Dynamic Matrix Control Algorithm Research Articles

Repetitive dynamic matrix control for systems with periodic specifications

This paper proposes a Repetitive Dynamic Matrix Control (RDMC) for systems with periodic specifications. The new algorithm is able to track periodic references and reject repetitive disturbances with a known period based on a modified prediction error. A repetitive version of the Generalized DMC (GDMC) is also proposed such that it can be applied to control open-loop unstable systems. Only the step-response coefficients are required to describe the dynamical system such that the RDMC preserves the modeling simplicity of the Dynamic Matrix Control (DMC). The proposed solution can be interpreted as an extension of the DMC for repetitive control applications. A data-driven filter design is proposed in order to ensure null prediction steady-state error in the presence of periodic disturbances even for unstable open-loop systems. Two case studies are presented to show the usefulness of the proposed strategy for control systems with periodic specification and to illustrate the typical advantages and drawbacks of the proposed repetitive control extension of the DMC algorithm.

An intelligent heating system based on the Internet of Things and STM32 microcontroller

Under the rapid growth of Internet of Things technology, many households are moving towards smart solutions. Addressing the inflexibility of temperature control in traditional heating systems, this research focuses on designing an intelligent heating system. To enhance flexibility and intelligence, an intelligent heating system based on the Internet of Things and STM32 microcontroller is proposed. Furthermore, the study identifies limitations of traditional proportional-integral-derivative control methods and establishes an optimization control model for heating system output temperature based on the Dynamic Matrix Control algorithm. Results indicate that the system's web interface successfully draws temperature curves, displaying clear data on detected temperature and humidity. The output temperature optimization control model shows a temperature rise of 2 °C and a temperature control error index of 0.0543 during the initial heating stage, and a control error index of 0.0353 during the mid-heating stage when the valve relative opening is close to 0. And the temperature control effect is better than traditional PID control, fuzzy PID control, genetic algorithm based PID control, and predictive feedback predictive control, without obvious indoor temperature overshoot phenomenon, which has certain advantages. In conclusion, the proposed system and model exhibit favorable application outcomes, offering technological support for the intelligent management of heating systems.

Truncation error correction by designing input-adjustment-output coefficients for dynamic matrix control based on cubic spline function

The truncation error is an important problem in the dynamic matrix control (DMC) algorithm. Generally, the dynamic information of a plant for the traditional DMC algorithm is determined by the step response. However, the step response of the plant is limited in practice, which leads to the truncation error of the modeling horizon in the feedback correction of DMC algorithm. A truncation error correction method based on cubic spline function is proposed for DMC algorithm, which is realized by designing coefficients and tracking the dynamic response of the system. In the feedback correction of DMC algorithm, the relationship between the correction parameter and the correction difference is constructed by the fitting of cubic spline functions on the intervals. A truncation error correction procedure is presented to calculate the correction parameters by inputting of the correction difference into the relationship. Then, the control increment and predicted model output are computed based on the correction parameters and updated shift matrix. Finally, numerical experiments demonstrate that the control performance of the proposed DMC algorithm has been much improved compared to that of traditional DMC algorithm.

Development of a three-term MPC and its application to an ultra-supercritical coal fired power plant

Most MPC (Model Predictive Control) algorithms used in industries and studied in the control academia use a two-term QP (quadratic programming), where the first term is the weighted norm of the output errors, and the second term is that of the input increments. In this work, a DMC (Dynamic Matrix Control) algorithm that uses three-term QP is developed and studied, where the third term is the weighted norm of the output increments. A relationship between the three-term DMC and the two-term DMC is established; and based on that, ideal closed-loop response curves are derived. These results are useful for the tuning of the three-term DMC. Then, a method for comparing two control methods is proposed and it is shown that the three-term DMC outperforms the two-term DMC. The findings are verified using simulation studies. Finally, the three-term DMC is successfully applied to a 1030 MW ultra-supercritical coal-fired power plant. According to simulation study using the identified model, in comparison to traditional two-term DMC, there is a roughly 10% reduction in the standard deviation of load tracking error for similar control efforts. In real-life tests on the power plant, the performance of the three-term DMC is compared to that of the existing PID controller. The load rate of change increased from 0.8%/min to 1.5%/min while the standard deviation of steam pressure decreased 38%; the standard deviations of the main steam temperature and reheat steam temperature decreased more than 40% with their mean values increased by more than 2 ∘C and 4 ∘C respectively.

Effectiveness of Dynamic Matrix Control algorithm with Laguerre functions

Effectiveness of Dynamic Matrix Control algorithm with Laguerre functions

Research on Multivariable Fuzzy Dynamic Matrix Control Algorithm

To improve the control quality of distillation tower systems that suffer from issues such as coupling, delay, and nonlinearity, traditional control methods have been ineffective. Consequently, this paper proposes using a variable-domain fuzzy dynamic matrix control algorithm for control system optimization. The traditional dynamic matrix control algorithm is augmented with a fuzzy controller, which is utilized to compensate for predicted output. The concept of variable domain is introduced to address the problems of poor adaptive ability and low control accuracy in the Fuzzy-DMC algorithm. Scaling factors are designed to adjust the fuzzy domain, enabling the fuzzy controller to compensate for predicted output even in the event of a significant model mismatch, resulting in improved control performance. The experimental results indicate that the algorithm proposed in this paper is superior to both traditional DMC and Fuzzy-DMC algorithms in terms of rise time, overshoot, and steady-state rate. In addition, this algorithm possesses a simple structure and does not modify the conventional DMC algorithm structure, making it theoretically applicable in practice.

Pseudo feedforward dynamic matrix control algorithm for desired closed-loop performance in MPC systems

As a practical approach, the dynamic matrix control (DMC) algorithm has been widely used in the control of chemical processes for decades. Nevertheless, there is no strong relationship between the tuning parameters of DMC and the closed-loop dynamics. In this article, a pseudo feedforward dynamic matrix control (PFFDMC) algorithm for realizing desired closed-loop performance in industrial systems is proposed. Building on insights from cascade control, a pseudo feedforward compensator is added in front of the process to precondition the overall system offline for expected characteristics achievement. Then, the actual manipulated variables can be obtained first by solving a modified objective function and then through matrix transformation. The proposed algorithm provides a quantitative relation between the pseudo feedforward sequence and the final setpoint tracking results rather than a qualitative way. Numerical simulations on SISO and MIMO systems are performed to verify the effectiveness of the proposed algorithm on performance criteria achievement.

A Generalised Dynamic Matrix Control for unstable processes based on filtered predictions

This paper presents a Generalised Dynamic Matrix Control (GDMC) algorithm that can be used to control open-loop unstable processes. In contrast to the Dynamic Matrix Control (DMC), the GDMC is able to provide internally stable predictions due to a generalised filtered approach. The conditions to achieve internal stability are shown and a new data-driven filter design procedure is proposed. Two simulation case studies are presented to illustrate the usefulness of the GDMC.

Modified hierarchical strategy for transient performance improvement of the ORC based waste heat recovery system

Organic Rankine Cycle (ORC) system outperforms in the low-grade waste heat recovery and has found its wide application in engineering practice. Due to the strong coupling multivariable nature of the ORC power unit, the traditional hierarchical control scheme, which is composed of real-time optimization (RTO) in the upper layer and model predictive control (MPC) in the lower one, is usually utilized in the control of the ORC system for good economic performance. The upper RTO solves an economic objective function in real time and obtains the optimal steady-state setpoints which are sent to the lower MPC layer for tracking. However, the disadvantage of the traditional hierarchical control scheme lies in its neglection to the transient characteristics with the evolution of the ORC system, which will finally lead to poor overall control performance. To address this problem, in this article, a modified hierarchical control strategy which is denoted as RTO-PFFDMC grounded on pseudo feedforward dynamic matrix control (PFFDMC) algorithm is proposed. The novel PFFDMC presented in this article is applied to replace the traditional dynamic matrix control (DMC) in the lower layer and thus achieve the closed-loop reference trajectory of ORC system expected by field engineers as closely as possible without cumbersome adjustment of tuning parameters. Simulations are performed to verify the effectiveness of the proposed strategy on transient performance in comparison with the traditional one.

Distributed Double-Layered Dynamic Matrix Control for Large-Scale System

A distributed double-layered dynamic matrix control is proposed for large-scale systems. In the scheme, a large-scale system is first decomposed into several low-dimensional subsystems, and then a double-layered dynamic matrix control algorithm with distributed structure is developed for these subsystems. The distributed open-loop prediction equation of each subsystem is formed based on the predicted output of each local subsystem and effects of its interconnecting neighbor subsystems. Due to simultaneous optimization, at each prediction, the coupling effects of neighbor subsystems are not available in time. Thus, the assumed value is utilized instead. In the economic optimization stage, conflicts may occur among different economic optimization goals. Utopia-tracking strategy is introduced to optimize multiple steady-state targets. Then, the obtained steady-state target values are taken as reference values and tracked in subsequent dynamic control. The actual control move for each subsystem is finally calculated. The proposed algorithm is tested on Shell heavy oil fractionator benchmark, and the effectiveness is demonstrated by comparing with the typical double-layered dynamic matrix control algorithm.

Estimation of battery open-circuit voltage and state of charge based on dynamic matrix control - extended Kalman filter algorithm

State of Charge (SOC) estimation is one of the most important functions of the battery management system for new energy vehicles. Extended Kalman Filter (EKF) algorithm has been widely used in SOC estimation of lithium-ion batteries (LiBs). However, the model parameters in the SOC estimation algorithm change with the aging of the battery, which makes EKF unable to obtain accurate estimation results. Because of these defects, a battery model is built based on the second-order RC equivalent circuit model. The parameters of the LiB model are identified by an off-line test and the battery simulation model is calibrated. Then, based on the simulation model, the influence of Open Circuit Voltage (OCV) deviation on SOC estimation accuracy of the EKF algorithm is quantitatively analyzed. The results show that the deviation of OCV will affect the accuracy of SOC estimation by the EKF algorithm. When the OCV deviation reaches 15 mV, the SOC estimation error will reach 5%. Subsequently, a method of updating model parameters based on the Dynamic Matrix Control (DMC) algorithm is proposed. And the DMC-EKF algorithm is used to estimate OCV and SOC. The results show that after the DMC algorithm is used to linearize the RC network, the identified OCV parameter deviation is <10 mV, and the SOC deviation estimated by the DMC- EKF algorithm is <5%, which can meet the application requirements. The EKF algorithm can estimate the SOC more accurately after updating the OCV by the DMC algorithm. Compared with EKF algorithm and UKF algorithm without online OCV updating, DMC-EKF algorithm reduces the maximum deviation of SOC estimation by at least 2%. The proposed DMC-EKF algorithm has good accuracy and robustness.

Dual-mode fast DMC algorithm for the control of ORC based waste heat recovery system

Organic Rankine Cycle (ORC) system stands out in low-grade waste heat recovery for its outstanding performance. Considering the fluctuating nature of the heat source, model predictive control (MPC) is used to control the ORC systems and has achieved good performance. However, with the increase of the number of variables and the expansion of the control/prediction horizon, MPC will take longer calculation time. This may bring about the incapacity to obtain optimization problem solutions in one sampling instant and finally, lead to the failure of the setpoint tracking. To address this problem, in this article, a dual-mode fast dynamic matrix control (FDMC) algorithm grounded on singular value decomposition (SVD) and dynamic matrix control (DMC) is proposed. The presented algorithm features in its calculation speed improvement on the premise of ensuring tracking performance. Two simulations on disturbance rejection and setpoint tracking are performed to verify the effectiveness and rapidity of the proposed algorithm in comparison with the traditional DMC approach.

Optimization control of a 330 MW drum boiler unit based on DMC algorithm and DEB strategy

This paper firstly established a nonlinear dynamic model of a 330 MW drum boiler unit, which has a clear physical meaning and is conducive to the design of coordinated control system (CCS). On this basis, the boiler energy storage coefficient is calculated, and its relationship with that in direct energy balance (DEB) strategy is analyzed. Secondly, this paper proposes a CCS based on dynamic matrix control (DMC) algorithm and DEB strategy, in which: (1) energy demand and status signals of DEB are taken as the setting point and process value of DMC controller, so as to overcome the internal disturbance of the boiler; (2) a compensation signal is constructed as the feedforward input of DMC controller, so as to overcome the external disturbance of the turbine and realize the timely utilization and supplement of boiler energy. Simulation shows: (1) there is a certain deviation in main steam pressure when the energy demand and status signals are taken as the setting point and process value, but this is an illusion of insufficient energy, and in fact the energy status can already meet the demand; (2) compared with the main steam valve, the constructed compensation signal takes into account more operating parameters of the unit, which greatly improves the accuracy of the compensation. Practical application shows: the grid dispatch order can be well tracked by the unit, the maximum deviation of main steam pressure is ±0.6 MPa in constant pressure mode, and that is ±1.2 MPa in sliding pressure mode, thereby improving the control performance of the unit under high, medium, low, and overall load conditions.

Two-layer structure strategy for large-scale systems integrating online adaptive constraints adjustment method and cooperative distributed DMC algorithm

In this paper, a distributed two-layer structure strategy for large-scale systems is described. In the upper level of the structure, usually known as the Steady State Target Optimizer (SSTO) layer, we fully consider the possible constraints in the industrial process as well as their priority order and put forward an online adaptive constraints adjustment (OACA) scheme to ensure the stable operation of the production device. Based on Pareto optimal, a new cooperative distributed dynamic matrix control (CDDMC) algorithm is proposed for the lower MPC layer. The algorithm makes use of the finite step response model and Dynamic Matrix Control (DMC) method which are commonly applied in the process industry, decomposes the large-scale system into multiple interconnected subsystems for a significantly reduced computational burden, and works over a cooperative way based on Jacobi-type iteration to achieve the global optimal solution. Then the convergence of the CDDMC algorithm is investigated and the offset-free control of the strategy is discussed. Finally, the two-layer structure distributed strategy is applied to two examples to analyze its applicability and effectiveness in comparison with the centralized one.

Optimization and Simulation of DMC Algorithm with Terminal Weight Based on LQR Controller

Based on the multivariable dynamic matrix control algorithm, there are many similarities between the dynamic matrix control algorithm and LQR in the form of state equation, state variable and objective function. We can use the objective function of LQR to improve the objective function of DMC and improve the control effect of the system. Using the given mathematical model, the terminal weighting matrix of LQR is applied to DMC algorithm, and the optimized multivariable dynamic matrix control algorithm is simulated. The results show that the algorithm can effectively reduce the response time of the system, make the system sink faster and reach the given value faster.

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.

Speed Control of Pipeline Inner Detector Based on Interval Dynamic Matrix Control With Additional Margin

Inpipe inspection technology is an important method for pipelines detection, and the smooth running speed of the inner detector is a prerequisite for ensuring the quality of inspection. Since the inner detector runs as a black box in the pipeline, it is difficult to observe the current speed state, and the energy source it carries is limited. To overcome the above problems, this article proposes an interval dynamic matrix control algorithm with additional margin (AM-IDMC). First, as an optimized control strategy, interval control can suppress disturbances and reduce energy consumption with smaller actions, which is a novel way to solve the speed control problem of the inner detector. Second, the dynamic matrix control can effectively predict the speed of the inner detector. At the same time, the additional margin method can avoid the actual speed from violating the expected interval to the greatest extent, allowing the controller to intervene in the control as soon as possible. Third, an adaptive penalty coefficient and interval reference trajectory are designed to ensure the rapidity and stability of the speed adjustment process. This article also systematically and completely builds the speed control model of the inner detector from pressurizing station and discharge device. The results have demonstrated that the AM-IDMC algorithm has good performance and has a good effect on the speed control of the inner detector.

Perturbation Analysis and Control of Mach Number 2.4-Meter Transonic Wind Tunnel

Because of the large domestic civil aircraft projects started in China a decade ago, there is a greater need to control the accuracy of the Mach number in aerodynamic tests, especially near the designed cruise point of large commercial aircraft. Nowadays the control accuracy of China Aerodynamics Research and Development Center 2.4-meter transonic wind tunnel Mach number is in the range of to when , which is far from the measurement accuracy of drag coefficient required for testing advanced aircraft. This value should result in a better-than-one drag count. As a consequence, it is imperative to improve the control accuracy of Mach number urgently. The nonlinearity, large time delays, and strong coupling of wind tunnel flowfield control, along with the variation of the model angle of attack, could cause the Mach number to deviate from the expected value. To solve these problems, a model predictive control method based on dynamic matrix control algorithm is proposed. This method builds a prediction model based on step response test. The accuracy of Mach number predictive control can be efficiently improved by performance optimization in the form of vector norms, rolling optimization, and feed-forward compensation. This control strategy has been successfully tested in the wind tunnel, and the control accuracy of Mach number has been remarkably enhanced, to the point where it can be controlled to within . This value satisfies the requirements of aerodynamic aircraft testing.

Design of Distributed Fractional Order PID Type Dynamic Matrix Controller for Large-Scale Process Systems

As a typical representative of distributed model predictive control, distributed dynamic matrix control (DDMC) is able to satisfy the basic control requirements for large-scale systems. However, the constraints and disturbances in actual industrial process usually lead to the slow set-point target tracking, large overshoot and weak anti-interference ability of the system. Therefore, the relevant requirements may not be met for some complex industrial processes. The existing distributed PID type dynamic matrix control (PID-DDMC) method can improve the control performance, but it maybe not accurate enough in some cases. Based on this background, this article introduces fractional order PID (FOPID) into distributed dynamic matrix control, and proposes a distributed fractional order PID type dynamic matrix control (FOPID-DDMC) algorithm. To compare with the conventional PID control, it expands the control and parameter setting range of the controller, and makes the control effect of the controller more accurate. Furthermore, the coupling effect among subsystems is dispelled by adopting the Nash optimal theory, and information interaction between the subsystems through network communication is realized, thereby, completing the optimization of the whole large-scale system. Finally, through a numerical simulation example and a level-temperature control process, the feasibility of the proposed algorithm is demonstrated by comparing with the traditional DDMC and PID-DDMC.

Fast Analytical Model Predictive Controllers and Their Implementation for STM32 ARM Microcontroller

This paper describes fast versions of model predictive control (MPC) algorithms and their practical implementation using the STM32 ARM microcontroller. Two MPC algorithms are considered: Dynamic Matrix Control (DMC) and Generalized Predictive Control (GPC). Computationally efficient Fast DMC (FDMC) and Fast GPC (FGPC) algorithms are derived in which the values of the manipulated variables are calculated from uncomplicated explicit formulas. To demonstrate effectiveness of the discussed algorithms, two emulated benchmark processes and a laboratory servo are considered. The influence of some tuning parameters on algorithms’ calculation time is studied. It is shown that for short sampling periods the classical DMC and GPC algorithms fail to work since calculations last longer than the sampling period, which is unacceptable. Conversely, the FDMC and FGPC algorithms require only hundreds or tens of microseconds and single microseconds, respectively. Hence, proposed algorithms may be used for very fast processes, with very short sampling time.