Multivariable Predictive Control Research Articles

Development of a fed-batch-scale anaerobic co-digestion control system based on multivariable output error state space and model predictive control

This paper describes a feeding control system for fed-batch-scale anaerobic co-digestion. The proposed system is based on the multivariable output error state space and uses model predictive control to regulate the biogas flow output of anaerobic co-digestion. This control system combines predictive modeling, receding-horizon optimization, and state feedback. An accurate linear model of anaerobic co-digestion is obtained through the multivariable output error state space method using experimental data, and the accuracy of the model is evaluated using a goodness-of-fit index and the root mean square error. After augmenting the model, a predictive control system is established. The system states are observed through a Kalman filter, and the constrained receding-horizon optimization problem is solved using quadratic programming. Finally, the stability of the control system is demonstrated from both open- and closed-loop perspectives. The control system is then constructed and used in actual experiments, with the target flow output set at 100 NmL/h. The final flow output indicates that the control system achieves good control performance. This research enables the biogas output of anaerobic co-digestion to be controlled from a linear perspective through a concise control algorithm with strong practical application prospects.

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.

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.

Fuzzy model based multivariable predictive control design for rapid and efficient speed-sensorless maximum power extraction of renewable wind generators

Introduction. A wind energy conversion system needs a maximum power point tracking algorithm. In the literature, several works have interested in the search for a maximum power point wind energy conversion system. Generally, their goals are to optimize the mechanical rotation or the generator torque and the direct current or the duty cycle switchers. The power output of a wind energy conversion system depends on the accuracy of the maximum power tracking controller, as wind speed changes constantly throughout the day. Maximum power point tracking systems that do not require mechanical sensors to measure the wind speed offer several advantages over systems using mechanical sensors. The novelty. The proposed work introduces an intelligent maximum power point tracking technique based on a fuzzy model and multivariable predictive controller to extract the maximum energy for a small-scale wind energy conversion system coupled to the electrical network. The suggested algorithm does not need the measurement of the wind velocity or the knowledge of turbine parameters. Purpose. Building an intelligent maximum power point tracking algorithm that does not use mechanical sensors to measure the wind speed and extracts the maximum possible power from the wind generator, and is simple and easy to implement. Methods. In this control approach, a fuzzy system is mainly utilized to generate the reference DC-current corresponding to the maximum power point based on the changes in the DC-power and the rectified DC-voltage. In contrast, the fuzzy model-based multivariable predictive regulator follows the resultant reference current with minimum steady-state error. The significant issues of the suggested maximum power point tracking method, such as the detailed design process and implementation of the two controllers, have been thoroughly investigated and presented. The considered maximum power point tracking approach has been applied to a wind system driving a 5 kW permanent magnet synchronous generator in variable speed mode through the simulation tests. Practical value. A practical implementation has been executed on a 5 kW test bench consisting of a dSPACEds1104 controller board, permanent magnet synchronous generator, and DC-motor drives to confirm the simulation results. Comparative experimental results under varying wind speed have confirmed the achievable significant performance enhancements on the maximum wind energy generation and overall system response by using the suggested control method compared with a traditional proportional integral maximum power point tracking controller.

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 predictive functional control of a compound power-split hybrid electric vehicle

The Corun hybrid system (CHS) is a deeply coupled multiple-input–multiple-output (MIMO) hybrid system. The two inputs are the torques of the two motors. The two outputs are the carrier speed and transmission output torque. Using the traditional control method, the multi-objective control quality cannot be guaranteed because of the adopted static decoupling method and proportional–integral–derivative (PID) controllers. In this paper, the problems of the traditional control method are carefully analyzed, and a new control method is proposed. Instead of static decoupling, dynamic decoupling is adopted to improve the decoupling control effect. A predictive functional controller instead of a PID controller is adopted to deal with the pure delay caused by controller area network (CAN) communication. The tracking effect of the target value is further improved by predictive functional controllers. For the two decoupled subsystems, that is, the integral system and the second-order underdamped system, two predictive functional controllers are designed. The new control method was verified by simulations and tests. The results show that the new control method is superior to the traditional control method for CHS.

MANAGING CHALLENGES AT MLNG SATU DISTILLATION COLUMNS

To realise the ultimate operating potential of distillation columns via maximising the yield throughput without compromising product quality at lower operating costs has always been an aspiration for Malaysia LNG Sdn Bhd (MLNG Satu). Existing Advanced Process Control (APC) has been helping the plant to deliver better process stability at the Fractionation Unit. Operating high-purity distillation columns in MLNG Satu imposes a challenge to APC control because of its non-linear and intensely interactive dynamics. In addition, frequent changes in feed compositions and feed flow must be dealt in a continuous basis, which failed to do so will results in a significant upset in the product compositions. The distillation process is also known to utilise a large amount of energy, which can significantly influence the overall plant profitability. Realising energy optimisation has a significant contribution towards overall operational costs in distillation columns’ operation. Therefore this has become a prime target when performing APC revamp that recently took place at MLNG Satu (De-ethaniser, De-propaniser, De-butaniser column). This abstract describes the challenges and implementing control strategies to establish a disturbance feedforward model, minimise energy consumption and maintain optimum product impurity. Although distillation processes are inherently non-linear, a process control system based on linear input-output model can be acquired if operated over a sufficiently small region. Hence, a linear multivariable predictive control is developed, provides multiobjective control handling based on objective hierarchy. The applied control strategy has successfully improvised the dynamic control performance, resulting in a reduction in product quality variability, increment in product yield, and minimisation of the unit operating cost. It is expected to bring more value as the APC controller uptime increases over time. Intangibly, the competency of plant operators in dealing with advanced technology, i.e., APC, to optimise plant operation, has been enhanced from control to supervisory role, allowing for overall plant optimisation to be done in minute intervals.
 Keywords: Advanced Process Control (APC), Non-Linear, Distillation Columns

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.

Constrained discrete model predictive control of an arm‐manipulator using Laguerre function

SummaryThis work presents a multivariable predictive controller applied on a redundant robotic manipulator with three degrees of freedom. The article focuses on the design of a discrete model‐based predictive controller (DMPC) using the Laguerre function as a control effort weighting method to enhance the solution of Hildreth's quadratic programming and to minimize the trade‐off problem in constrained case. The Laguerre functions are used to simplify and enhance the control horizon effect through parsimonious control trajectory, thus reducing the computational load required to find the optimal control solution. Furthermore, these results can be confirmed by simulations and experimental tests on the manipulator and comparing it to the traditional DMPC approach and the discrete linear quadratic regulator.

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.

A Constrained Non-Linear Model Predictive Controller for the Rotor Flux-Oriented Control of an Induction Motor Drive

Predictive controllers have been extensively studied and applied to electrical drives, mainly because they provide fast dynamic responses and are suitable for multi-variable control and non-linear systems. Many approaches perform the prediction and optimization process on-line, which requires a high computational capacity for fast dynamics, such as, for example, the control of AC electric motors. Due to the complexity of embedding constraints in controller design, which demands a high computational capacity to solve the optimization problem, off-line approaches are one of the choices to overcome this problem. However, these strategies do not deal with the inherent constraints of the drive system, which significantly simplifies the design of the controller. This paper proposes a non-linear and multi-variable predictive controller to control the speed and rotor flux of an induction motor, where the constraints are treated after the controller design. Besides dealing with the constraints of the electric drive system, our proposal allows increasing the stability of the system when the model does not incorporate disturbances and when parameter incompatibilities occur. Several computer simulations and experimental tests were performed to evaluate the behavior of the proposed controller, showing good performance to track the controlled variables under normal operating conditions, under load disturbances, parametric incompatibility, and at a very low rotor speed.

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).