes and the performance of the speed and current is satisfactory.

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 amortized running time of the composed MPC with a well-trained neural network. In addition, the scheme maintains closed-loop stability with any neural networks of proper input and output dimensions, alleviating the need for certifying optimality of the neural network in safety-critical applications. Note to Practitioners—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.

Explicit model predictive control (MPC) addresses the problem of removing one of the main drawbacks of MPC, namely the need to solve a mathematical program on line to compute the control action. This computation prevents the application of MPC in several contexts, either because the computer technology needed to solve the optimization problem within the sampling time is too expensive or simply infeasible, or because the computer code implementing the numerical solver causes software certification concerns,especially in safety critical applications.Explicit MPC allows one to solve the optimization problem off-line for a given range of operating conditions of interest. By exploiting multiparametric programming techniques, explicit MPC computes the optimal control action off line as an “explicit” function of the state and reference vectors, so that on-line operations reduce to a simple function evaluation. Such a function is piecewise affine in most cases, so that the MPC controller maps into a lookup table of linear gains.In this paper we survey the main contributions on explicit MPC appeared in the scientific literature. After recalling the basic concepts and problem formulations of MPC, we review the main approaches to solve explicit MPC problems, including a novel and simple suboptimal practical approach to reduce the complexity of the explicit form. The paper concludes with some comments on future research directions.

The power grid requires doubly‐fed induction generators (DFIGs) to effectively suppress rotor currents and provide reactive power support during low voltage ride‐through (LVRT) events. However, traditional virtual impedance methods struggle to flexibly coordinate different control objectives under various fault conditions, thereby failing to fully realize their control potential. To address this, this paper proposes a decoupled virtual impedance control strategy. Virtual resistance and inductance are independently designed to suppress zero‐sequence and negative‐sequence overcurrents, achieving effective overcurrent mitigation. Furthermore, explicit model predictive control (E‐MPC) is employed to dynamically adjust the virtual impedance values, enhancing the LVRT capability of DFIGs. Additionally, the E‐MPC cost function incorporates reactive power support to coordinate current suppression and voltage support. Since the control law of E‐MPC is designed offline, the online computation time can be greatly reduced. The proposed strategy is verified by 1.5 MW DFIG model in Matlab/Simulink and experiment. Results show that LVRT performances under diverse fault conditions have been significantly improved.

This paper shows how explicit model predictive control (MPC) strategies can be implemented in Python. They use a pre-calculated map between state measurements and control inputs to simplify and accelerate the calculation of optimal control inputs. By shifting majority of the computational effort off-line, the concept of explicit MPC offers a significantly faster and cheaper implementation of model predictive control. We show how explicit MPC feedbacks are designed and exported to a self-contained Python code that can be easily merged with existing applications. Two examples are provided to illustrate the procedure. One considers the design of an artificial player for a videogame. The second one tackles the problem of quadrocopter control.

Due to the nonlinear and underactuated characteristics of unmanned surface vehicle system and the uncertainty of environmental model, it is hard to establish accurate dynamic model and control law obtained by traditional algorithm which is too complex and has no engineering practice realization. In this paper, based on deep reinforcement learning algorithm of deep deterministic policy gradients, the line of sight algorithm is used firstly to obtains the expected value of heading angle of USV according to the current time position and the expected trajectory of USV. Meanwhile, we adopt the double Gaussian reward function to evaluate the training action, so as to obtain the optimal control action to realize the accurate tracking control. Finally, compared with explicit model predictive controller and linear quadratic regulator, the designed track controller based on DDPG has shorter adjusting time and smaller overshoot than explicit model predictive controller and linear quadratic regulator.

In this article, a nonlinear disturbance observer‐based multiple‐model adaptive explicit model predictive control (NDO‐MMAEMPC) scheme is developed for a nonlinear MIMO system with parametric uncertainty as well as an external disturbance. The proposed method manages external disturbances without affecting the degree of smoothness of the control signals. Further, to cope with the unknown system uncertainty, blending‐based adaptive identification schemes are used for the same class of systems. For each identification model, an explicit nonlinear model predictive controller is computed off‐line for the corresponding model in advance, which saves computation power during operation. The generated control inputs from the set of explicit controllers are being blended online using adaptive weight. An extended Kalman filter algorithm is employed for the estimation of the unavailable states of the nonlinear system. Using an aerodynamic laboratory setup, the effectiveness of the proposed control algorithm is verified.

Explicit Model Predictive Control (MPC) is an attractive control strategy, especially when one aims at a fast, computationally less demanding implementation of MPC. Although leading to a fast implementation of optimization-based control, the main downside of explicit MPC is its high complexity in terms of memory occupancy, which often limits practical applicability of such a control methodology. Therefore in this paper we propose to obtain simple explicit MPC controllers that provide guarantees of recursive satisfaction of input and state constraints. The task is accomplished by optimizing, off-line, the parameters of the feedback law such that an integrated square error between the optimal, but complex controller and its simpler replacement is minimized. We show that the task can be formulated as a quadratic optimization problem which always yields an admissible solution. In this way, suboptimality of simple feedbacks with respect to their complex optimal counterparts is significantly mitigated.

This paper considers the optimal reference tracking control of an electropneumatic clutch actuator. To control both supply to and exhaust from the clutch actuator chamber, one pair of on/off valves is used. The on/off valves are controlled by pulse-width modulation. The fast dynamics of the clutch actuator and the presence of both state and input constraints makes it appropriate to design an explicit Model Predictive Controller (MPC), where the only computation performed on-line would be a piecewise linear function evaluation. A multi-parametric Nonlinear Programming approach is applied to design the explicit MPC. In order to reduce the computational burden, the design of the explicit controller is based on a simplified 3-rd order model of the clutch actuator. The controller performance is verified by simulating with the full 5-th order model of the actuator dynamics. Also, the closed-loop response is compared to that of an explicit MPC controller without pulse-width modulation, where the valves are directly commanded fully open or fully closed.

Explicit model predictive control of gas–liquid separation plant via orthogonal search tree partitioning

The Lunar Gravity Compensation Facility (LGCF) is a critical component in ground tests for a crewed lunar roving vehicle (CLRV). The track-following servo subsystem’s performance is of critical importance in the LGCF, as it needs to achieve high-precision tracking of the CLRV’s fast, wide range of motion in the horizontal direction. The subsystem must also operate within various constraints, including those related to speed, acceleration, and position. These requirements introduce new challenges to both the design and control of the subsystem. To tackle these challenges, this paper employs a Permanent-Magnet Synchronous Motor (PMSM) vector control method based on Space Vector Pulse Width Modulation (SVPWM) to achieve accurate speed tracking. Additionally, this paper presents an Explicit Model Predictive Control (EMPC) strategy for precise position servo control of the track-following system under multi-parameter constraints. The simulation model of the track-following servo subsystem is established based on the above methods. The simulation results demonstrate that the position tracking error of the gravity compensation system, constructed using the above method combined with EMPC control, is less than 0.2 m. The control performance of the EMPC is significantly better than those of the PI and LQI controllers. The influence of errors on the drawbar pull is within 12.5%, and its effect on the compensation force is negligible. These results provide theoretical support for the design of a track-following servo subsystem.

Over the last decade, anesthesia research community witnessed numerous advances in controllers and their implementation platforms to control the depth of anesthesia (DoA) in a patient undergoing surgery. Today's operating theaters are extremely complex and crowded. New surgical techniques bring new medical technologies and more devices in the operation rooms, which often results in complex configurations, computer based control, and cable clutter. In an effort to reduce hardware size and to the improve quality control of anesthesia, we present a field programmable gate array (FPGA) based explicit model predictive control (EMPC) scheme which can take into account the control and state constraints that naturally arise in anesthesia. Real-time implementation of model predictive control (MPC), mainly requires solving an optimization problem at regular time intervals. We propose an FPGA-based EMPC-on-a-chip algorithm with customized 32-bit floating-point addition, substation, and multiplication algorithms. Simulation results with four compartmental PK-PD model, input constraints and a variable bispectral index (BIS) set-point are presented. The real-time simulation results are achieved with Xilinx's Vertex 4 XC4VLX25-10FF668 FPGA.