Multivariable Model Predictive Control Research Articles

Multivariable robust tube-based nonlinear model predictive control of mammalian cell cultures

In this paper, the application of a robust nonlinear model predictive control (NMPC) framework to mammalian cell cultures is proposed, dealing with possible large kinetic parameter uncertainties. Industrial constraints formulated in view of good manufacturing practice and quality-by-design approach are also considered, namely the assurance that all state trajectories are contained within a corridor defined by lower and upper safety bounds. The latter are assimilated to the well-known tube-based paradigm which is used to formulate the corresponding robust NMPC problem. Both classical and tube-based NMPC performances are assessed in numerical simulations where specific key-species are regulated while dealing with an uncertain plant model. The capability of the tube-based method to reduce the impact of the parameter variations on the state trajectories and the violation of the constraints is highlighted, suggesting the transfer of the method on a real pharmaceutical process.

Research on partition control of direct air‐cooling condenser based on multivariable Hammerstein CARMA model predictive control

AbstractPartition control of the fan array within a direct air‐cooling condenser (DACC) is recognized as a highly effective energy‐saving measure and a means to mitigate the adverse effects of ambient winds. This study focuses on the development of a dynamic partition model, which establishes the relationship between mass flow rate and fan array speed under windy conditions. The model is grounded in multivariable Hammerstein controlled autoregressive moving average (H‐CARMA) systems. Additionally, an innovative extended stochastic gradient algorithm, founded on the hierarchical identification principle, is introduced to estimate the model's unknown parameters. The recursive least square is employed as a benchmark to verify the accuracy and efficiency of the approach. Subsequently, leveraging the identified model, the model predictive controller based on the differential evolution method is designed to derive the optimal control law. Finally, simulation test and analysis are carried out to testify the effectiveness of our control strategy. The experiment result shows that the dynamic characteristics of the system have been significantly improved and the fan power consumption is reduced by 3.5% compared to the PID controller.

Multivariable discrete MPC with exponential cost function on the automation of the anesthesia process

AbstractThe automation of the delivery of anesthesia infusion rate in a general medical procedure consists of calculating the adequate infusion to regulate a patient's hypnosis state. In this procedure, the patient model has been considered as a Single‐Input Single‐Output system. However, the anesthesiologist introduces other medications, such as analgesics. Therefore, this contribution considers a closed‐loop formulation with two drugs as input control variables: propofol as an anesthetic, and remifentanil as an analgesic. Then, through the mathematical model description, this paper introduces a multiple‐input and multiple‐output (MIMO) model predictive control (MPC) to regulate the deep of hypnosis (DOH) based on the co‐administration of propofol and remifentanil. Since the control variables must be positive during the procedure, the MPC is formulated as a constrained optimization problem. Quadratic programming solves the optimization problem by designing and developing an exponential cost function, which allows the rapid convergence of the MPC optimization algorithm. Finally, the proposed MPC formulation is tested on 12 patients in silico, simulating a 60‐min general surgery. The simulated results verify the performance of the proposed MPC.

Model Predictive Control-Based Multivariable Controller for Traffic Flows in Automated Freeway Systems

Uncertainties and disturbances in traffic flows will result in performance degradation and even the critical instability of automated freeway systems. To handle these issues, a multivariable model predictive controller is proposed in this article, taking the speed and density of traffic flows as the control objectives and accounting for the uncertainty caused by ramps. Specifically, a state-space macroscopic traffic flow model is established based on a macroscopic traffic flow model. Then, a multivariable model predictive controller is developed based on the state-space model, and a sequence quadratic program algorithm is designed to find the optimal inputs. Finally, extensive simulations and comparisons are conducted. The results from the simulations verify that the proposed controller can make the density and speed of traffic flows approach a desired value more quickly and without chattering. In addition, the controller can effectively avoid traffic congestion and has better stability in the presence of disturbances.

Multivariable Model Predictive Control to Control Bio-H2 Production from Biomass

Two significant units in biomass-based hydrogen plants are the compressor and steam reformer. The compressor works to achieve high pressure for further operations, while the steam reformer produces H2 gas. For the units to operate well against disturbances that may occur (regulatory control) or changes in the set point (servo control), as well as the interactions between the relevant process variables, a Multivariable Model Predictive Control (MMPC) is considered as a controller. The determination of MMPC parameters, including the sampling time (T), prediction horizon (P), and control horizon (M), is crucial for achieving such objectives. Therefore, in this study, MMPC parameter adjustment was performed. The Integral of Absolute Error (IAE) and Integral of Square Error (ISE) were used as control performance indicators. For comparison, we considered the IAE and ISE from the Single-Input Single-Output (SISO)-based Model Predictive Control (MPC) from previous research. As a result, the optimum MMPC parameters were found to be T = 1, P = 341, and M = 121 for the compressor unit, and T = 1, P = 45, and M = 21 for the steam reformer unit. The average increases in control performance (IAE and ISE), compared to the MPC (SISO) used in previous research, were 85.84% for compressor unit 1, 61.39% for compressor unit 2, 94.57% for compressor unit 3, and 73.35% for compressor unit 4. Meanwhile, in the steam reformer unit, the increases in control performance were 63.34% for the heater and 80.16% for the combustor.

Multivariable sequential model predictive control of LCL‐type grid connected inverter

The conventional single variable indirect model predictive control (SIMPC) of LCL-type three-level grid- connected inverter (GCI) is to indirectly control the grid current by controlling the output current of the inverter, which usually produces large errors and reduces the system anti-disturbance performance. Although the previously proposed multivariable weighted model predictive control (MWMPC) method of LCL-type GCI can directly control many variables, such as grid current, it requires setting the weight coefficient for each variable and involves a substantial amount of calculation. To due with these problems, this paper proposes a multivariable sequential model predictive control (MSMPC) method for LCL-type three-level GCI. The inverter output current, the filter capacitor voltage, and the grid current are gradually predicted and optimized under the variable control sequence of the LCL-type GCI mathematical model. Under the premise of achieving direct control of the variables above, this method can reduce the number of weighting coefficients and gradually contract the optimization space to reduce the computation required for multivariable prediction and optimization. This paper compares the proposed MSMPC to the conventional SIMPC and MWMPC in steady state, transient state performance, and anti-disturbance performance. The effectiveness of the proposed MSMPC is demonstrated through simulation and experimentation.

Implementation of an embedded model predictive controller for a novel medical oxygen concentrator

Medical Oxygen Concentrators (MOCs) produce high purity oxygen from ambient air for medical therapies, and can range in size from large stationary units to small ultra-portable devices. These devices use a complex Rapid Pressure Swing Adsorption (RPSA) cyclic process which is subject to many process disturbances. Feedback control is required to operate a MOC reliably in different operating conditions and in presence of disturbances. Recently, a multivariable Model Predictive Controller (MPC) for a single-bed MOC device was developed in simulation, and we now present an implementation of this MPC for a lab-scale MOC device. The single-bed MOC uses a four-step RPSA cycle which can be controlled in real-time by adjusting the four cycle step durations to control the product oxygen concentration and product storage tank pressure. The MPC uses a linear model, identified using experimental sub-space system identification techniques, and an embedded convex quadratic optimization problem for making control decisions. This work presents the implementation of this MPC algorithm using Raspberry Pi hardware for the single-bed MOC device. The complete closed-loop system is evaluated using various set point tracking and disturbance case studies.

Full Operational Envelope Control of a Wind Turbine Using Model Predictive Control

This study presents a full operational envelope controller for a full nonlinear 5 MW Supergen exemplar wind turbine based on multivariable model predictive control (MPC). Below the rated wind speed, the primary objective of the controller is to maximize the energy capture. Above the rated wind speed, the controller maintains the rated power. The controller switches between control modes according to the prevailing wind speed to maintain control over the full envelope of operating regions. A linearized model is derived from a model of an exemplar 5 MW Supergen wind turbine in state-space form. The linearized model is then used to realize a feedback MPC (FB-MPC) and feedforward MPC (FF-MPC) to consider the lack and incorporation, respectively, of wind speed information. The switching strategy is tracked on the torque–speed plane. Simulations are performed at multiple wind speeds to evaluate the robustness and switching performances of the designed controllers by applying them to a full nonlinear 5 MW Matlab/SIMULINK model of the same exemplar Supergen wind turbine. Improved tracking is achieved over the full envelope with FF-MPC rather than FB-MPC. Simulation results are presented in the time and frequency domain in addition to the torque–speed plane demonstrating that the control performance is improved without an increase in the control activity (i.e., pitch action) of the turbine; that is, the controller’s gain crossover frequency remains within the acceptable range, around 1 rad/s. Note that most work presented in the literature focus on specific wind speeds only; that is, either only below rated wind speed or above rated wind speed. In contrast, the controllers reported here cover the full envelope of operation regions, making this work more practical and novel.

Methanol–Water Purification Control Using Multi-Loop PI Controllers Based on Linear Set Point and Disturbance Models

Dimethyl ether (DME), derived from methanol, has been issued as an alternative to diesel and LPG. This study will continue the research of an optimized process control design for DME purification plants, specifically the methanol purification process. This way, water can be separated, and the main product, methanol, can be recycled for DME synthesis. A setpoint-based linear model of a methanol–water purification system has been developed with four controlled variables (CV) with objectives to; maintain a separated liquid water stream in the bottom stage (Stage 30) of the distillation column for methanol–water separation at 11.22%, keep the purified liquid methanol at a condenser at 58.81 °C and 49.96% of level, and the last CV is the cooler in the distillate stream, to keep the purified methanol’s top product at 40.75 °C. To complete the model, a first order plus dead time (FOPDT) disturbance model is created against the inlet temperature and flow rate of the feed, the major cause of disturbances in the industry. Using a traditional proportional integral controller connected to each controlled variable, a multi-loop control system is formed with optimization and compared to the disturbance rejection of multivariable model predictive control (MMPC). The final improvement against the feed temperature and flow for CV1, CV2, CV3, and CV4 is shown by, respectively, Integral Absolute Error (IAE) values of 79.49%, 99.90%, 100%, and 99.99% and Integral Square Error (ISE) values of 97.1%, 100%, 99.99%, and 100%.

Multivariable model predictive control of a compound power-split hybrid electric vehicle during the tip-in/out process

For a compound power split hybrid system, such as the Corun hybrid system (CHS), a frequently encountered problem is determining how to compensate for the inertia torque of the transmission via the torque distribution of the two motors. The equivalent inertia of the transmission is variable and depends on the angular acceleration. According to the traditional control scheme, the target torque of the motors is distributed by simplifying the output angular acceleration to 0. This simplification introduces deviations in the torque distribution, and it is difficult to guarantee the quality of the two control quantities simultaneously. Recent research has also focused only on the control quality of one of the outputs. To solve this problem, a direct MIMO control scheme is proposed in this paper that directly calculates the target torques of the two motors based on control deviations. A multivariable model predictive controller (MPC) was designed for the control of transient processes. The simulation results showed that the proposed control method can improve the control accuracy of two objectives significantly, and it has an excellent ability to reject torque disturbances.

A Holistic, Model-Predictive Process Control for Friction Stir Welding Processes Including a 1D FDM Multi-Layer Temperature Distribution Model

Friction press joining is an innovative joining process for bonding plastics and metals without additives in an overlap configuration. This paper presents for the first time a model-based approach for designing a multi-variable model predictive control (MPC) for friction press joining. For system modeling, a differential equation based on the heat flows was proposed and modeled as a torque-dependent function. With this model, it is possible to consider cross-effects between the axial force and the friction zone temperature. With this theoretical approach, adaptive model-predictive process control was implemented and validated for different material combinations (EN AW-6082-T6; EN AW-2024-T3; PE-HD; PA6-GF30; PPS-CF). It could be shown that the MPC has excellent control accuracy even when model uncertainties are introduced. Based on these findings, a 1D Finite Differential Method multi-layer model was developed to calculate the temperature in the plastic component, which is not measurable in situ (r = 0.93). These investigations demonstrate the high potential of the multi-variable MPC for plastic-metal direct joining.

Tuning of Multivariable Model Predictive Control for Industrial Tasks

This work is concerned with the tuning of the parameters of Model Predictive Control (MPC) algorithms when used for industrial tasks, i.e., compensation of disturbances that affect the process (process uncontrolled inputs and measurement noises). The discussed simulation optimisation tuning procedure is quite computationally simple since the consecutive parameters are optimised separately, and it requires only a very limited number of simulations. It makes it possible to perform a multicriteria control assessment as a few control quality measures may be taken into account. The effectiveness of the tuning method is demonstrated for a multivariable distillation column. Two cases are considered: a perfect model case and a more practical case in which the model is characterised by some error. It is shown that the discussed tuning approach makes it possible to obtain very good control quality, much better than in the most common case in which all tuning parameters are constant.

Multivariable Model Predictive Control for a Virtual Synchronous Generation-Based Current Source Inverter

Three-phase current-source inverters are an alternative solution for interfacing photovoltaic modules to the utility thanks to its voltage boosting ability. This paper presents a virtual synchronous generator strategy for a three-phase current-source inverter using a multivariable model predictive control. The proposed method can ensure operations in both grid-connected and islanded modes while achieving virtual inertia features to stabilize the grid frequency and active damping to reduce grid current distortions caused by an output CL filter included on the grid side of the system. The obtained simulation results in the PSCAD/EMTDC environment software verify the effectiveness and the excellent performance of the proposed method.

Multivariable robust MPC design for neutralisation plant: Experimental analysis

The paper provides an extensive experimental analysis of offset-free multivariable robust model predictive control (MPC) of a neutralisation plant. The behaviour of the neutralisation plant was nonlinear and asymmetric. The controlled variable was a pH value of the outlet stream, and the manipulated variables were the inlet volumetric flow rates of the acid and base. The observer was designed to estimate the system states. Operating conditions make the tuning of the robust controller a challenging task. First, the conventional robust MPC was designed. The control setup was tuned and experimentally analysed in various operating conditions. Based on the measured data, the novel approach of the real-time compensation of the asymmetric behavior was investigated. Implementation of the proposed control strategy leads to improved control performance. The real-time compensation of asymmetric behaviour can be considered for the control of other systems with nonlinear behaviour.

Model Predictive Control for Helium Compression Station: Simulation and experimental Results

This paper deals with multivariable on-line model predictive control (MPC) for helium Warm Compression Stations (WCS). During WCS operation, control algorithms must ensure that the operational constraints are respected. These constraints can be imposed by the system itself (valves open from 0 to 100%, compressor maximum electrical current and pressures, …), or imposed by the users (valves which must remain closed or open to a minimum other than 0, pressures which should not be too low or too high). The MPC controller takes into account the constraints and set points into one optimization problem, which makes it the ideal candidate to control the WCS. The papers presents experimental results obtained on the SBT WCS, showing that the WCS is running safely while taking into account the constraints. The experimental tests shows that using MPC leads to high stability and fast disturbance rejection such as those induced by a turbine or a compressor stop, which is a key-aspect in the case of large-scale cryogenic refrigeration. The proposed control scheme can be used to achieve precise control of pressures in normal operation or to avoid reaching a stopping criteria (such as excessive pressures) under high disturbances (such as the pulsed heat load expected to take place in future fusion reactors).

Multivariable non-minimum state space model predictive control based on disturbance observer

In order to suppress the influence of lumped system disturbance, such as external disturbance and internal disturbance caused by model mismatch and coupling between variables, more effectively, a multivariable non-minimum state space predictive control method based on disturbance observer (MNMSSPC-D) is proposed in this paper. Most of the existing methods based on the feedback control and feedforward compensation cannot guarantee optimal output. Unlike the existing methods, the proposed method extends the estimated disturbance and output variables into the state variables, forming a multivariable non-minimum state space (MNMSS) prediction model, and then uses the rolling optimization principle in predictive control to design the controller based on the formed prediction model. The main advantages of the proposed method are that the state can be guaranteed to be available to the MNMSS model and the optimal control performance and anti-disturbance ability of system can be obtained by the designed controller. The proposed MNMSSPC-D method is verified by the simulation with a heavy oil fractionator.

Tuning of multivariable model predictive controllers through expert bandit feedback

For certain industrial control applications an explicit function capturing the non-trivial trade-off between competing objectives in closed loop performance is not available. In such scenarios it is common practice to use the human innate ability to implicitly learn such a relationship and manually tune the corresponding controller to achieve the desirable closed loop performance. This approach has its deficiencies because of individual variations due to experience levels and preferences in the absence of an explicit calibration metric. Moreover, as the complexity of the underlying system and/or the controller increase, in the effort to achieve better performance, so does the tuning time and the associated tuning cost. To reduce the overall tuning cost, a tuning framework is proposed herein, whereby a supervised machine learning is used to extract the human-learned cost function and an optimisation algorithm that can efficiently deal with a large number of variables, is used for optimising the extracted cost function. Given the interest in the implementation across many industrial domains and the associated high degree of freedom present in the corresponding tuning process, a Model Predictive Controller applied to air path control in a diesel engine is tuned for the purpose of demonstrating the potential of the framework.

Analytical Tuning Method of MPC Controllers for MIMO First-Order Plus Fractional Dead Time Systems

An analytical model predictive control (MPC) tuning method for multivariable first-order plus fractional dead time systems is presented in this paper. First, the decoupling condition of the closed-loop system is derived, based on which the considered multivariable MPC tuning problem is simplified to a pole placement problem. Given such a simplification, an analytical tuning method guaranteeing the closed-loop stability as well as pre-specified time-domain performance is developed. Finally, simulation examples are provided to show the effectiveness of the proposed method.

Application of Multivariable Model Predictive Control (4x4) for Dimethyl Ether Purification from Methanol

Application of Multivariable Model Predictive Control (4x4) for Dimethyl Ether Purification from Methanol

Design and implementation of MPC for turbofan engine control system

The objective of an aircraft engine control system is to provide required thrust as well as protection against the physical and operational limits. Model predictive control (MPC) technique is an attractive approach that incorporates input/output constraints in its optimization process to fulfill the control requirements of an aircraft engine. However, due to heavy computational burden of MPC, the real-time implementation of this algorithm is challenging and selection of MPC design parameters is crucial. This paper presents the design and hardware implementation of MPC algorithm as well as its HIL testing for turbofan engine control. In addition, a feedback correction technique is employed to compensate the effect of plant-model mismatch. For this purpose, a thermodynamic nonlinear engine model is firstly developed. A multivariable model predictive controller is then designed based on a discrete-time linearized state-space model where the horizons are obtained through a genetic algorithm optimization procedure. Moreover, this controller is implemented on an appropriate hardware taking the real-time aspects into account. Finally, an HIL platform is developed for testing the turbofan engine electronic control unit (ECU). For this purpose, a multi-level throttle command is applied to the ECU and the performance of the engine is evaluated. The results indicate that the controller satisfies all the engine constraints, and confirm the successful software and hardware implementation of the control algorithm in real-time.