Modeling a multivariable reactor and on-line model predictive control

A nonlinear first principle model is developed for a laboratory-scaled multivariable chemical reactor rig in this paper and the on-line model predictive control (MPC) is implemented to the rig. The reactor has three variables-temperature, pH, and dissolved oxygen with nonlinear dynamics-and is therefore used as a pilot system for the biochemical industry. A nonlinear discrete-time model is derived for each of the three output variables and their model parameters are estimated from the real data using an adaptive optimization method. The developed model is used in a nonlinear MPC scheme. An accurate multistep-ahead prediction is obtained for MPC, where the extended Kalman filter is used to estimate system unknown states. The on-line control is implemented and a satisfactory tracking performance is achieved. The MPC is compared with three decentralized PID controllers and the advantage of the nonlinear MPC over the PID is clearly shown.     

Nonlinear predictive control of a boiler-turbine unit: A state-space approach with successive on-line model linearisation and quadratic optimisation

This paper details development of a Model Predictive Control (MPC) algorithm for a boiler-turbine unit, which is a nonlinear multiple-input multiple-output process. The control objective is to follow set-point changes imposed on two state (output) variables and to satisfy constraints imposed on three inputs and one output. In order to obtain a computationally efficient control scheme, the state-space model is successively linearised on-line for the current operating point and used for prediction. In consequence, the future control policy is easily calculated from a quadratic optimisation problem. For state estimation the extended Kalman filter is used. It is demonstrated that the MPC strategy based on constant linear models does not work satisfactorily for the boiler-turbine unit whereas the discussed algorithm with on-line successive model linearisation gives practically the same trajectories as the truly nonlinear MPC controller with nonlinear optimisation repeated at each sampling instant.     

A distributed model predictive control based load frequency control scheme for multi-area interconnected power system using discrete-time Laguerre functions

This paper proposes a distributed model predictive control based load frequency control (MPC-LFC) scheme to improve control performances in the frequency regulation of power system. In order to reduce the computational burden in the rolling optimization with a sufficiently large prediction horizon, the orthonormal Laguerre functions are utilized to approximate the predicted control trajectory. The closed-loop stability of the proposed MPC scheme is achieved by adding a terminal equality constraint to the online quadratic optimization and taking the cost function as the Lyapunov function. Furthermore, the treatments of some typical constraints in load frequency control have been studied based on the specific Laguerre-based formulations. Simulations have been conducted in two different interconnected power systems to validate the effectiveness of the proposed distributed MPC-LFC as well as its superiority over the comparative methods.     

Fuel cell starvation control using model predictive technique with Laguerre and exponential weight functions

Fuel cell system is a complicated system that requires an efficient controller. Model predictive control is a prime candidate for its optimization and constraint handling features. In this work, an improved model predictive control (MPC) with Laguerre and exponential weight functions is proposed to control fuel cell oxygen starvation problem. To get the best performance of MPC, the control and prediction horizons are selected as large as possible within the computation limit. An exponential weight function is applied to place more emphasis on the current time and less emphasis on the future time in the optimization process. This leads to stable numerical solution for large prediction horizons. Laguerre functions are used to capture most of the control trajectory, while reducing the controller computation time and memory for large prediction horizons. Robustness and stability of the proposed controller are assessed using Monte-Carlo simulations. Results verify that the modified MPC is able to mimic the performance of the infinite horizon controller, discrete linear quadratic regulator (DLQR). The controller computation time is reduced approximately by one order of magnitude compared to traditional MPC scheme. Results from Monte-Carlo simulations prove that the proposed controller is robust and stable up to system parameters uncertainty of 40%.     

Extended model predictive control scheme for smooth path following of autonomous vehicles

This paper presents an extended model predictive control (MPC) scheme for implementing optimal path following of autonomous vehicles, which has multiple constraints and an integrated model of vehicle and road dynamics. Road curvature and inclination factors are used in the construction of the vehicle dynamic model to describe its lateral and roll dynamics accurately. Sideslip, rollover, and vehicle envelopes are used as multiple constraints in the MPC controller formulation. Then, an extended MPC method solved by differential evolution optimization algorithm is proposed to realize optimal smooth path following based on driving path features. Finally, simulation and real experiments are carried out to evaluate the feasibility and the effectiveness of the extended MPC scheme. Results indicate that the proposed method can obtain the smooth transition to follow the optimal drivable path and satisfy the lateral dynamic stability and environmental constraints, which can improve the path following quality for better ride comfort and road availability of autonomous vehicles.     

Nonlinear predictive control for Hammerstein–Wiener systems

This paper discusses a nonlinear Model Predictive Control (MPC) algorithm for multiple-input multiple-output dynamic systems represented by cascade Hammerstein–Wiener models. The block-oriented Hammerstein–Wiener model, which consists of a linear dynamic block embedded between two nonlinear steady-state blocks, may be successfully used to describe numerous processes. A direct application of such a model for prediction in MPC results in a nonlinear optimisation problem which must be solved at each sampling instant on-line. To reduce the computational burden, a linear approximation of the predicted system trajectory linearised along the future control scenario is successively found on-line and used for prediction. Thanks to linearisation, the presented algorithm needs only quadratic optimisation, time-consuming and difficult on-line nonlinear optimisation is not necessary. In contrast to some control approaches for cascade models, the presented algorithm does not need inverse of the steady-state blocks of the model. For two benchmark systems, it is demonstrated that the algorithm gives control accuracy very similar to that obtained in the MPC approach with nonlinear optimisation while performance of linear MPC and MPC with simplified linearisation is much worse.     

A simplified predictive control algorithm for disturbance rejection

Model predictive control (MPC) offers several advantages for control of chemical processes. However, the standard MPC may do a poor job in suppressing the effects of certain disturbances. This shortcoming is mainly due to the assumption that disturbances remain constant over the prediction horizon. In this paper, a simple disturbance predictor (SDP) is developed to provide predictions of the unmodeled deterministic disturbances for a simplified MPC algorithm. The prediction is developed by curve fitting of the past information. A tuning parameter is employed to handle a variety of disturbance dynamics and a procedure is presented to find an optimum value of the tuning parameter online. A comparison is made with the commonly used disturbance prediction on three example problems. The results show that an improved regulatory performance and zero offset can be achieved under both regular and ramp output disturbances by using the proposed disturbance predictor.     

Model predictive controller-based multi-model control system for longitudinal stability of distributed drive electric vehicle

Distributed drive electric vehicle(DDEV) has been widely researched recently, its longitudinal stability is a very important research topic. Conventional wheel slip ratio control strategies are usually designed for one special operating mode and the optimal performance cannot be obtained as DDEV works under various operating modes. In this paper, a novel model predictive controller-based multi-model control system (MPC-MMCS) is proposed to solve the longitudinal stability problem of DDEV. Firstly, the operation state of DDEV is summarized as three kinds of typical operating modes. A submodel set is established to accurately represent the state value of the corresponding operating mode. Secondly, the matching degree between the state of actual DDEV and each submodel is analyzed. The matching degree is expressed as the weight coefficient and calculated by a modified recursive Bayes theorem. Thirdly, a nonlinear MPC is designed to achieve the optimal wheel slip ratio for each submodel. The optimal design of MPC is realized by parallel chaos optimization algorithm(PCOA)with computational accuracy and efficiency. Finally, the control output of MPC-MMCS is computed by the weighted output of each MPC to achieve smooth switching between operating modes. The proposed MPC-MMCS is evaluated on eight degrees of freedom(8DOF)DDEV model simulation platform and simulation results of different condition show the benefits of the proposed control system.     

T–S fuzzy model predictive speed control of electrical vehicles

This paper proposes a novel nonlinear model predictive controller (MPC) in terms of linear matrix inequalities (LMIs). The proposed MPC is based on Takagi–Sugeno (TS) fuzzy model, a non-parallel distributed compensation (non-PDC) fuzzy controller and a non-quadratic Lyapunov function (NQLF). Utilizing the non-PDC controller together with the Lyapunov theorem guarantees the stabilization issue of this MPC. In this approach, at each sampling time a quadratic cost function with an infinite prediction and control horizon is minimized such that constraints on the control input Euclidean norm are satisfied. To show the merits of the proposed approach, a nonlinear electric vehicle (EV) system with parameter uncertainty is considered as a case study. Indeed, the main goal of this study is to force the speed of EV to track a desired value. The experimental data, a new European driving cycle (NEDC), is used in order to examine the performance of the proposed controller. First, the equivalent TS model of the original nonlinear system is derived. After that, in order to evaluate the proficiency of the proposed controller, the achieved results of the proposed approach are compared with those of the conventional MPC controller and the optimal Fuzzy PI controller (OFPI), which are the latest research on the problem in hand.     

Output feedback model predictive control of hydraulic systems with disturbances compensation

Enhancing the robustness of output feedback control has always been an important issue in hydraulic servo systems. In this paper, an output feedback model predictive controller (MPC) with the integration of an extended state observer (ESO) is proposed for hydraulic systems. The ESO was designed to estimate not only the unmeasured system states but also the disturbances, which will be synthesized into the design of the output prediction equation. Based on the mechanism of receding horizon and repeating optimization of MPC, the output prediction equation will be updated in real time and the future behavior of the system will be accurately predicted since the disturbances are compensated effectively. Hence, the ability of the traditional MPC to suppress disturbances will be improved evidently. The experiment results show that the proposed controller has high-performance nature and strong robustness against various model uncertainties, which verifies the effectiveness of the proposed control strategy.     

Comparative Study of Trajectory Tracking Control for Automated Vehicles via Model Predictive Control and Robust H-infinity State Feedback Control

A comparative study of model predictive control(MPC) schemes and robust H_∞ state feedback control(RSC) method for trajectory tracking is proposed in this paper. The main objective of this paper is to compare MPC and RSC controllers' performance in tracking predefined trajectory under different scenarios. MPC controller is designed based on the simple longitudinal-yaw-lateral motions of a single-track vehicle with a linear tire, which is an approximation of the more realistic model of a vehicle with double-track motion with a non-linear tire mode. RSC is designed on the basis of the same method as adopted for the MPC controller to achieve a fair comparison. Then, three test cases are built in CarSim-Simulink joint platform. Specifically, the verification test is used to test the tracking accuracy of MPC and RSC controller under well road conditions. Besides, the double lane change test with low road adhesion is designed to find the maximum velocity that both controllers can carry out while guaranteeing stability. Furthermore, an extreme curve test is built where the road adhesion changes suddenly, in order to test the performance of both controllers under extreme conditions. Finally, the advantages and disadvantages of MPC and RSC under different scenarios are also discussed.     

Practical approach to tuning MPC

This paper presents the results of a heuristic approach for developing model predictive control (MPC) tuning rules. The tuning has been applied and tested in easy-to-use MPC. Process modeling in this MPC uses normalized input/ output range. As a result there is no need for tuning outputs, a procedure known as adjusting equal concern error. Penalties on moves are set as a function of process dead time as the primary factor, with some correction from process gain. The default calculation delivers robust control, which tolerates up to triple increase in process static gain. If control is too aggressive, further on-line adjustment can be done by set point reference trajectory. Test results show that this tuning is robust for process gain change, however, it is much less efficient in compensating for process dead-time changes. It was found that dead-time mismatch is much better compensated with the model correction filter. Combining the three handles, i.e., penalties on moves, reference trajectory, and model filter, easy and intuitively understandable MPC tuning was achieved. The findings are illustrated by numerous MPC simulated tests.     

不可靠WSN时钟同步网络化输出反馈MPC量化分析

在Cyber-Physical环境下,时钟同步双向信息交换过程中,包含时钟信息的数据包丢失将对时钟同步性能产生影响。讨论了现代控制理论状态空间模型的输出反馈Tubes-MPC时钟同步方法。由分离原理,设计了本地化的状态估计器与控制器,实现了输出反馈Tubes-MPC时钟同步的指数稳定。以不完全量测下的观测模型为基础,定量分析了统计意义下的同步误差方差上界与下界,并采用MPC中Set-Theory-in-Control方法,将完全量测下的干扰误差集合运算于由丢包所引入的附加的估计误差集合,建立了集合约束下的模型预测优化模型。已构建的统一框架下的输出反馈Tubes-MPC时钟同步系统化方法,综合考量了控制理论在线计算复杂度与网络控制观点应用的可行性,对无线网络的不可靠性、网络规模、收敛性能具有鲁棒性,进一步容易扩展为网络级绝对时钟状态空间模型。     

A comparison of a novel robust decentralised control strategy and MPC for industrial high purity,high recovery,multicomponent distillation

In this work we have developed a novel, robust practical control structure to regulate an industrial methanol distillation column. This proposed control scheme is based on a override control framework and can manage a non-key trace ethanol product impurity specification while maintaining high product recovery. For comparison purposes, a MPC with a discrete process model (based on step tests) was also developed and tested. The results from process disturbance testing shows that, both the MPC and the proposed controller were capable of maintaining both the trace level ethanol specification in the distillate (X_D) and high product recovery (β). Closer analysis revealed that the MPC controller has a tighter X_D control, while the proposed controller was tighter in β control. The tight X_D control allowed the MPC to operate at a higher X_D set point (closer to the 10 ppm AA grade methanol standard), allowing for savings in energy usage. Despite the energy savings of the MPC, the proposed control scheme has lower installation and running costs. An economic analysis revealed a multitude of other external economic and plant design factors, that should be considered when making a decision between the two controllers. In general, we found relatively high energy costs favour MPC.     

Distributed control architecture for real-time model predictive control for system-level harmonic mitigation in power systems

It can be challenging to design and implement Model Predictive Control (MPC) schemes in systems with fast dynamics. As MPCs often introduce high computational loads, it can be hard to assure real-time properties required by the dynamic system. An understanding of the system’s behavior, to exploit system properties that can benefit real-time implementation is imperative. Moreover, MPC implementations on embedded local devices rarely allows flexibility to changes in model and control philosophy, due to increased complexity and computational loads. A change in control philosophy (run-time) can be quite relevant in power systems that can change from an integrated to a segregated state. This paper proposes a distributed control hierarchy with a real-time MPC implementation, designed as a higher-level control unit, to feed a lower-level control device with references. The higher-level control unit’s objective in this paper is to generate the control reference of an Active Power Filter for system-level harmonic mitigation. In particular, a novel system architecture, which incorporates the higher-level MPC control and handles distribution of control action to low-level controllers, as well as receiving measurements used by the MPC, is proposed to obtain the application’s real-time properties and control flexibility. The higher-level MPC control, which is designed as a distributed control node, can be swapped with another controller (or control philosophy) if the control objective or the dynamic system changes. A standard optimization framework and standard software and hardware technology is used, and the MPC is designed on the basis of repetitive and distributed control, which allows the use of relatively low control update rate. A simulator architecture is implemented with the aim of mimicking a Hardware-In-Loop (HIL) simulator test to evaluate the application’s real-time properties, as well as the application’s resource usage. The results demonstrates that the implementation of the harmonic mitigation application exhibits the real-time requirements of the application with acceptable resource usage.     

具有状态约束的电液伺服系统模型参考鲁棒自适应控制

针对电液伺服系统中的模型不确定性和状态约束问题,设计了一种模型参考鲁棒自适应控制(MRRAC)方法。将电液伺服系统的近似模型作为模型预测控制(MPC)的设计对象,在设计过程中考虑状态约束,并生成受约束的状态期望,作为后续伺服控制方法的参考指令。为了克服液压系统中的模型不确定性,基于反步法设计了鲁棒自适应控制器(RAC),实现了兼顾模型不确定性和状态约束的伺服控制。基于Lyapunov稳定性理论证明了所设计控制策略的闭环渐近稳定性,且系统所有信号均有界。仿真结果表明,控制器对于系统模型不确定性具有较强的鲁棒性,且可实现对指定状态的有效约束,充分验证了该控制策略的有效性。     

A novel auto-tuning PID control mechanism for nonlinear systems

In this paper, a novel Runge–Kutta (RK) discretization-based model-predictive auto-tuning proportional-integral-derivative controller (RK-PID) is introduced for the control of continuous-time nonlinear systems. The parameters of the PID controller are tuned using RK model of the system through prediction error-square minimization where the predicted information of tracking error provides an enhanced tuning of the parameters. Based on the model-predictive control (MPC) approach, the proposed mechanism provides necessary PID parameter adaptations while generating additive correction terms to assist the initially inadequate PID controller. Efficiency of the proposed mechanism has been tested on two experimental real-time systems: an unstable single-input single-output (SISO) nonlinear magnetic-levitation system and a nonlinear multi-input multi-output (MIMO) liquid-level system. RK-PID has been compared to standard PID, standard nonlinear MPC (NMPC), RK-MPC and conventional sliding-mode control (SMC) methods in terms of control performance, robustness, computational complexity and design issue. The proposed mechanism exhibits acceptable tuning and control performance with very small steady-state tracking errors, and provides very short settling time for parameter convergence.     

Improved design of constrained model predictive tracking control for batch processes against unknown uncertainties

In this paper, an improved constrained tracking control design is proposed for batch processes under uncertainties. A new process model that facilitates process state and tracking error augmentation with further additional tuning is first proposed. Then a subsequent controller design is formulated using robust stable constrained MPC optimization. Unlike conventional robust model predictive control (MPC), the proposed method enables the controller design to bear more degrees of tuning so that improved tracking control can be acquired, which is very important since uncertainties exist inevitably in practice and cause model/plant mismatches. An injection molding process is introduced to illustrate the effectiveness of the proposed MPC approach in comparison with conventional robust MPC.