Synthesis of PID controller for unstable and integrating processes

Properly designed controllers provide stable closed-loop response for open-loop unstable processes. Internal model controller equivalent PID tuning rules for low order unstable plus dead time systems are synthesized in this work. The controller is approximated near the vicinity of zero (origin). Controller parameters are derived by equating the closed-loop response to a control-signature (desired closed-loop response) involving a user defined tuning parameter, λ. Simulations are carried out to show the performance of the proposed tuning scheme for both set point and disturbance rejection cases.     

NONLINEAR MODEL PREDICTIVE CONTROL

Nonlinear Model Predictive Control (NMPC), a strategy for constrained, feedback control of nonlinear processes, has been developed. The algorithm uses a simultaneous solution and optimization approach to determine the open-loop optimal manipulated variable trajectory at each sampling instant. Feedback is incorporated via an estimator, which uses process measurements to infer unmeasured state and disturbance values. These are used by the controller to determine the future optimal control policy. This scheme can be used to control processes described by different kinds of models, such as nonlinear ordinary differential/algebraic equations, partial differential/algebraic equations, integra-differential equations and delay equations. The advantages of the proposed NMPC scheme are demonstrated with the start-up of a non-isothermal, non-adiabatic CSTR with an irreversible, first-order reaction. The set-point corresponds to an open-loop unstable steady state. Comparisons have been made with controllers designed using (1) nonlinear variable transformations, (2) a linear controller tuned using the internal model control approach, and (3) open-loop optimal control. NMPC was able to bring the controlled variable to its set-point quickly and smoothly from a wide variety of initial conditions. Unlike the other controllers, NMPC dealt with constraints in an explicit manner without any degradation in the quality of control. NMPC also demonstrated superior performance in the presence of a moderate amount of error in the model parameters, and the process was brought to its set-point without steady-state offset.     

Computation of multiloop controllers having desired closed-loop responses

For n-by-n multivariable processes, multiloop controllers have n degrees of freedom and hence the n diagonal elements of closed-loop transfer functions can be designed to have desired closed-loop responses. Multiloop controllers having desired closed-loop responses can be considered as an extension of the single-input single-output internal model control and they can be used as reference controllers. However, computations of such multiloop controllers have not been well developed. The Newton-Raphson method and the iterative sequential loop closing method can be used, but they can suffer from a divergence problem for some processes. Here, the continuation method is applied to obtain multiloop control systems with desired closed-loop responses for a robust computation. The multiloop controllers with desired closed-loop responses can be used to obtain dynamic interaction measures and design multiloop PID controllers.     

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.     

PROCESS/MODEL MISMATCH COMPENSATION FOR MODEL-BASED CONTROLLERS

Process model-based control algorithms that employ a process model directly in the controller, have been shown to produce good control performance and robust behaviour, despite process modelling errors. However, when the process/model mismatch is large, the closed-loop response, while still being better than responses obtained by conventional controllers, will be degraded. This paper presents a new approach to compensate for process/model mismatch errors, and is based upon the Generic Model Control (GMC) algorithm. This approach is applicable to both linear and nonlinear model-based algorithms. Simulation results are presented to illustrate the efficiency of the approach     

基于期望闭环系统响应的网络化串级控制系统PID整定

研究有常数网络诱导时延的一类典型网络化串级控制系统的PID控制器参数整定问题。系统中的网络诱导时延为常数,主对象和副对象均为一阶惯性加纯迟延环节(FOPDT)。主控制器是有超前滞后校正环节的PID,副控制器是带有滤波环节的PID。基于过程模型和期望闭环系统响应整定PID参数,采用一阶P偄de近似纯迟延环节,以解析的形式推导出了主控制器和副控制器整定参数的表达式,并采用双线性变换法得到离散时间PID控制器。提出了网络化串级控制系统的控制性能综合指标,并基于TrueTime工具箱在不同网络诱导时延时对网络化串级控制系统进行了仿真研究。仿真结果和性能指标计算结果均验证了所提算法的可行性和有效性。     

Bounded robust control of constrained multivariable nonlinear processes

This work focuses on control of multi-input multi-output (MIMO) nonlinear processes with uncertain dynamics and actuator constraints. A Lyapunov-based nonlinear controller design approach that accounts explicitly and simultaneously for process nonlinearities, plant-model mismatch, and input constraints, is proposed. Under the assumption that all process states are accessible for measurement, the approach leads to the explicit synthesis of bounded robust multivariable nonlinear state feedback controllers with well-characterized stability and performance properties. The controllers enforce stability and robust asymptotic reference-input tracking in the constrained uncertain closed-loop system and provide, at the same time, an explicit characterization of the region of guaranteed closed-loop stability. When full state measurements are not available, a combination of the state feedback controllers with high-gain state observes and appropriate saturation filters, is employed to synthesize bounded robust multivariable output feedback controllers that require only measurements of the outputs for practical implementation. The resulting output feedback design is shown to inherit the same closed-loop stability and performance properties of the state feedback controllers and, in addition, recover the closed-loop stability region obtained under state feedback, provided that the observer gain is sufficiently large. The developed state and output feedback controllers are applied successfully to non-isothermal chemical reactor examples with uncertainty, input constraints, and incomplete state measurements. Finally, we conclude the paper with a discussion that attempts to put in perspective the proposed Lyapunov-based control approach with respect to the nonlinear model predictive control (MPC) approach and discuss the implications of our results for the practical implementation of MPC, in control of uncertain nonlinear processes with input constraints.     

PI controller design for a class of distributed parameter systems

In this paper, the regulation problem of convection governed dynamical processes described by linear distributed parameter models with position-independent inputs is addressed by combining the method of characteristics (MC) and the Malek-Zavarei and Jamshidi theorem. In this approach, the MC is used to transform the first order partial differential equations model of such processes into a set of time-delayed ordinary differential equations whose elements are used to generate certain matrices that satisfy linear matrix inequalities that render the proportional integral (PI) control parameters that guarantee the process stability. The performance of the proposed PI controller is tested via numerical simulations in the temperature regulation of a linear heat exchanger and compared to a tightly tuned classical PI controller. The application of the proposed controller is extended to regulate the outlet concentration in a nonlinear non-isothermal plug flow reactor. It is shown that the proposed controller is able to handle the infinite dimensional nature of the process model yielding smooth and unsaturated responses around the predetermined set-point trajectory in the face of load changes, time varying boundary conditions and set-point changes.     

INTEGRATING THE EFFECTS OF PROCESS CONTROLLERS WITH STEADY-STATE, EQUATION-BASED SIMULATION

Process controllers have a significant influence on the steady-state, as well as the dynamic, behavior of chemical processes. Thus, the steady-state simulation of processes should include the effects of control. A new method for including controllers in steady-state simulation is presented in this paper. The method provides equations that represent the steady-state control algorithm and can be solved simultaneously with the process model to yield the steady-slate behaviour of the closed-loop system. Most importantly, the controller models include saturation effects and can be formulated and solved within an open-form model. The method is general and can be applied to single-loop controllers, to complex control designs including split range and signal select, and to several single-loop controllers in a multiloop controller design.     

搅拌混合器设计过程的模拟

在化学、制药、食品等工业的许多过程中,均涉及物料的混合,面临着关于混合设备的选择,设计、放大和优化的问题。为了解决这些问题,需要开发一种具有友好的图形用户界面,很高的可靠性和网络功能的设计软件。其目标是使工程师们可以针对易混合的液体混合物,固液混合,气液混合和传热这些混合过程选择和设计搅拌设备。使用编程工具——Java语言开发了搅拌混合器设计软件。     

Decentralized fault-tolerant control system design for unstable processes

Fault-tolerant control is an important issue in control of mission critical processes. In this paper, a new approach to fault-tolerant control of unstable processes is proposed based on the Passivity Theorem. The control system is designed in two sequential steps: A multi-loop proportional controller is used to stabilize the unstable process; a passivity-based decentralized unconditionally stabilizing (DUS) controller is then applied to the stabilized process. While the multi-loop stabilizing controllers need to be built with redundancy, the DUS controller is inherently fault tolerant and can maintain closed-loop stability when any of its loops fail. By using a stabilizing proportional controller with the fewest loops, control redundancy can be reduced to the minimum level.     

积分和不稳定时滞对象的改进内模控制

针对化工过程中一阶积分和不稳定时滞对象,基于内模控制提出了两自由度控制方案。首先根据鲁棒控制理论H2最优性能指标设计设定值跟踪控制器,然后采用期望闭环补灵敏度函数确定扰动抑制控制器。设定值跟踪控制器和扰动抑制控制器可通过性能参数独立调节而无需再取折衷,同时保证系统具有较好的鲁棒稳定性。最后通过仿真实例验证了该控制方案的有效性。     

Analytical design of PID controller cascaded with a lead-lag filter for time-delay processes

An analytical method for the design of a proportional-integral-derivative (PID) controller cascaded with a second-order lead-lag filter is proposed for various types of time-delay process. The proposed design method is based on the IMC-PID method to obtain a desired, closed-loop response. The process dead time is approximated by using the appropriate Pade expansion to convert the ideal feedback controller to the proposed PID·filter structure with little loss of accuracy. The resulting PID·filter controller efficiently compensates for the dominant process poles and zeros and significantly improves the closed-loop performance. The simulation results demonstrate the superior performance of the proposed PID·filter controller over the conventional PID controllers. A guideline for the closed-loop time constant, λ, is also suggested for the FOPDT and SOPDT models.     

FEEDBACK LINEARIZATION DESIGNS FOR UNCERTAIN NONLINEAR TIME-DELAY PROCESSES: A COMPARATIVE STUDY

This work concerns the phenomena in which the feedback linearization control is applied to uncertain nonlinear time-delay processes. Under the I/O linearization algorithm, both nonlinear controllers are used to stabilize the closed-loop system with transformed delay inputs. When the effect of input perturbations can converge to zero or asymptotically vanish, these nonlinear feedback designs with only an adjustable parameter can directly improve the tracking performance. The simple linearizing controller can directly regulate the system output at unstable operating point. Combined with deadtime compensation the nonlinear predictive controller with the aid of appropriate state prediction is valid for the real process in the presence of large time delay. Finally, via computer simulation and test of control ability of both feedback control designs the useful comparative results are presented.     

Model parameter estimation and feedback control of surface roughness in a sputtering process

This work focuses on model parameter estimation and model-based output feedback control of surface roughness in a sputtering process which involves two surface micro-processes: atom erosion and surface diffusion. This sputtering process is simulated using a kinetic Monte Carlo (kMC) simulation method and its surface height evolution can be adequately described by the stochastic Kuramoto-Sivashinsky equation (KSE), a fourth-order nonlinear stochastic partial differential equation (PDE). First, we estimate the four parameters of the stochastic KSE so that the expected surface roughness profile predicted by the stochastic KSE is close (in a least-square sense) to the profile of the kMC simulation of the same process. To perform this model parameter estimation task, we initially formulate the nonlinear stochastic KSE into a system of infinite nonlinear stochastic ordinary differential equations (ODEs). A finite-dimensional approximation of the stochastic KSE is then constructed that captures the dominant mode contribution to the state and the evolution of the state covariance of the stochastic ODE system is derived. Then, a kMC simulator is used to generate representative surface snapshots during process evolution to obtain values of the state vector of the stochastic ODE system. Subsequently, the state covariance of the stochastic ODE system that corresponds to the sputtering process is computed based on the kMC simulation results. Finally, the model parameters of the nonlinear stochastic KSE are obtained by using least-squares fitting so that the state covariance computed from the stochastic KSE process model matches that computed from kMC simulations. Subsequently, we use appropriate finite-dimensional approximations of the identified stochastic KSE model to design state and output feedback controllers, which are applied to the kMC model of the sputtering process. Extensive closed-loop system simulations demonstrate that the controllers reduce the expected surface roughness by 55% compared to the corresponding values under open-loop operation.     

Smith predictor based fractional-order PI control for time-delay processes

A new fractional-order proportional-integral controller embedded in a Smith predictor is systematically proposed based on fractional calculus and Bode’s ideal transfer function. The analytical tuning rules are first derived by using the frequency domain for a first-order-plus-dead-time process model, and then are easily applied to various dynamics, including both the integer-order and fractional-order dynamic processes. The proposed method consistently affords superior closed-loop performance for both servo and regulatory problems, since the design scheme is simple, straightforward, and can be easily implemented in the process industry. A variety of examples are employed to illustrate the simplicity, flexibility, and effectiveness of the proposed SP-FOPI controller in comparison with other reported controllers in terms of minimum the integral absolute error with a constraint on the maximum sensitivity value.     

Tuning digital PI controllers for minimal variance in manipulated input moves applied to imbalanced systems with delay

Determining the discrete-time proportional plus integral (PI) controller tuning parameters to achieve the smallest possible variance in the manipulated input moves, for a given variance in the controlled output, is the subject of this article. Previous researchers have developed tuning rules for PI and PI permutated nonlinear controllers to achieve what is commonly referred to as “level-flow smoothing”, or “averaging level control”, on imbalanced or integrating processes with delay, such as liquid level and gas pressure systems. The intent of this note is to demonstrate a new and simple technique of tuning digital PI controllers which utilizes either open or closed-loop historical data to estimate the process gain, dead-time and expected flow disturbance magnitude from which the digital PI tuning constants can be easily derived. By parameterizing the closed-loop system as a function of the PI tuning constants, we can simultaneously minimize the expected variation in the process input move and output responses while at the same time ensuring nominal stability of the overall system. In order to demonstrate the technique, an illustrative example is included which highlights the new procedure on an oil refinery liquid surge drum level process.     

FEEDBACK LINEARIZATION DESIGNS FOR UNCERTAIN NONLINEAR TIME-DELAY PROCESSES: A COMPARATIVE STUDY

This work concerns the phenomena in which the feedback linearization control is applied to uncertain nonlinear time-delay processes. Under the I/O linearization algorithm, both nonlinear controllers are used to stabilize the closed-loop system with transformed delay inputs. When the effect of input perturbations can converge to zero or asymptotically vanish, these nonlinear feedback designs with only an adjustable parameter can directly improve the tracking performance. The simple linearizing controller can directly regulate the system output at unstable operating point. Combined with deadtime compensation the nonlinear predictive controller with the aid of appropriate state prediction is valid for the real process in the presence of large time delay. Finally, via computer simulation and test of control ability of both feedback control designs the useful comparative results are presented.     

改进Smith预估控制器的解析设计

针对化工过程常见的积分和不稳定时滞对象,基于改进的史密斯预测控制提出了两自由度控制方案。首先根据鲁棒控制理论H2最优性能指标设计设定值跟踪控制器,然后在分析稳定性和抗扰性的基础上设计了扰动抑制控制器,设定值跟踪控制器和扰动抑制控制器可通过性能参数独立调节和优化。同时针对存在的乘性不确定性过程分析了系统的鲁棒稳定性。最后通过仿真实例验证了该控制方案的有效性。     

A new direct-synthesis tuning method for pi-controllers

A new efficient tuning method for proportional-integral (PI) controllers is proposed using overdamped closed-loop dynamics of the system. In line with other direct-synthesis and IMC methods, this new approach uses the desired closed-loop response to satisfy usual control and tuning objectives, but unlike the most other tuning methods hitherto-reported for PID controllers, it does not require that a process model be identified. Yet this new direct-synthesis (NDS) method is capable of making the controller perform the dual control functions of both good set-point tracking and disturbance rejection. Furthermore, it turns out that the new tuning method works equally well for difficult cases like large time delay and nonminimum phase processes. Finally, it can be said that this NDS method can be easily implemented and understood by the plant operating personnel because it has been developed emphasizing its on-site utility.