Model Predictive Control Design Research Articles

Model Predictive Control for the Flowrate Control Loop of the FESTO MPS PA Compact Workstation

Model Predictive Control techniques offer favorable characteristics for the process control sector and have been used in industry since the 1980s. Some of the advantages of the Model Predictive Control techniques are that the process model can capture both static and dynamic interactions between input, output, and disturbance variables; the existing constraints on inputs and outputs are considered systematically, and the control calculations can be coordinated with the calculation of optimum set-points. This study aims to design and implement a Model Predictive controller for the flowrate control loop of the FESTO MPS PA Compact Workstation. The designed Model Predictive controller has an important advantage because it is easy to conFig. how much energy should be used using well-designed tuning parameters. First, a dynamic model of the plant is obtained using Pseudo-Random Binary Signal input. The obtained model is used to define the objective function, determine the aspects to be optimized and analyze and identify the restrictions and limitations of the control algorithm. For the implementation of the model predictive control algorithm, LabVIEW software was used because it can execute a graphic visualization of the operation of the plant, and it offers ActiveX controls that are needed for interfacing with the MPS PA compact workstation. Finally, the controller's behavior was analyzed, and comments about the obtained results and conclusions on this line of research are presented.

The LISA DFACS: Model Predictive Control design for the test mass release phase

This paper presents a Model Predictive Control (MPC) design for the test mass release phase of the LISA space mission. LISA is a gravitational wave observatory consisting of a triangular constellation of three spacecraft. The gravitational waves are detected by measuring the relative distance between free falling test masses by means of a laser interferometer. Each test mass is a cubic body located inside an electrostatic suspension that is initially locked by a clamp mechanism. Once the plungers are retracted, the test masses are released with high initial offsets and velocities. To detect the gravitational waves, each test mass must be accurately positioned at the cage centre and its attitude must be aligned with the local cage frame. However, the low actuation authority of the electrostatic suspension along with the critical initial conditions, make the attitude and translation control a difficult task. MPC is a suitable technique for this application because it can systematically account for command saturations, state constraints and can provide optimal (or sub-optimal) control inputs by solving an optimization problem online. In this paper, an MPC controller is designed and validated by means of Monte Carlo simulations, achieving satisfactory results.

Design of Model Predictive Controller for Solar Pv Integrated Upqc Operating with Dual Compensating Strategy

Design of Model Predictive Controller for Solar Pv Integrated Upqc Operating with Dual Compensating Strategy

Optimal design of model predictive controller based on transient search optimization applied to robotic manipulators.

Due to nonlinearity and uncertainty of the robotic manipulator, the design of the robot controller has a crucial impact on its performance of motion and trajectory tracking. In this paper, the linear parameter varying (LPV) - model predictive controller (MPC) of a two-link robot manipulator is established and then the controller's optimal parameters are determined via a newly developed meta-heuristic algorithm, transient search optimization (TSO). The proposed control method is verified by set point and nonlinear trajectory tracking. In the test of set-point tracking, the LPV-MPC scheme optimized by TSO has better performance compared to the computed torque controller (CTC) schemes tuned by TSO or other metaheuristic algorithms. In addition, good performances can also be observed in the tests of nonlinear trajectory tracking via the LPV-MPC scheme by TSO. Moreover, the robustness of the method to structural uncertainty is verified by setting a large system parameter deviation. Results reveal that we achieved some improvements in the optimization of MPC of the robot manipulator by employing the proposed method.

Robust Multi-Model Predictive Control via Integral Sliding Modes

This paper presents a novel optimal control approach for systems represented by a multi-model, i.e., a finite set of models, each one corresponding to a different operating point. The proposed control scheme is based on the combined use of model predictive control (MPC) and first order integral sliding mode control. The sliding mode control component plays the important role of rejecting matched uncertainty terms possibly affecting the plant, thus making the controlled equivalent system behave as the nominal multi-model. A min-max multi-model MPC problem is solved using the equivalent system without further robustness oriented add-ons. In addition, the MPC design is performed so as to keep the computational complexity limited, thus facilitating the practical applicability of the proposal. Simulation results show the effectiveness of the proposed control approach.

Efficient Implementation and Sampling Period Analysis of MPC for Water Distribution Networks*

In this paper we consider the design and implementation of Model Predictive Control (MPC) for water distribution networks (WDNs). First, we define the nonlinear differential algebraic equations that model a WDN, using both classical methods and simplified pump implementations. Then the cost function used in the MPC algorithm is formulated, where extra steps are taken to build a quadratic and convex cost function. The entire control problem is solved using a tailored sequential quadratic programming (SQP) method. The resulting control algorithm for WDNs is tested on a small distribution network to both illustrate the effectiveness and to perform additional tests on the effects of reducing the sampling period. The simulation results of this experiment indicate that the presented SQP–MPC can be implemented at faster rates than 1 hour and that this results in improved economic benefits.

Robust sample-based model predictive control of a greenhouse system with parametric uncertainty

Achieving optimal resource use efficiency is a key challenge in modern greenhouse production systems. Optimal performance in terms of crop yield and resource efficiency can in theory be achieved via optimal control. Standard optimal controllers are not designed to deal with uncertainty, whereas considerable model prediction errors occur due to the mismatch between the model and the real system. This paper explores the relation between parametric uncertainty, and performance with respect to crop yield, CO2 demand, ventilation demand, and heating energy. This is done using the following steps 1) extension of an existing controller model with parametric uncertainty, 2) design of a sample-based robust model predictive controller and 3) analysis of control performance under increasing parametric uncertainty. The results predict that control performance is significantly sensitive to parametric uncertainty. A relative parameter uncertainty of 20%, reduced crop yield with 11% compared to the case without uncertainty. Furthermore, a 20% uncertainty decreased CO2 demand with 80%, whereas it increased ventilation demand with 96%, and increased heating energy demand with 90%.

On the Practical Design of Tube-enhanced Multi-stage Nonlinear Model Predictive Control

Tube-enhanced multi-stage nonlinear model predictive control is a robust control scheme that can handle a wide range of uncertainties with reduced conservatism and manageable computational complexity. In this paper, we elaborate on the flexibility of the approach from an application point of view. We discuss the path to making design decisions to implement the novel scheme systematically. We illustrate the critical steps in the design and implementation of the scheme for an industrial example.

Modelling and predictive control for a RTM mold

The objective of this work is the control of a Resin Transfer Moulding (RTM) mold trying to obtain a temperature in the whole cavity as much homogeneous as possible. This is a complex process, mainly because of two factors: temperature distribution in a complex geometry and variability of the system parameters. In order to solve these difficulties, a design procedure based on models is carried out. Firstly, the detailed modelling of the thermal system, discretized and solved by means of finite elements (FEM) and validated by thermal tests in the physical mold. Then, a simplified reduced-order model (ROM) is obtained by means of ARX approach based on the former model. Finally, the design of a  robust MPC (Model Predictive Control) which is able to take the system variability, the geometry complexity and the limitations of the actuation systems (resistances) into account. In order to afford the nonlinearities intrinsically present in the system, in addition to the controller, a perturbation estimator is implemented, which evaluates the changes produced in the mold with regard to the expected behaviour according to the ROM. In this way, the control system is able to detect the variations and compensate them in real time. These algorithms are validated both by simulation and experimentally. From this verification, it follows that the application of these modelling, estimation and control techniques allows to control the mold with temperature variations much tighter than for PID standard controllers.

Performance Analysis of Economic Model Predictive Control on a Solar-Powered Direct Contact Membrane Distillation System

This paper proposes an economic model predictive control (EMPC) design for a Direct Contact Membrane Distillation powered by a solar collector system which aims at enhancing its economical performances. A differential algebraic equations-based model is used for the design of the EMPC control. Moreover, a nonlinear observer is developed for the estimation of the unmeasured state. A neural network is proposed to predict the unknown solar irradiance for future horizon where a solar model provides temperature predictions. The proposed control design has been validated in simulation using data provided by a partial differential equation-based model mimicking the real plant.

Preserving State and Control Privacies in Networked Systems With Tokenized Polytopic Transforms

This brief studies the problem of preserving state and control privacies in a networked system where the plant is a constrained discrete-time linear system with bounded disturbances. Our approach to this problem is a privacy-preserving control scheme which assigns integer tokens to the combination of affine transforms and qualifying polytopes within state constraints. Specifically, we utilize the piecewise affine property of a feedback control law obtained with the explicit model predictive control technique and design tokenized affine transforms for the control law and the polytopic partition of its domain. The qualifying polytopes are referred to as subregions and virtual subregions which are generated within the partitioned domain mentioned above. We show that the proposed scheme is semantically secure against privacy extraction by an eavesdropper. Simulation results demonstrate the validity of the proposed scheme in preserving state and control privacies.

Iterative Model Predictive Control for Piecewise Systems

In this letter, we present an iterative Model Predictive Control (MPC) design for piecewise nonlinear systems. We consider finite time control tasks where the goal of the controller is to steer the system from a starting configuration to a goal state while minimizing a cost function. First, we present an algorithm that leverages a feasible trajectory that completes the task to construct a control policy which guarantees that state and input constraints are recursively satisfied and that the closed-loop system reaches the goal state in finite time. Utilizing this construction, we present a policy iteration scheme that iteratively generates safe trajectories which have non-decreasing performance. Finally, we test the proposed strategy on a discretized Spring Loaded Inverted Pendulum (SLIP) model with massless legs. We show that our methodology is robust to changes in initial conditions and disturbances acting on the system. Furthermore, we demonstrate the effectiveness of our policy iteration algorithm in a minimum time control task.

Decentralized Stability Enhancement of DFIG-Based Wind Farms in Large Power Systems: Koopman Theoretic Approach

This paper proposes a data-centric model predictive control (MPC) for supplemental control of a DFIG-based wind farm (WF) to improve power system stability. The proposed method is designed to control active and reactive power injections via power converters to reduce the oscillations produced by the WF during disturbance conditions. Without prior knowledge of the system model, this approach utilizes the states measurements of the DFIG subsystem for control design. Therefore, a data-driven optimal controller with a decentralized feature is developed. The learning process is based on Koopman operator theory where the unknown nonlinear dynamics of the DFIG is reconstructed by lifting the nonlinear dynamics to a linear space with an approximate linear state evolution. Extended dynamic mode decomposition (EDMD) is then applied to determine the lifted-state space matrices for the proposed Koopman-based model predictive controller (KMPC) design. The effectiveness of the proposed scheme is tested on New England IEEE 68-bus 16-machine system under three-phase fault conditions. The results ascertain the effectiveness of the proposed scheme to enhance the system damping characteristics.

Development of a Python tool based on model predictive control for an optimal management of the Calais canal

Model predictive control (MPC) has been widely employed to control a large variety of water systems, such as dams, irrigation canals, inland waterways, drinking water networks and wastewater treatment plants. Its predictive capabilities and the possibility to incorporate constraints make MPC well suited to address several, and sometimes opposite, management objectives linked to water systems. The design of MPC for water systems is usually performed via dedicated software (e.g., Matlab) and tested in simulation using dedicated hydraulic software. However, the implementation of MPC strategies in real systems requires additional development to allow for its embedding within the information systems that are used by system managers. A possible solution is to create a tool based on Python that can be easily integrated with the information systems of managers, and within which existing Matlab solutions can be incorporated. In this paper, the development a ready-to-use Python tool using a hierarchical MPC approach designed for the management of the Calais Canal is presented.

An Experimental Study on MPC based Joint Torque Control for Flexible Joint Robots

This paper presents an experimental evaluation of joint torque control in a flexible joint robot using a model predictive control approach. The control of elastic robots is challenging due to the underactuated nature of the connected link and motor dynamics. A typical solution is to formulate the controller in a cascaded way with an outer loop controller for the nonlinear link side dynamics in combination with an inner loop controller for the joint torque. In this paper the inner loop torque controller utilizes a model predictive control design in order to take actuator constraints into account and, in case of a special choice of the torque reference and control gains, to avoid the computation of higher time derivatives in the desired joint torque. We compare two different controller implementations, which differ in the choice of the reference model. In particular, we investigate on the use of the natural open loop dynamics for the reference model. The controllers are evaluated in detail using a simulation study as well as in experiments on a single joint testbed.

Explicit model predictive control for PDEs: The case of a heat equation

Explicit model predictive control design is carefully developed for discrete-time linear plants on Hilbert spaces, and we highlight the role of the so-called Slater condition in the reliable explicit solution of the MPC optimization. We then proceed to present an explicit MPC algorithm that accounts for the stabilization and input constraints satisfaction. We do structure preserving temporal discretization of the infinite-dimensional parabolic PDE system by application of the Cayley transformation. The salient feature of explicit MPC design is the realization of the region-free approach in explicit MPC design with identification of active constraint sets to realize optimal stabilization and constraints satisfaction. Finally, the resulting design is illustrated by the application to the PDE model given by an unstable heat equation with boundary actuation and Neumann boundary conditions. The example demonstrates simultaneous stabilization and input constraints satisfaction on the one hand, and on the ability to deal with a relatively high plant dimension and a long optimization horizon on the other hand.

Model Predictive Controller Design For Bioprocesses Based On Machine Learning Algorithms

The optimization of critical quality attributes in biopharmaceutical processes demands the development of a scalable and optimal control scheme to meet the process constraints and objectives. In this paper, we designed a model predictive controller (MPC) to find the optimal feeding strategy to maximize cell growth and metabolite production in fed-batch bioprocesses. Due to high complexity of bioprocesses and lack of high-fidelity first principle models, we evaluated the use of machine learning algorithms in the forecast model to aid in our development. By taking advantage of the bioprocess model, this controller aims to maximize the protein production daily for each batch. The control scheme of the bioprocess is defined as an optimization problem to be solved while all metabolites and cell culture process variables are maintained within the specification. To evaluate the performance of the controller, we designed and implemented MPC with the best model to a bioreactor in a real experiment. The experimental validation confirms more than 2% improvement in final protein production compared to average historical experiments.

Nonlinearity handling in MPC for Power Congestion management in sub-transmission areas

This paper proposes congestion management solutions based on Model Predictive Control (MPC) principles for transmission network zones. The contribution resides in the use of logical variables for describing the nonlinearities related to the modelling of the physical aspects in power curtailment, or some desired control goals. This allows for the representation of the nonlinear model of a sub-transmission zone with a storage device in a linear Mixed Logical Dynamical (MLD) formulation, then paving the way to the utilisation of linear mixed integer programming for the optimization problem. Moreover, part of the contribution considers supplementary temporal specifications for the energy storage device utilisation. This is modelled using additional temporal and logical variables as part of the system state and control signal. Consequently, the extended model of the power network zone is formulated as a linear MLD system and integrated to the MPC design. The proposed controllers are validated through simulations on an industrial case-study.

Distributed Model Predictive Control for Connected and Automated Vehicles in the Presence of Uncertainty

Abstract This article focuses on the development of distributed robust model predictive control (MPC) methods for multiple connected and automated vehicles (CAVs) to ensure their safe operation in the presence of uncertainty. The proposed layered control framework includes reference trajectory generation, distributionally robust obstacle occupancy set computation, distributed state constraint set evaluation, data-driven linear model representation, and robust tube-based MPC design. To enable distributed operation among the CAVs, we present a method, which exploits sampling-based reference trajectory generation and distributed constraint set evaluation methods, that decouples the coupled collision avoidance constraint among the CAVs. This is followed by data-driven linear model representation of the nonlinear system to evaluate the convex equivalent of the nonlinear control problem. Finally, to ensure safe operation in the presence of uncertainty, this article employs a robust tube-based MPC method. For a multiple CAV lane change problem, simulation results show the efficacy of the proposed controller in terms of computational efficiency and the ability to generate safe and smooth CAV trajectories in a distributed fashion.

An Improved Model Predictive Fast Frequency Control for Power System Stability Against Unknown Time-Delay Switch Attack

A modern power grid is a cyber-physical system, which are vulnerable to cyber attacks. A recently found attack, the time-delay switch attack (TDSA), is made by inserting time delays into communication channels. A TDSA can be highly destructive to a power system as it can lead to instability. This paper presents a novel model predictive control (MPC) for fast frequency controller in a power system which can effectively mitigate the unknown TDSA. The MPC recently has received great attentions to be applied as FFC in a power system. Most of the MPC design are based on discrete-time model, whose future plant behaviour is calculated through iteration, rather than convolution. Nevertheless, one crucial step in the derivation of discrete-time MPC (DTMPC) is to capture the control trajectory over a finite prediction horizon. This imposes a challenge in designing a DTMPC to counteract the time-delay with unknown time length. Thus, a continuous-time MPC (CTMPC) is proposed to deal with TDSA. To overcome the unknown time delay, we synthesize an accurate time-delay estimator and sequential state predictor (SSP), are designed to accurately estimate and effectively counteract the unknown and random TDSA. All presented case studies are based on a real Taipower system and justification of the effectiveness of the proposed method was verified.