Quadratic Dynamic Matrix Control Research Articles

Modelling and Quadratic Dynamic Matrix Control of a DC Motor System with Non-linearities Consideration

Abstract: DC motor’s models that have often been used to test and validate control algorithms with, even the most robust ones, have usually been simplistic: limiting the generalization and applicability of the results obtained. This article presents a modeling approach for a DC motor system consisting of a Buck converter and driving a load at the end of the shaft, in which the nonlinearities of each of its sub-parts are taken into account in the model of the overall system. The model was simulated and its step responses were compared to those of the linear model and conventional nonlinear models with a significant difference (Pvalue<0.001). This model was then used to test the Fast Nonlinear Quadratic Dynamic Matrix Control (FNLQDMC). The letter has demonstrated good performance in simulation in terms of setpoint tracking, constraint handling, and computational load savings during online optimization problem solving

Dynamic Control of a Fiber Manufacturing Process Using Deep Reinforcement Learning

This article presents a model-free deep reinforcement learning (DRL) approach for controlling a fiber drawing system. The custom DRL-based control system predictively regulates fiber diameter and produces a fiber with a desired, constant or nonconstant, diameter trajectory, i.e., diameter variation along the fiber length. Physical models of the system are not used. The system was trained and tested on a compact fiber drawing system, which has nonlinear delayed dynamics and stochastic behaviors. For a reference trajectory with random step changes, after 1 h of training, the DRL controller showed the same root-mean-squared error (RMSE) as an optimized PI controller; after 3 h of training, it achieved the performance of a quadratic dynamic matrix controller (QDMC). While the PI feedback controller showed 3.5 s of time lag in a step response, the DRL controller showed less than a second of time lag. Controller performance tests on trajectories not used in the training process are conducted; for a sine sweep reference trajectory, the DRL controller maintained an RMSE under 40 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mu \text{m}$</tex-math></inline-formula> up to a frequency of 45 mHz, compared to 25 mHz for QDMC.

Fast constrained nonlinear model predictive control for implementation on microcontrollers

Abstract Model predictive control (MPC) is based on the systematic resolution of an online optimization problem at each time step. In practice, the computation cost is often very high, especially for the non-linear case under constraints, thus complicating the application of MPC to real-time systems. This paper proposes to improve the non-linear quadratic dynamic matrix control (NLQDMC) algorithm for MPC by solving constrained optimization problems only when necessary, and defaulting to the unconstrained solution whenever possible. The new algorithm is called fast NLQDMC (FNLQDMC) and is applied to the control of a nonlinear system comprised of converter and a DC machine, and implemented in a microcontroller board. The results obtained show that, depending to the setpoint profiles, this algorithm saves more than 64% computation of the constrained problem compared to the conventional NLQDMC, while keeping identical performance in terms of setpoint tracking and constraint satisfactions.

Multistep, Newton-type control strategies for constrained, nonlinear processes

In this paper we consider the development of moving time horizon strategies where optimal controller moves are determined from a model linearized about a nominal trajectory, and only the first step is implemented. In a nonlinear analogy to Quadratic Dynamic Matrix Control (QDMC), this approach solves a single quadratic program (QP) over the time horizon and easily incorporates bounds on control inputs and outputs.

Comparison of model predictive control strategies for a fluidized catalytic cracker

A FCC model is used to compare five different Model Predictive Control (MPC) strategies. The FCC process is a complex petrochemical unit with catalyst recycling that makes its behaviour highly nonlinear. The FCC comprises a riser, a separator and a regenerator with important heat coupling due to the endothermic cracking reactions of gas oil in the riser and the exothermic combustion reactions in the regenerator. The riser and the regenerator exhibit fast and slow dynamics respectively. The temperatures at riser top and in the regenerator should be controlled by manipulation of catalyst and air flow rates. All these nonlinear and coupled characteristics render the multivariable control problem difficult and thus the FCC process constitutes a valuable benchmark for comparing control strategies. Here, the performances of Dynamic Matrix Control, Quadratic Dynamic Matrix Control, MPC control with penalty on the outputs, NonLinear MPC control, Observer Based MPC control are compared.

Model Predictive Control of an Integrated Continuous Pharmaceutical Manufacturing Pilot Plant

This paper considers the model predictive control (MPC) of critical quality attributes (CQAs) of products in an end-to-end continuous pharmaceutical manufacturing pilot plant, which was designed and constructed at the Novartis-MIT Center for Continuous Manufacturing. Feedback control is crucial for achieving the stringent regulatory requirements on CQAs of pharmaceutical products in the presence of process uncertainties and disturbances. To this end, a key challenge arises from complex plant-wide dynamics of the integrated process units in a continuous pharmaceutical process, that is, dynamical interactions between several process units. This paper presents two plant-wide MPC designs for the end-to-end continuous pharmaceutical manufacturing pilot plant using the quadratic dynamic matrix control algorithm. The plant-wide MPC designs are based on different modeling approaches—subspace identification and linearization of nonlinear differential-algebraic equations that yield, respectively, linear low-dimensi...

Model-Based Closed-Loop Control of the Hydraulic Fracturing Process

Hydraulic fracturing is a technique for enhancing the extraction of oil and gas from deep underground sources. Two important goals during this process are to achieve a final fracture with a predefined geometry and to have a proper distribution of proppant material within the fracture to keep the fracture walls open and allow oil and gas to flow to the surface. The hydraulic fracturing system contains limited real-time measurements of the actual fracture conditions largely due to the remote subterranean location where the fracture propagates. The fracturing process is characterized by multiphase transport, proppant settling, and coupling of fluid and fracture growth mechanics, all occurring within a time-varying spatial domain. These features present a challenge for the implementation of online feedback control of the fracture growth and proppant placement, and there are very few accounts of attempting this goal in the open literature. To address these issues, the current work proposes a control strategy that allows for closed-loop model-based control of the hydraulic fracturing process. Previous work introduced a dynamic fracture model capable of describing the fracture propagation, fluid and particle transport, proppant bank formation, and fracture closure processes necessary to determine the fracture state evolution and predict the fracture’s final performance. The QDMC (quadratic-dynamic matrix control) form of model-based control is studied. A particle filter provides a means for effective state estimation due to limited real-time measurements. Controlling the fracture geometry and proppant distribution within a hydraulic fracture is a novel application for real-time model-based control. Results of a numerical study are provided to demonstrate the performance of the closed-loop system.

Observer based and Quadratic Dynamic Matrix Control of a Fluid Catalytic Cracking Unit: A Comparison Study

This paper deals with the application of two computer based model predictive control algorithms to a complex process. This process is a fluid catalytic cracking unit (FCC). The FCC model used for this study is inspired from Lee and Skogestad. The algorithms used are quadratic dynamic matrix control(QDMC) and observer base model predictive control(OBMPC). A disturbance rejection is tested by introducing some change in the feed rate. Despite the important nonlinearities of the FCC, The two linear model predictive control algorithms are able to maintain a smooth multivariable control of the plant, while taking into account the constraints. But, OBMPC algorthm is more efficient in following the set points even in the present of disturbances than QDMC algorithm.

Control of a Benchmark Boiler Process Model with DMC and QDMC

Abstract Boiler control is an important issue for all steam generating power plants. In this paper, model predictive control was applied in a control-oriented benchmark boiler simulation model by F. Morilla (2011). In the boiler benchmark case, the advantage of model predictive approach is the ability to inherently take into account the coupling between subsystems and constraints in the system (rate constraints, variable constraints). Well-established model predictive control approaches, Dynamic Matrix Control (DMC) and the constraint-handling Quadratic DMC (QDMC) were used for SISO and MIMO boiler control cases. Controllers were built, implemented and tested with the benchmark model in Matlab and Simulink environment. The study has been used for educational purposes with M.Sc. students to give an insight of model predictive control design procedure.

Rotary Dryer Control Using a Grey-Box Neural Model Scheme

The application of a Grey-box Neural Model (GNM) in a nonlinear model predictive control scheme (NMPC) of a direct rotary dyer is presented in this work. The GNM, which is based on the combination of phenomenological models and empirical artificial neural network (ANN) models, was properly developed and validated by using experimental fish-meal rotary drying information. The GNM was created by combining the rotary dryer mass and energy balances and a feed forward neural network (FFNN), trained off-line to estimate the drying rate and the volumetric heat transfer coefficient. The GNM results allowed us to obtain the relation between the controlled variable (solid moisture content) and the manipulated variable (gas phase entrance temperature) used in the predictive control strategy. Two NMPC control strategies, one with a fixed extended prediction horizon and another with an extended range prediction horizon, were applied to a simulated industrial fish-meal drying process. The results showed that a correct rotary dryer representation can be obtained by using a GNM approach. Due to the representation capability of the GNM approach, excellent control performances of the NMPCs were observed when the process variables were subject to disturbances. As analyzed in this work, the fixed extended prediction horizon MPC surpassed recognized control methodologies (quadratic dynamic matrix control).

Modeling and Control of a Complex Interacting Process

In this paper, two efficient control algorithms are discussed viz., Linear Quadratic Regulator (LQR) and Dynamic Matrix Controller (DMC) and their applicability has been demonstrated through case study with a complex interacting process viz., a laboratory based four tank liquid storage system. The process has Two Input Two Output (TITO) structure and is available for experimental study. A mathematical model of the process has been developed using first principles. Model parameters have been estimated through the experimentation results. The performance of the controllers (LQR and DMC) has been compared to that of industrially more accepted PID controller.

FPGA based QDMC control for reverse-osmosis water desalination system

Model-based predictive control (MPC) is a widely used advanced control algorithm in process industries, such as chemical plants and oil refineries. Quadratic dynamic matrix control (QDMC) is one of the popular MPC strategies. In this paper, the QDMC controller is used to control a simulated reverse-osmosis (RO) water desalination system with spiral wound element (SWM). A cascaded control system was designed with the QDMC controller and a PID controller for the desalination process, where the QDMC controller optimizes the set point of the PID controller and directly controls one output. In order to make the implementation more convenient, this paper also studies the implementation of QDMC control system based on a field programmable gate array (FPGA) chip. A support software is developed to help engineers adjust the parameters of the QDMC controller. Since the QDMC controller is implemented in an embedded system, the overall system cost is reduced, which is helpful to the application of RO desalination system.

Control of Reactive Distillation Column: A Review

The objective of this paper is to give a critical survey of the present status within the field of control of a reactive distillation column. Control of a reactive distillation column is a challenging task due to process nonlinearity and complex interactions between the vapor-liquid equilibrium and chemical reactions. There are different types of control methodologies, which have been studied in the reactive distillation, ranging from a simple proportional-integral (PI) controller to advanced model predictive controllers (MPC) such as dynamic matrix control (DMC), quadratic dynamic matrix control (QDMC), robust multivariable predictive control technology (RMPCT), generalized predictive control (GPC), and other advanced control techniques. With the goals of optimal performance, energy conservation and cost effectiveness of process operations in industries, the design of optimal controllers and controller performance assessment have received great attention in both industries and academia. The main objective of control is to maintain the product purity within the desired range.

Model predictive control for wastewater treatment process with feedforward compensation

Being an optimizing technology, model predictive control (MPC) can now be found in a wide variety of application fields. The main and most obvious control goal to be achieved in a wastewater treatment plant is to fulfill the effluent quality standards, while minimizing the operational costs. In order to maintain the effluent quality within regulation-specified limits, the MPC strategy has been applied to the Benchmark Simulation Model 1 (BSM1) simulation benchmark of wastewater treatment process. After the discussion of open loop responses of outputs to manipulated inputs and measured influent disturbances, the strategies of feedback by linear dynamic matrix control (DMC), quadratic dynamic matrix control (QDMC) and nonlinear model predictive control (NLMPC), and improvement by feedforward based on influent flow rate or ammonium concentration have been investigated. The simulation results indicate that good performance was achieved under steady influent characteristics, especially concerning the nitrogen-related species. Compared to DMC and QDMC, NLMPC with penalty function brings little improvement. Two measured disturbances have been used for feedforward control, the influent flow rate and ammonium concentration. It is shown that the performance of feedforward with respect to the influent ammonium concentration is much higher than for the feedforward with respect to the influent flow rate. However, this latter is slightly better than the DMC feedback. The best performance is obtained by combining both feedforward controllers with respect to the influent ammonium concentration and flow rate. In all cases, the improvement of performance is correlated with more aeration energy consumption.

Synthesis of state estimator-based control algorithms to apply on a distillation column

This work concerns the development of different discrete-time multivariable non-linear globally linearising control (GLC) algorithms for a binary distillation column (BDC). The proposed algorithms make the closed-loop system linear in an input/output (I/O) sense. The GLC control strategy is constructed with a transformer, also known as I/O linearising state feedback law, which accounts for process non-linearities; an estimator, which estimates the required unmeasured states and a quadratic dynamic matrix controller (QDMC) that is employed as an external controller around the globally linearised system. Three different GLC structures in conjunction with QDMC have been designed based on the availability of state information of the example distillation process. The proposed controllers have been compared in terms of set point tracking and disturbance rejection performance via numerical simulations. The study also includes the effects of parametric uncertainties on the controller responses.

Reduced-order methodologies for feedback control of particle size distribution in semi-batch emulsion copolymerization

Within-batch feedback control strategies are developed for the regulation of the particle size distribution (PSD) in a semibatch vinyl acetate (VAc)/butyl acrylate (BuA) emulsion copolymerization system. These strategies are also applicable for regulation of distributions in other particulate systems governed by population balances. In the first strategy, PID controllers are employed for regulating nucleation and growth events through tracking the nominal trajectories of total number of particles and the solids content by manipulating the feed-rates of the more reactive monomer, BuA, and the surfactant. The second control strategy is based on tracking nominal trajectories of the moments of the distribution with a quadratic dynamic matrix controller (QDMC). To determine the appropriate number of moments to describe the PSD during various stages of a nominal batch, a maximum-entropy approach is utilized. In the final and most complex approach, a nonlinear model predictive controller is designed utilizing the detailed population balance model of the system. The ill-conditioning resulting from the high-dimensionality of the resulting dynamical system is removed by principal component analysis (PCA)-based model order reduction and a multi-rate estimator is designed to compensate for the measurement delay associated with the PSD measurements.

Multi-objective constraint optimizing IOL control of distillation column with nonlinear observer

Performance of input–output linearizing (IOL) controllers suffers due to constraints on input and output variables. This problem is successfully tackled by augmenting IOL controllers with quadratic dynamic matrix controller (QDMC). However, this has created a constraint-mapping problem for coupled MIMO systems like distillation column. A multi-objective optimization problem needs to be solved to map the constraints on inputs. A suitable transformation technique is proposed to convert this multi-objective optimization problem to a single objective one. This makes the controller less computationally intensive and easy to implement. This controller (IOL-QDMC) along with nonlinear observer is implemented on a binary distillation column for dual composition control. Its performance is evaluated against a quadratic dynamic matrix controller (QDMC) and input–output linearization with PI controller (IOL-PI).

COMPARISON AMONG PI, DMC, QDMC, AND GPC ALGORITHMS IN THE CONTROL OF THE SPOUTED BED DRYER

This article presents comparative analysis between the classical PI (proportional-integral control) and MPC (model predictive control) techniques for a drying process on spouted beds. The on-line experimental setups were carried out in a laboratory-scale plant of a spouted bed dryer. The main objective was to optimize the plant operation by searching for the best control structure to be used in future scale enlargement. The major drawbacks encountered in this kind of system were high interactivity among variables, a malfunction as a result of calculated variables out of the operational window, and modeling mismatch. Despite the robustness of the operational PI, the control actions of this strategy did not overcome the variable interactions. The DMC (dynamic matrix control) and the QDMC (quadratic dynamic matrix control) algorithms performed satisfactorily over the major drawbacks. Special attention was given to the latter algorithm due to its ability to hold the variables under constrained oscillations. However, the best results were found for the adaptive GPC (generalized predictive control) algorithm whose actions prevailed over the modeling mismatch due to the strong nonlinear behavior intrinsic to the process. The main goal of the present work is to describe a procedure that can be standardized for other types of dryers and different scales. This is especially the case for the adaptive GPC, whose control structure is independent of the dryer nature and scale and whose implementation does not require previous identification procedures (self-tuning) and/or structural changes.

MODEL PREDICTIVE CONTROL OF A SIMULATED MOVING BED

Chromatographic processes for performing difficult separations such as enantiomers separation with high purity are an expanding technology. An interesting alternative to the expensive conventional batch chromatography is the true moving bed, a counter-current continuous process. However, for feasibility reasons, the TMB cannot be realized. The simulated moving bed (SMB) is realized in practice by connecting several single chromatographic columns in series and simulating the movement of solid by cyclic switching of the inlet and outlet ports. The complex dynamics, important non linearity, and multivariable character of the SMB make its control a challenging task. At this stage of the study, model predictive control (MPC) under the form of quadratic dynamic matrix control (QDMC) is applied on the TMB and the SMB. The numerical simulations of reference trajectory tracking performed show that the QDMC is well adapted for TMB control while the control of the SMB remains improvable.

Industrial Trials of Paste Drying in Spouted Beds Under QDMC

Spouted bed has been extensively investigated by many authors for years, but the issue of controlling its operation still remains in basic developing stages. The present work consists of the application of an advanced control strategy (QDMC—Quadratic Dynamic Matrix Control) to automate the operation of a large-scale spouted bed dryer. The work on control strategies for spouted bed was motivated by the lack of references on this subject and the encouraging results obtained by Corrêa et al. (Corrêa, N.A.; Freire, J.T.; Corrêa, R.G. Improving operability of spouted beds using a simple optimizing control structure. Brazilian Journal of Chemical Engineering 1999 16 (4), 359–368; Corrêa N.A. Corrêa, R.G.; Freire, J.T. Adaptive control of paste drying in spouted bed using the GPC algorithm. Brazilian Journal of Chemical Engineering 2000 17 (4–7), 639–648; Corrêa, N.A.; Corrêa, R.G.; Freire, J.T. Self-tuning control of egg drying in spouted bed using the GPC algorithm. Drying Technology 2002 20 (4), 813–828.) for a laboratory-scale apparatus. The industrial-scale spouted bed dryer has a height of 4 m and a diameter of 66 cm. The same configuration of data acquisition unit, sensors, and interface developed for the laboratory-scale unit was employed. The dryer is capable of processing up to 20 L/h of pasty material. The powder moisture content (Ys), inferred from measurements of temperature at the exhaustion of the bed bulk, and the powder production rate (Pr), measured on-line by an electronic balance, are the controlled variables. The manipulated variables are: the paste inflow rate (W), regulated by an automatic pump, and the electrical power supply for air heating (P), regulated by a thyristor. The bed pressure drop, the airflow rate, and the information from the environment are monitored by means of an interfaced microcomputer. Experimental runs of drying up to 400 kg/day of an Al2O3 10% aqueous suspension were carried out. The results showed that the QDMC control is robust with respect to the main variables involved and is efficient in maintaining the operation of the bed under the constraints of the system. The major aim concerning the scale-up of spouted bed, which is the determination of the minimum amount of energy required to ensure spout stability, was accomplished by the constrained control strategy.