Solution of low-dimensional constrained model predictive control problems

Large benefits are possible by utilizing the solution of the constrained optimization problem involved in model predictive control. For a special case of these problems, the solution can be obtained relatively easily from its relationship with the unconstrained optimum. In this paper, a visualization of the relationship between the constrained and unconstrained optimum is presented. Based upon this relationship, a method for finding the constrained optimum is proposed that is suitable for low-dimensional control systems. A comparison with a linear programming formulation on 2 × 2 and 3 × 3 problems shows that the computational effort can be 10–35 times lower. For such processes, the proposed approach may allow one to avail the benefits of optimization by using the small process control systems already present in many plants.     

Design and analysis of tilt integral derivative controller with filter for load frequency control of multi-area interconnected power systems

In this paper, a novel Tilt Integral Derivative controller with Filter (TIDF) is proposed for Load Frequency Control (LFC) of multi-area power systems. Initially, a two-area power system is considered and the parameters of the TIDF controller are optimized using Differential Evolution (DE) algorithm employing an Integral of Time multiplied Absolute Error (ITAE) criterion. The superiority of the proposed approach is demonstrated by comparing the results with some recently published heuristic approaches such as Firefly Algorithm (FA), Genetic Algorithm (GA) and Particle Swarm Optimization (PSO) optimized PID controllers for the same interconnected power system. Investigations reveal that proposed TIDF controllers provide better dynamic response compared to PID controller in terms of minimum undershoots and settling times of frequency as well as tie-line power deviations following a disturbance. The proposed approach is also extended to two widely used three area test systems considering nonlinearities such as Generation Rate Constraint (GRC) and Governor Dead Band (GDB). To improve the performance of the system, a Thyristor Controlled Series Compensator (TCSC) is also considered and the performance of TIDF controller in presence of TCSC is investigated. It is observed that system performance improves with the inclusion of TCSC. Finally, sensitivity analysis is carried out to test the robustness of the proposed controller by varying the system parameters, operating condition and load pattern. It is observed that the proposed controllers are robust and perform satisfactorily with variations in operating condition, system parameters and load pattern.     

Stabilizing model predictive control for constrained nonlinear distributed delay systems

In this paper, a model predictive control scheme with guaranteed closed-loop asymptotic stability is proposed for a class of constrained nonlinear time-delay systems with discrete and distributed delays. A suitable terminal cost functional and also an appropriate terminal region are utilized to achieve asymptotic stability. To determine the terminal cost, a locally asymptotically stabilizing controller is designed and an appropriate Lyapunov-Krasoskii functional of the locally stabilized system is employed as the terminal cost. Furthermore, an invariant set for locally stabilized system which is established by using the Razumikhin Theorem is used as the terminal region. Simple conditions are derived to obtain terminal cost and terminal region in terms of Bilinear Matrix Inequalities. The method is illustrated by a numerical example.     

Application of full order sliding mode control based on different areas power system with load frequency control

In the traditional sliding mode control method, there always exist the singularity due to the reduced order of the control method. In order to eliminate the singularity, I propose a new full order sliding mode control method in this article, which has been firstly applied to load frequency control. The full order sliding mode control method includes the terminal sliding mode control (TSM) and the linear sliding mode control (LSM). TSM has the good characteristic of eliminating the singularity due to the avoidance of derivative of terms with fractional power factors. While the LSM is easy to design and has fast time convergence comparing to TSM. The model is based on the system with different kinds of turbine or the same kind of turbine, which contains the nonlinearities. The control purpose is to adjust the frequency deviation to zero. Through the simulation results, it is shown that the frequency deviation can be kept to zero in the condition of different load disturbances by the two approaches, which approves the robustness of the proposed methods. In addition, we compare the two methods with the traditional sliding mode control (SMC), which proves the superiority of the two methods in terms of chattering and response time.     

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.     

Modeling and distributed gain scheduling strategy for load frequency control in smart grids with communication topology changes

In this paper, we investigate the modeling and distributed control problems for the load frequency control (LFC) in a smart grid. In contrast with existing works, we consider more practical and real scenarios, where the communication topology of the smart grid changes because of either link failures or packet losses. These topology changes are modeled as a time-varying communication topology matrix. By using this matrix, a new closed-loop power system model is proposed to integrate the communication topology changes into the dynamics of a physical power system. The globally asymptotical stability of this closed-loop power system is analyzed. A distributed gain scheduling LFC strategy is proposed to compensate for the potential degradation of dynamic performance (mean square errors of state vectors) of the power system under communication topology changes. In comparison to conventional centralized control approaches, the proposed method can improve the robustness of the smart grid to the variation of the communication network as well as to reduce computation load. Simulation results show that the proposed distributed gain scheduling approach is capable to improve the robustness of the smart grid to communication topology changes.     

Distributed model predictive control for constrained nonlinear systems with decoupled local dynamics

This paper considers the distributed model predictive control (MPC) of nonlinear large-scale systems with dynamically decoupled subsystems. According to the coupled state in the overall cost function of centralized MPC, the neighbors are confirmed and fixed for each subsystem, and the overall objective function is disassembled into each local optimization. In order to guarantee the closed-loop stability of distributed MPC algorithm, the overall compatibility constraint for centralized MPC algorithm is decomposed into each local controller. The communication between each subsystem and its neighbors is relatively low, only the current states before optimization and the optimized input variables after optimization are being transferred. For each local controller, the quasi-infinite horizon MPC algorithm is adopted, and the global closed-loop system is proven to be exponentially stable.     

Grouped-neural network modeling for model predictive control

A group of feed-forward neural networks (NNs), each providing the prediction of an individual process output at a future step, is used as the dynamic prediction model for the model-based predictive control (MPC) scheme in the proposed work. These NNs are parallel (independent) rather than cascaded--they are trained and implemented in parallel. Therefore, the complexity and effort in the training stage is decreased and compounded error propagation is eliminated from the prediction. A new strategy of compensating for the process-model mismatch under this grouped-NN model structure is also developed. Effectiveness of the scheme as a general nonlinear MPC is demonstrated by simulation results.     

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.     

基于频域分析的预测控制鲁棒性设计

从分析预测控制的内模机理出发，把系统稳定鲁棒性和品质鲁棒性要求作为内模控制器设计的两个约束条件，利用控制理论中频域分析的方法把离散控制系统的控制器设计转化到频域进行分析，推导出满足系统稳定鲁棒性和品质鲁棒性条件的内模控制器，从而得出预测控制鲁棒性设计的条件，使控制系统能较好的抑制外部扰动所产生的影响。仿真实验结果表明该设计比传统的CHR和Cohen-Coon整定算法有更优异的控制效果。     

Control of nonlinear processes by using linear model predictive control algorithms

Most chemical processes are inherently nonlinear. However, because of their simplicity, linear control algorithms have been used for the control of nonlinear processes. In this study, the use of the dynamic matrix control algorithm and a simplified model predictive control algorithm for control of a bench-scale pH neutralization process is investigated. The nonlinearity is handled by dividing the operating region into sub-regions and by switching the controller model as the process moves from one sub-region to another. A simple modification for model predictive control algorithms is presented to handle the switching. The simulation and experimental results show that the modification can provide a significant improvement in the control of nonlinear processes.     

A new model predictive control algorithm by reducing the computing time of cost function minimization for NPC inverter in three-phase power grids

This paper presents a new control strategy based on finite-control-set model-predictive control (FCS-MPC) for Neutral-point-clamped (NPC) three-level converters. Containing some advantages like fast dynamic response, easy inclusion of constraints and simple control loop, makes the FCS-MPC method attractive to use as a switching strategy for converters. However, the large amount of required calculations is a problem in the widespread of this method. In this way, to resolve this problem this paper presents a modified method that effectively reduces the computation load compare with conventional FCS-MPC method and at the same time does not affect on control performance. The proposed method can be used for exchanging power between electrical grid and DC resources by providing active and reactive power compensations. Experiments on three-level converter for three Power Factor Correction (PFC), inductive and capacitive compensation modes verify the good and comparable performance. The results have been simulated using MATLAB/SIMULINK software.     

Distributed fault-tolerant model predictive control for intermittent fault: A cooperative way

For intermittent actuator faults of large-scale system, a cooperative distributed fault-tolerant model predictive control (DFTMPC) is presented. The actuator plug and play strategy is adopted in the interconnected systems with physical coupling making fault estimation and controller redesign unnecessary. The actuator plug and play process is modeled as a distributed switching model, and there a theoretical stability analysis is provided with switching form of model predictive control (MPC) cost functions. The novel cooperative distributed fault-tolerant performance index is raised in a global view for distributed model predictive control. A simulation example is taken to show the e?ectiveness of the proposed method.     

A robust adaptive load frequency control for micro-grids

The goal of this study is to introduce a novel robust load frequency control (LFC) strategy for micro-grid(s) (MG(s)) in islanded mode operation. Admittedly, power generators in MG(s) cannot supply steady electric power output and sometimes cause unbalance between supply and demand. Battery energy storage system (BESS) is one of the effective solutions to these problems. Due to the high cost of the BESS, a new idea of Vehicle-to-Grid (V2G) is that a battery of Electric-Vehicle (EV) can be applied as a tantamount large-scale BESS in MG(s). As a result, a new robust control strategy for an islanded micro-grid (MG) is introduced that can consider electric vehicles׳ (EV(s)) effect. Moreover, in this paper, a new combination of the General Type II Fuzzy Logic Sets (GT2FLS) and the Modified Harmony Search Algorithm (MHSA) technique is applied for adaptive tuning of proportional-integral (PI) controller. Implementing General Type II Fuzzy Systems is computationally expensive. However, using a recently introduced α-plane representation, GT2FLS can be seen as a composition of several Interval Type II Fuzzy Logic Systems (IT2FLS) with a corresponding level of α for each. Real-data from an offshore wind farm in Sweden and solar radiation data in Aberdeen (United Kingdom) was used in order to examine the performance of the proposed novel controller. A comparison is made between the achieved results of Optimal Fuzzy-PI (OFPI) controller and those of Optimal Interval Type II Fuzzy-PI (IT2FPI) controller, which are of most recent advances in the area at hand. The Simulation results prove the successfulness and effectiveness of the proposed controller.     

Robust output feedback distributed model predictive control of networked systems with communication delays in the presence of disturbance

In this work, an output feedback cooperative distributed model predictive control is developed for a class of networked systems composed of interacting subsystems interconnected through their states, in which it handles bounded disturbances and time varying communication delays. A distributed buffer based prediction strategy is used to compensate bounded delays and predict those states, which are coupled between subsystems that their actual values may not available due to delays. In the design of robust distributed model predictive control, distributed moving horizon estimation is employed so that convergence and boundedness of the estimation error are ensured. Furthermore, robust exponential stability of the closed loop system is established. The effectiveness of the proposed method is illustrated using two interconnected continuous stirred tank reactors.     

A novel optimized hybrid fuzzy logic intelligent PID controller for an interconnected multi-area power system with physical constraints and boiler dynamics

In the fast developing world nowadays, load frequency control (LFC) is considered to be a most significant role for providing the power supply with good quality in the power system. To deliver a reliable power, LFC system requires highly competent and intelligent control technique. Hence, in this article, a novel hybrid fuzzy logic intelligent proportional-integral-derivative (FLiPID) controller has been proposed for LFC of interconnected multi-area power systems. A four-area interconnected thermal power system incorporated with physical constraints and boiler dynamics is considered and the adjustable parameters of the FLiPID controller are optimized using particle swarm optimization (PSO) scheme employing an integral square error (ISE) criterion. The proposed method has been established to enhance the power system performances as well as to reduce the oscillations of uncertainties due to variations in the system parameters and load perturbations. The supremacy of the suggested method is demonstrated by comparing the simulation results with some recently reported heuristic methods such as fuzzy logic proportional-integral (FLPI) and intelligent proportional-integral-derivative (PID) controllers for the same electrical power system. the investigations showed that the FLiPID controller provides a better dynamic performance and outperform compared to the other approaches in terms of the settling time, and minimum undershoots of the frequency as well as tie-line power flow deviations following a perturbation, in addition to perform appropriate settlement of integral absolute error (IAE). Finally, the sensitivity analysis of the plant is inspected by varying the system parameters and operating load conditions from their nominal values. It is observed that the suggested controller based optimization algorithm is robust and perform satisfactorily with the variations in operating load condition, system parameters and load pattern.     

Multi-objective optimization for model predictive control

This paper presents a technique of multi-objective optimization for Model Predictive Control (MPC) where the optimization has three levels of the objective function, in order of priority: handling constraints, maximizing economics, and maintaining control. The greatest weights are assigned dynamically to control or constraint variables that are predicted to be out of their limits. The weights assigned for economics have to out-weigh those assigned for control objectives. Control variables (CV) can be controlled at fixed targets or within one- or two-sided ranges around the targets. Manipulated Variables (MV) can have assigned targets too, which may be predefined values or current actual values. This MV functionality is extremely useful when economic objectives are not defined for some or all the MVs. To achieve this complex operation, handle process outputs predicted to go out of limits, and have a guaranteed solution for any condition, the technique makes use of the priority structure, penalties on slack variables, and redefinition of the constraint and control model. An engineering implementation of this approach is shown in the MPC embedded in an industrial control system. The optimization and control of a distillation column, the standard Shell heavy oil fractionator (HOF) problem, is adequately achieved with this MPC.     

Model predictive control based on reduced order models applied to belt conveyor system

In the paper, a model predictive controller based on reduced order model is proposed to control belt conveyor system, which is an electro-mechanics complex system with long visco-elastic body. Firstly, in order to design low-degree controller, the balanced truncation method is used for belt conveyor model reduction. Secondly, MPC algorithm based on reduced order model for belt conveyor system is presented. Because of the error bound between the full-order model and reduced order model, two Kalman state estimators are applied in the control scheme to achieve better system performance. Finally, the simulation experiments are shown that balanced truncation method can significantly reduce the model order with high-accuracy and model predictive control based on reduced-model performs well in controlling the belt conveyor system.     

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.