Abstract : Predictive control (PC) is an advanced optimization control algorithm based on models, employing rolling implementation and feedback correction. Also known as Model Predictive Control (MMC), it is a type of computer control algorithm that emerged in the industrial sectors of Europe and America in the mid-to-late 1970s. This paper discusses the development and current status of predictive control theory, mainly including the stability and robustness of predictive control systems. It also analyzes the current development and application of predictive control in industrial control and its potential future research directions.
Keywords : predictive control; stability; robustness
introduction
Predictive control is an advanced optimization control algorithm based on models, rolling implementation and combined with feedback correction. It is also called model predictive control. It is a new type of computer control algorithm that emerged in the industrial field of Europe and the United States in the mid-to-late 1970s [1]. It does not require high accuracy of the controlled object model, is suitable for systems with large pure time delay and inertia, and has good control quality. Compared with PID control and optimal control and adaptive control, it is more suitable for application in complex industrial process control with many uncertain factors and large time delay. Nowadays, predictive control methods have been applied in petrochemical, power, machinery and metal industries, achieving very good application results and significant economic benefits.
1. Development and Current Status of Predictive Control Algorithms
1.1 Generation Mechanism and Basic Characteristics
In 1978, reference [2] first elaborated in detail the motivation, mechanism, and application effects of this type of algorithm in industrial processes. Since then, predictive control has appeared in the field of control as the unified name for this new type of control algorithm. Prediction is the prediction of the future output state of a system by using known, past nonparametric data models and current input and output information.
Predictive control is welcomed and successfully applied in industrial practice mainly because it has three basic characteristics: predictive model, rolling optimization and feedback correction [3].
The function of a predictive model is to predict the future output of an object based on its historical information and future inputs. It emphasizes the function of the model rather than its structural form, thus providing a basis for comparing the merits of control strategies.
Rolling optimization determines future control actions by finding the optimal performance metric, which relates to the system's future behavior. In predictive control, optimization is not performed offline once, but repeatedly online. This is the meaning of rolling optimization and the fundamental difference between predictive control and traditional optimal control.
The feedback mechanism is undergoing rolling optimization, with each iteration optimizing the mechanism segment by segment over time. At each moment, a local optimization index is proposed that is based on that moment and only involves the prediction time domain, and repeated online optimization is performed.
1.2 Development of Predictive Control Algorithms
Since Richallet et al. proposed the Model Predictive Heuristic Control Algorithm (MPHC) in 1978, predictive control has been greatly developed. Dozens of algorithms have been proposed, including Model Algorithm Control (MAC), Dynamic Matrix Control (DMC), Generalized Predictive Control (GPC), Predictive Function Control (PFC), Generalized Predictive Pole Placement Control (GPP), Internal Model Control (IMC), and Inference Control (IC). These algorithms have been successfully applied in the control of complex industrial processes and have been welcomed and praised by the engineering community. The predictive control discussed at present includes MAC and DMC from industrial production processes, as well as GPC, GPP, and Internal Model Control (IMC) from adaptive control. These are the products of collaboration between the engineering and control theory communities. Among them, Dynamic Matrix Control (DMC), Model Algorithm Control (MAC), and Generalized Predictive Control (GPC) are the three most influential predictive control algorithms [4].
The DMC algorithm is a predictive control algorithm based on the step response of an object. It is suitable for asymptotically stable linear objects. For weakly nonlinear objects, linearization can be performed first at the operating point; for unstable objects, conventional PID control can be used to stabilize them first, and then the DMC algorithm can be used. MAC, also known as Model Predictive Heuristic Control (MPHC), is similar to DMC and is also suitable for asymptotically stable linear objects, but its design premise is their impulse response. As a self-tuning control algorithm, GPC was proposed for stochastic discrete systems and developed from self-tuning control. Therefore, it retains the principle of self-tuning, that is, during the control process, the model parameters are continuously estimated online through actual input and output information, and the control law is corrected accordingly to achieve online identification and correction.
2 Novel Predictive Control Algorithm
In recent years, new theories and algorithms have emerged in the field of control, such as neural networks, fuzzy control, and fuzzy neural networks. These theories, combined with MPC (Multi-Level Control), have led to new theories and methods. These mainly include the following:
(1) Combining neural networks with predictive control, reference [5] proposes a new DMC predictive control algorithm based on BP neural network. In this algorithm, the BP neural network predicts future errors based on a series of past error information and performs online compensation for model prediction errors. As an important supplement to model prediction, it can overcome the influence of various uncertainties and complex changes on system stability.
(2) Combining fuzzy neural networks with predictive control, reference [6] proposed a fuzzy neural network controller based on fuzzy prediction. Using fuzzy neural networks and combining fuzzy prediction, a new controller design method was proposed. In view of the characteristics of large time delay, the manual operation process was simulated, and fuzzy prediction was made based on the influence of the changes in input and output states on the large time delay during the control process. The predicted state was then fed back to the fuzzy neural network, and the fuzzy neural network was trained in this way to achieve effective control.
(3) Combination of predictive control and fuzzy control. Reference [7] proposed a solution to compensate the control quantity by using fuzzy reasoning in the case of model mismatch in general predictive function control. The predictive function control based on fuzzy compensation was applied to the combustion control system of chain grate boiler. Through system simulation, the results show that this controller has strong robustness, adaptability and high control accuracy.
(4) Combining predictive control with adaptive control, Reference [8] proposed a multi-model adaptive predictive controller based on a predictive function controller designed with a local model and a model switching algorithm for the nonlinear processes that exist in reality. This controller can handle high-order objects, achieve seamless switching during control, and ensure the stable operation of the system.
(5) Combining multiple control theories with MPC, the literature [9] proposed a solution based on neural network to identify parameters and compensate control quantities through fuzzy reasoning. The fuzzy compensation prediction function control based on neural network was applied to the boiler combustion control system. Through continuous system simulation, the results showed that this control has strong robustness, high control accuracy, is easy to adjust parameters, and is easy to tune.
3 Performance Analysis of Predictive Control
Closed-loop performance studies of predictive control primarily focus on stability and robustness, while the design and improvement of control algorithms also concentrate on ensuring system stability and enhancing robustness. For constrained MPCs and systems with open-loop instability, non-minimum phase, or time delays, stability studies are challenging both in the infinite time domain and the constrained finite time domain. Robustness refers to the stability of a system when modeling errors or disturbances exist. Research on the robustness of predictive control can be broadly divided into robustness analysis and robustness design. Reference [10] proposed a design method for a fuzzy state variable predictive controller based on LMI. It introduced an index function into the traditional fuzzy state regulator, combined with the idea of predictive control, and theoretically proved that the closed-loop fuzzy predictive control system has global asymptotic stability. Reference [11] discussed the robust stability of the DCS-based predictive PID controller under parameter uncertainty. It used Kharitonov's theorem and marginal theory to analyze the robust stability of the input and output under parameter uncertainty. Reference [12] applied model predictive control to the slurry concentration control system of the hydrogenation reaction unit of the PTA plant and the advanced control and optimization of the dissolution and dehydration tower in the oxidation unit. It developed an advanced control algorithm to study the robust stability of multivariable input and output.
4. Analysis of the Application of Predictive Control in Industrial Fields
Predictive control is not the product of a single unified theory, but rather has gradually developed in the process of industrial practice. Compared with other traditional control algorithms, MPC has more advantages in adapting to and being suitable for industrial environments [13]:
(1) Modeling is relatively convenient and the accuracy requirements of the model are not high, which is in line with the development trend of modern process industry.
(2) The convolution and model described by non-minimum have a larger margin of information, which is conducive to improving the robustness of the system;
(3) It has rolling optimization characteristics, which can compensate for the uncertainty of the controlled object caused by model mismatch, distortion, interference, etc. to a certain extent. It has good tracking performance and strong anti-interference ability, which is more in line with the actual requirements of the process industry.
(4) It can be extended to constrained, delayed, non-minimum phase and nonlinear processes, and can effectively handle multivariable and constrained problems, and can achieve multi-objective optimization.
(5) Robustness is adjustable and has good dynamic control effect.
Due to the aforementioned advantages, MPC has been widely used and achieved great success in industrial process control fields such as petroleum, chemical, and power industries. For example, the DMC controller, represented by the new generation controller DMCplus developed by AspenTech, has been applied in many petrochemical enterprises in my country with remarkable results. The APC-Adcon advanced multivariable robust predictive control software package from Zhejiang Supcon Software Technology Co., Ltd. supports mainstream DCS systems such as SUPCONJX-300X from Zhejiang Supcon, TDC-3000 from Honeywell, and CENTTUMCS and CS3000 from Yokogawa. The MATLAB software package developed by MathWorks includes a Model Predictive Control Toolbox, which allows users to achieve corresponding functions with a single function call, offering convenience, speed, and high efficiency. It has been widely used in control system design, debugging, and computer simulation.
5. Problems and Development Directions in Predictive Control Research
Theoretically, MPC algorithms are quite abundant, and several developed algorithms are mature; however, many theoretical and applied problems remain unresolved. Future attention should be paid to the following aspects:
(1) Stability and robustness of multivariable systems; Although MPC technology has been developed for a long time, it has always been very difficult to study the stability and robustness of MPC systems. A fundamental issue in MPC is the robustness to model uncertainty and noise. Due to the lack of a systematic and unified framework, the study of stability and robustness has always been a weak link in MPC research, whether it is an algorithm based on parametric models or an algorithm based on nonparametric models. This is a major direction for future research.
(2) Seeking new predictive control algorithms and strategies; the development of predictive control is attributed to practitioners rather than the control theorists, and the algorithms lack deeper theoretical support. Therefore, predictive control should not merely stop at the theoretical level of improving existing MPC algorithms, but should focus on the research of new algorithms and seek new ideas and breakthroughs in the three major mechanisms of MPC: predictive models, feedback correction methods, and optimization strategies. Currently, nonlinear MPC and combined MPC will become one of the most important directions for predictive control; future research directions include the synergistic effect of system identification and MPC, constrained MPC algorithms, modeling and parameter estimation of nonlinear systems, and quantitative analysis of the stability and robustness of multivariable constrained systems in predictive control problems in industrial production processes.
(3) Strengthen theoretical application and high-performance software development; advanced algorithms must be implemented in software to be applied in industrial control. While many commercially available advanced control software programs exist abroad, most are only applicable to one or a certain type of algorithm, lacking versatility, and their high price restricts their application in China. Meanwhile, domestic predictive control software lags behind. Strengthening theoretical application and the development of specialized control software has good industrialization prospects and a broad market capacity, and is one of the development directions for high-tech industrial automation in China.
(4) Strengthen the research on intelligent predictive control; With the widespread configuration of computer systems and the increasing scale of industrial production, people have higher and higher requirements for industrial control. In response to practical problems such as uncertainty description, uncertainty environment optimization, multi-objective optimization, expert systems, and high-speed computing in industrial processes, predictive control needs to draw on the ideas of artificial intelligence, control theory and other aspects in a measured way, and develop in the direction of multi-layer intelligent control.
Predictive control, as a novel control method, has already played a crucial role in many fields and will undoubtedly have a significant impact on the control of future industrial processes. Although many pressing theoretical and practical problems remain to be solved in this field, and its industrial applications will continue to raise new challenges, its fundamental principles and adaptability to complex systems are undeniably attractive. In-depth research and widespread application of predictive control will have a positive impact on the development of my country's national economy and the improvement of industrial automation levels. Furthermore, a deeper understanding of the predictive control concept will provide strong support for the integrated optimization of industrial processes.
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Li Ruihong, Master's degree, Teaching Assistant, specializing in control theory and control engineering.
Li Juwei, PhD, Lecturer, specializing in optimal control and complex system modeling.
Shen Jiansen, PhD, Lecturer, mainly engaged in process control and complex system modeling.
