TYPE 1 DIABETIC PATIENT INSULIN DELIVERY USING ASYMMETRIC PI CONTROL

Type 1 diabetes is characterized by the destruction of the only insulin producing cells in the body. The typical course of action consists of daily insulin injections or an insulin pump. Assuming available methods for online monitoring of glucose concentrations, feedback control can be applied to this problem to improve regulation of glucose concentrations. A control algorithm is presented for feedback control of glucose levels in Type 1 patients. The control problem may be viewed as asymmetric, with negative variation from normal values treated with a more aggressive response than positive deviation. A simple asymmetric proportional-integral (PI) controller is presented where controller parameters vary depending on the sign of the current error value. Optimal closed-loop tuning parameters for the asymmetric control system are determined using local search methods. The asymmetric control system is then considered for robustness analysis using standard techniques from linear systems theory.     

A feedback glucose control strategy for type II diabetes mellitus based on fuzzy logic

Most patients with severe Type II diabetes mellitus, characterised by both insulin resistance and β‐cell failure, eventually require insulin therapy. According to the nonlinear dynamics of homeostasis of blood glucose, proportional‐integral (PI) controller, modified by penalising the feedback error using a fuzzy inference system has been developed to maintain normoglycaemia in a simulated patient using a closed‐loop insulin infusion pump. The simulation employs a compartment model proposed by Vahidi et al. [Vahidi et al., Biochem. Eng. J. 2011, 55(1), 7–16]. The results demonstrate that the fuzzy‐based PI controller is superior to a conventional PI controller for the regulation of blood glucose by insulin infusion for Type II diabetic patients. © 2012 Canadian Society for Chemical Engineering     

A comparative study of different types of controllers used for blood glucose regulation system

Maintaining the glucose concentration in normoglycemic range in Type I diabetic patients is challenging. In this study H_∞ control is applied for the insulin delivery to prevent the hyperglycaemic levels in a type I diabetic patient. A nonlinear model is linearized around nominal condition and reduced for control synthesis. H_∞ controller was compared with the two other types of controller and performance results shows evaluatory results.     

混杂系统基于参数规划的状态反馈预测控制

In this article, state feedback predictive controller for hybrid system via parametric programming is proposed. First, mixed logic dynamic （MLD） modeling mechanism for hybrid system is analyzed, which has a distinguished advantage to deal with the logic rules and constraints of a plant. Model predictive control algorithm with moving horizon state estimator （MHE） is presented. The estimator is adopted to estimate the current state of the plant with process disturbance and measurement noise, and the state estimated are utilized in the predictive controller for both regulation and tracking problems of the hybrid system based on MLD model. Off-line parametric programming is adopted and then on-line mixed integer programming problem can be treated as the parameter programming with estimated state as the parameters. A three tank system is used for computer simulation, results show that the proposed MHE based predictive control via parametric programming is effective for hybrid system with model/olant mismatch, and has a potential for the engineering applications.     

Dynamic output feedback covariance control of stochastic dissipative partial differential equations

In this work, we develop a method for dynamic output feedback covariance control of the state covariance of linear dissipative stochastic partial differential equations (PDEs) using spatially distributed control actuation and sensing with noise. Such stochastic PDEs arise naturally in the modeling of surface height profile evolution in thin film growth and sputtering processes. We begin with the formulation of the stochastic PDE into a system of infinite stochastic ordinary differential equations (ODEs) by using modal decomposition. A finite-dimensional approximation is then obtained to capture the dominant mode contribution to the surface roughness profile (i.e., the covariance of the surface height profile). Subsequently, a state feedback controller and a Kalman-Bucy filter are designed on the basis of the finite-dimensional approximation. The dynamic output feedback covariance controller is subsequently obtained by combining the state feedback controller and the state estimator. The steady-state expected surface covariance under the dynamic output feedback controller is then estimated on the basis of the closed-loop finite-dimensional system. An analysis is performed to obtain a theoretical estimate of the expected surface covariance of the closed-loop infinite-dimensional system. Applications of the linear dynamic output feedback controller to both the linearized and the nonlinear stochastic Kuramoto-Sivashinsky equations (KSEs) are presented. Finally, nonlinear state feedback controller and nonlinear output feedback controller designs are also presented and applied to the nonlinear stochastic KSE.     

Gain scheduling PID control for directed self-assembly of colloidal particles in microfluidic devices

Directed self-assembly provides a promising route to fabricate small-scale structures for various engineering applications. The use of the external fields of variable strength and frequency allows for active controls to be implemented. For assembling specific structural features, precise control over a local particle density is often needed, which can be achieved using feedback control. However, the strong nonlinear behavior of directed self-assembly complicates such control. In this work, a gain-scheduling feedback control strategy for directed self-assembly of colloidal particles is presented. The process gain is described by an empirical steady-state model, which is used for scheduling a proportional-integral feedback controller. The automated controller is implemented experimentally in a microfluidic device for directed self-assembly of colloidal particles. The gain-scheduled controller shows a significantly improved dynamic performance compared with a conventional proportional-integral controller over a broad range of operating parameters.     

Assessment of controller performance: a relay feedback approach

Assessment of control loop performance is one of the important tasks to be carried out in a plant, regardless of the control strategy. The present work utilizes the shape information from single relay feedback test to assess the performance of a feedback system. The process considered is a typical first-order plus dead time process and the controller used is PI type of controller. An ideal relay is introduced in the feedback loop before the controller. The shape of the relay output characterizes the performance of the controller. The mismatch in the integral time can also be observed from the shape. Based on the shape information, analytical expressions for relay feedback responses are derived and straightforward procedures are evolved to assess the performance of the controller. The proposed scheme assesses the controller performance and computes the new tuning parameters, in case retuning of the controller is necessary. The robustness of the method is also tested for second-order plus dead time as well as for higher order systems. More importantly the present approach employs only one relay test for (1) assessment and (2) retuning of the controller. It provides a reliable way that is compatible even to a non-expert operator to assess the controller performance.     

不对称系统输入反馈预测控制及可控性分析

研究了生产过程中一类特殊的非线性系统,不对称系统的预测控制方法。在正反方向的控制作用下,这类系统表现出不对称动态特性。此类系统的理论研究特别是控制方法研究十分有限。针对基于正反方向上的线性模型设计的正反模型预测控制方法与传统预测控制方法在结构上的差异进行了分析,说明了由于这种结构上的差异可能导致的模型失配及控制效果不佳,然后采用输入反馈方法对不对称系统正反模型预测控制方法进行了修正,将实际施加给对象的控制作用通过反馈形式纳入到下一步正反方向控制律的求解中。并且在无约束的条件下分析了正反模型预测控制方法的可控性。最后通过pH值控制的仿真实验验证了此两种不对称系统正反模型预测控制方法的控制效果。     

A method for robustness analysis of controlled nonlinear systems

This paper presents an approach to analyzing robustness properties of nonlinear systems under feedback control. The core idea is to apply numerical bifurcation analysis to the closed-loop process, using the controller/observer tuning parameters, the set points, and parameters describing model uncertainty (parametric as well as unmodeled dynamics) as bifurcation parameters. By analyzing the Hopf bifurcation and saddle-node bifurcation loci with respect to these parameters, bounds on the controller tuning are identified which can serve as a measure for the robustness of the controlled system. These bounds depend upon the type as well as the degree of mismatch that exists between the plant and the model used for controller design.The method is illustrated by analyzing three control systems which are applied to a continuously operated stirred tank reactor: a state feedback linearizing controller and two output feedback linearizing controllers. While model uncertainty has only a minor effect on the tuning of the state feedback linearizing controller, this does not represent a very realistic scenario. However, when an observer is implemented in addition to the controller and an output feedback linearizing scheme is investigated, it is found that the plant-model mismatch has a much more profound impact on the tuning of the observer than it has on the controller tuning. In addition, two observer designs with different level of complexity are investigated and it is found that a scheme which makes use of additional knowledge about the system will not necessarily result in better stability properties as the level of uncertainty in the model increases. These investigations are carried out using the robustness analysis scheme introduced in this paper.     

Double-command fuzzy control of a nonlinear CSTR

In this research, double-command control of a nonlinear chemical system is addressed. The system is a stirred tank reactor; two flows of liquid with different concentrations enter the system through two valves and another flow exits the tank with a concentration between the two input concentrations. Fuzzy logic was employed to design a model-free double-command controller for this system in the simulation environment. In order to avoid output chattering and frequent change of control command (leading to frequent closing-opening of control valves, in practice) a damper rule is added to the fuzzy control system. A feedforward (steady state) control law is also derived from the nonlinear mathematical model of the system to be added to feedback (fuzzy) controller generating transient control command. The hybrid control system leads to a very smooth change of control input, which suits real applications. The proposed control system offers much lower error integral, control command change and processing time in comparison with neuro-predictive controllers.     

Decentralized Control System Design under Uncertainty Using Mixed‐Integer Optimization

Decentralized control system design comprises the selection of a suitable control structure and controller parameters. In this contribution, the optimal control structure and the optimal controller parameters are determined simultaneously using mixed‐integer dynamic optimization (MIDO) under uncertainty, to account for nonlinear process dynamics and various disturbance scenarios. Application of the sigma point method is proposed in order to approximate the expectation and the variance of a chosen performance index with a minimum number of points to solve the MIDO problem under uncertainty. The proposed methodology is demonstrated with a benchmark problem of an inferential control for a reactive distillation column. The results are compared with established heuristic design methods and with previous deterministic approaches.     

Delay‐range‐dependent guaranteed cost control for batch processes with state delay

A guaranteed cost control scheme is proposed for batch processes described by a two‐dimensional (2‐D) system with uncertainties and interval time‐varying delay. First, a 2‐D controller, which includes a robust feedback control to ensure performances over time and an iterative learning control to improve the tracking performance from cycle to cycle, is formulated. The guaranteed cost law concept of the proposed 2‐D controller is then introduced. Subsequently, by introducing the Lyapunov–Krasovskii function and adding a differential inequality to the Lyapunov function for the 2‐D system, sufficient conditions for the existence of the robust guaranteed cost controller are derived in terms of matrix inequalities. A design procedure for the controller is also presented. Furthermore, a convex optimization problem with linear matrix inequality (LMI) constraints is formulated to design the optimal guaranteed cost controller that minimizes the upper bound of the closed‐loop system cost. The proposed control law can stabilize the closed‐loop system as well as guarantee H_∞ performance level and a cost function with upper bounds for all admissible uncertainties. The results can be easily extended to the constant delay case. Finally, an illustrative example is given to demonstrate the effectiveness and advantages of the proposed 2‐D design approach. © 2013 American Institute of Chemical Engineers AIChE J, 59: 2033–2045, 2013     

Optimization‐Based Nonlinear Centralized Controller Tuning of Liquid‐Liquid Extraction Processes

Abstract

The control problem of an agitated contactor is considered in this work. A Scheibel extraction column is modeled using the non‐equilibrium backflow mixing cell model. Model dynamic analysis shows that this process is highly nonlinear, thus the control problem solution of such a system needs to tackle the process nonlinearity efficiently. The control problem of this process is solved by developing a multivariable nonlinear control system implemented in MATLAB?. In this control methodology, a new controller tuning method is adopted, in which the time‐domain control parameter‐tuning problem is solved as a constrained optimization problem. A MIMO (multi‐input multi‐output) PI controller structure is used in this strategy. The centralized controller uses a 2×2 transfer function and accounts for loops interaction. The controller parameters are tuned using an optimization‐based algorithm with constraints imposed on the process variables reference trajectories. Incremental tuning procedure is performed until the extractor output variables transient response satisfies a preset uncertainty which bounds around the reference trajectory. A decentralized model‐based IMC (internal model control) control strategy is compared with the newly developed centralized MIMO PI control one. Stability and robustness tests are applied to the two algorithms. The performance of the MIMO PI controller is found to be superior to that of the conventional IMC controller in terms of stability, robustness, loops interaction handling, and step‐change tracking characteristics.     

鲁棒模型预测控制系统的评估基准

在控制系统的性能评估中,基准的设计是个重要问题。将基本设计极限理论推广到模型预测控制系统(MPC),建立性能评估基准。直接考虑多输入多输出系统的频域扰动,建立输出反馈鲁棒模型预测控制器。此控制器仅仅依赖于过程参数,也是令闭环系统达到控制性能极限的基准控制器。建立了用于评估的性能指标,提出基于此基准的性能评估程序,用以评价其他模型预测控制系统的性能。数学算例证实了这一评估程序的有效性。     

High dose flaxseed oil supplementation may affect fasting blood serum glucose management in human type 2 diabetics

Type 2 diabetes is characterized partially by elevated fasting blood serum glucose and insulin concentrations and the percentage of hemoglobin as HbA1c. It was hypothesized that each of blood glucose and its co-factors insulin and HbA1c and would show a more favorable profile as the result of flaxseed oil supplementation. Patients were recruited at random from a population pool responding to a recruitment advertisement in the local newspaper and 2 area physicians. Completing the trial were 10 flaxseed oil males, 8 flaxseed oil females, 8 safflower (placebo) oil males and 6 safflower oil females. Patients visited on two pre-treatment occasions each three months apart (visits 1 and 2). At visit 2 subjects were randomly assigned in double blind fashion and in equal gender numbers to take flaxseed oil or safflower oil for three further months until visit 3. Oil consumption in both groups was approximately 10 g/d. ALA intake in the intervention group was approximately 5.5 g/d. Power was 0.80 to see a difference of 1 mmol of glucose /L using 12 subjects per group with a p < 0.05. Flaxseed oil had no impact on fasting blood serum glucose, insulin or HbA1c levels. It is concluded that high doses of flaxseed oil have no effect on glycemic control in type 2 diabetics.     

Boundary control synthesis for a lithium‐ion battery thermal regulation problem

The thermal regulation problem for a lithium ion (Li‐ion) battery with boundary control actuation is considered. The model of the transient temperature dynamics of the battery is given by a nonhomogeneous parabolic partial differential equation (PDE) on a two‐dimensional spatial domain which accounts for the time‐varying heat generation during the battery discharge cycle. The spatial domain is given as a disk with radial and angular coordinates which captures the nonradially symmetric heat‐transfer phenomena due to the application of the control input along a portion of the spatial domain boundary. The Li‐ion battery model is formulated within an appropriately defined infinite‐dimensional function space setting which is suitable for spectral controller synthesis. The key challenges in the output feedback model‐based controller design addressed in this work are: the dependence of the state on time‐varying system parameters, the restriction of the input along a portion of the battery domain boundary, the observer‐based optimal boundary control design where the separation principle is utilized to demonstrate the stability of the closed loop system, and the realization of the outback feedback control problem based on state measurement and interpolation of the temperature field. Numerical results for simulation case studies are presented. © 2013 American Institute of Chemical Engineers AIChE J, 59: 3782–3796, 2013     

Controller adjustment for improved nominal performance and robustness—II. Robust geometric control of a distillation column

In Part I of this paper a general frequency domain method to adjust multivariable controllers with respect to both nominal performance and robustness are presented. In Part II this method is used to examine and improve the control of a binary distillation column. The selected control strategies are conventional PI control and geometric control. The PI controller is adjusted in order to obtain satisfactory robustness properties. The basic geometric controller is extended with feedback from state variables which do not alter the nominal disturbance rejection. Both constant gain feedback and integration are examined. The included control parameters are adjusted for improved nominal performance and for robustness. The major result is that the adjusted geometric controller has a robustness which equals that of the adjusted conventional PI controller. However, the nominal performance of the geometric controller is superior to that of conventional PI control. Thus we expect the adjusted geometric controller to have improved performance on a real column compared to that of conventional PI control.     

AN EXOTHERMIC CONTINUOUS STIRRED TANK REACTOR IS FEEDBACK EQUIVALENT TO A LINEAR SYSTEM

This brief paper demonstrates the concept of linear feedback equivalence for an exothermic eontinu-ous stirred tank reactor with first order kinetics. Feedback control is achieved by finding a transformation for the nonlinear system which carries this system into a linear controllable system in Brunovsky canonical form. A linear state feedback controller is then designed which achieves control over a broad range of operating conditions. This example demonstrates how recent developments in nonlinear control theory can be applied to chemical systems without relying on the usual methods of local linearization.     

模糊自适应PI控制在空调系统中的研究

以空气焓差法试验台空调系统的温度控制系统为具体仿真对象建立了数学模型,该空调系统可以看作是一阶惯性加纯滞后的环节,而且对象的过程参数和时延时间是时变的,传统的PID控制无法获得理想的控制效果。提出了一种无需辨识环节的具有智能的模糊自适应PI的控制算法并将其应用在该空调系统中,该算法对模糊控制和PI控制进行有机结合,根据实际控制经验,通过模糊控制规则对控制回路中PI控制器的参数进行实时整定,并将该控制算法和经过良好整定的PI控制器在空调系统中的控制性能进行比较。仿真结果表明,模糊自适应PI控制提高了系统的鲁棒性、减小了超调量、提高了抗干扰能力、缩短了调整时间。     

Experimental simultaneous state and parameter identification of a pH neutralization process based on an extended Kalman Filter

The pH neutralization process is a representative nonlinear process. If a change in feed or buffer streams is introduced, the characteristics of the titration curve are altered and the way of change in titration curve is highly nonlinear. Moreover, if the changes are introduced in the middle of operation, then the nature of the process becomes nonlinear and time-varying. This is the one of the reason why conventional PID controller may fail. Even though the use of buffer solution may alleviate the nonlinearity, the improvement may be limited. A better way to tackle this type of process is to use nonlinear model-based control techniques with online parameter estimation. However, in most cases, the measurements of the process are not adequate enough so that the full state feedback control techniques can be utilized. If the states and crucial parameters are estimated online simultaneously, the effectiveness of the nonlinear state feedback control can be greatly enhanced. Thus, in this study, the capability of simultaneous estimation of states and parameters using Extended Kalman Filter (EKF) are experimentally investigated for a pH neutralization process. The process is modelled using reaction invariants and the concentrations of reaction invariants of the effluent stream (states) and the feed concentrations (parameters) are estimated online. From the comparison of experiments and simulations, it is found that the states and parameters can efficiently be identified simultaneously with EKF so that the estimated information can be exploited by state-feedback control techniques