改进型预测函数控制在感应电机功率优化中的应用

在对感应电机效率优化问题进行研究的基础上,考虑到传统方法在电机动态时无法同时兼顾响应性能和效率优化的缺陷,设计了一种新型分数阶PI(FOPI)预测函数控制策略.该控制策略将预测函数控制和分数阶PI两种算法相结合,构建具有分数阶比例、积分性质的多变量预测函数控制器,兼顾了感应电机动态效率与转速响应速度的优点.应用于电动机效率优化的最大转矩电流比控制方面,采用前馈补偿解耦设计的思路,将系统分解成两个具有可测扰动的子系统.仿真实验表明新型控制策略具有在线识别模型识别模型参数,跟踪效果好,抗干扰能力强,无超调,稳态误差小,取得了良好的控制效果.     

基于最大灵敏度的加热系统分数阶内模控制

针对加热系统热传导过程模型不精确和系统参数不确定性问题, 提出一种新的基于最大灵敏度的分数阶内模控制方案. 采用分数阶模型描述加热系统可以提高精度, 而内模控制能够很好地处理系统参数不确定性问题. 利用最大灵敏度整定分数阶控制器参数, 并以此获得强鲁棒性控制系统. 数值结果验证了所提出的分数阶内模控制方案的有效性, 具有比整数阶内模控制方案更好的控制性能.

     

分数阶PI^λD^μ控制器控制性能的研究

现实控制系统研究中存在很多分数阶系统,因此对系统提出了分数阶PI~λD~μ控制器,控制器将传统整数阶PID控制器的微分与积分阶数扩展到分数,增加了两个参数微分阶数μ和积分阶数λ.为了对比研究分数阶系统分别在分数阶PI~λD~μ控制器控制下和在整数阶PID控制器控制下的系统性能,针对一个典型的分数阶系统,分别设计两类控制器,再进行性能比较.实验仿真结果表明,与整数阶PID控制器相比,该系统在分数阶PI~λD~μ控制器控制下整个闭环系统具备较好的动、静态性能,并且鲁棒性较强,说明分数阶PI~λD~μ控制器控制性能的优越性以及当被控系统为分数阶系统时应该设计分数阶PI~λD~μ控制器.     

纸浆间歇蒸煮过程的分数阶建模及内模控制

纸浆间歇蒸煮是在高温高压密封的蒸煮锅中进行，是一个复杂的黑箱过程.针对间歇蒸煮过程的非线性和系统参数不确定性问题，在机理建模的基础上，通过函数拟合及数值逼近对模型的非线性部分进行数学近似，建立了间歇蒸煮过程的分数阶模型.针对分数阶系统，采用内模控制原理设计分数阶PID控制器，以简化分数阶控制器的可调参数，并基于最大灵敏度及稳定裕度整定控制器参数，使系统在保证期望的动态性能条件下，获得较好的鲁棒性.仿真结果表明，间歇蒸煮过程的分数阶内模控制在超调、响应速度和鲁棒性方面优于整数阶控制.     

对角CARIMA模型多变量广义预测控制改进算法

为了增强多变量广义预测控制算法(MGPC)的实用性,对其实现形式进行了进一步的简化.利用对角CARIMA模型的结构特点,先对系统中单个输出变量期望值的自由响应部分进行分解推导,将其表达成自由响应项系数与系统输入输出变量已知值乘积的形式,得到此输出变量的预测表达式,然后将系统所有输出变量的预测表达式代入目标函数中,得到的控制增量等于控制器系数与参考轨迹、过程输入输出历史数据的乘积.控制器系数只与模型参数及设计参数有关,求解控制量时不再需要进行模型输出预报,控制器结构简单,实现容易.对比实验结果表明了该方法保持了常规MGPC方法的优秀控制性能.     

时滞系统分数阶PI?? 极点配置控制器设计

利用参数空间法研究用PIλ控制器实现时滞系统的闭环极点配置问题。复平面上的阻尼角扇形区域和相对稳定度区域(该两区域构成一个梯形区域)被映射到控制器参数平面,相应的控制器参数可以将闭环极点配置在梯形区域内,从而保证所要求的系统性能。仿真结果显示,对于适当选取的分数阶PIλ控制器的参数,采用分数阶控制器可以取得比整数阶控制器更好的控制效果,从极点配置的角度揭示了分数阶控制器的优越性。     

基于D分解的分数阶PID控制器的图形化参数整定

针对二自由度分数阶PID控制器设计的参数多,结构复杂等复杂问题,提出了一种基于D分解法和主导极点配置的新型参数整定方法。其基本原理首先基于动态响应指标约束进行主导极点配置,在确保闭环系统的响应特性良好的条件下确定系统超调量和调节时间,由此经过转换得到未知参数之间的函数关系。其次,使用D分解法,将未知参数在不影响的控制性能的条件下由多减少,再由相关参数取得系统性能稳定的参数域中优化,最后以差分进化算法为导向,以两种方法取得的相关约束条件为指标取得最优控制器参数,在确保所选极点的优势下使所设计的控制器达到理想的控制性能。最终,将所设计的控制器通过应用在整数阶和分数阶被控对象上,使用仿真验证新方法的鲁棒性和快速性,同时也表现了新方法的有效性和实用性。     

多变量时滞非方系统的分数阶Smith预估控制

针对多变量时滞非方系统,提出一种基于反向解耦的分数阶Smith预估控制方法.首先,将反向解耦方法推广应用于$m\times n$非方系统中,给出非方解耦矩阵的设计方法,同时为了保证解耦矩阵的稳定正则,给出其实现的必要条件以及条件不满足时的补偿方法;然后,针对解耦后的各个单回路系统设计分数阶Smith预估控制器,根据内模控制与Smith预估控制结构上的等价关系简化控制器的设计,克服时滞环节对系统性能的影响,并且基于最大灵敏度推导出一种控制器参数解析整定方法;最后,通过典型的Shell标准控制问题对所提出方法进行验证.仿真结果表明,反向解耦方法设计简单易于实现,能达到系统完全解耦,控制器参数较少,整定方便,并且具有良好的跟踪能力、抗干扰性和鲁棒性.     

基于参数辨识的自适应解耦控制算法的研究

多变量模型的复杂结构、强耦合性、被控对象参数的未知、慢时变等问题要求控制器必须具有良好的自适应性,针对以上问题提出了一种基于改进的广义最小方差闭环自适应解耦控制器实现更好的自适应,其由参数可调的控制器和自适应控制律组成,此控制器通过将闭环系统方程的传递函数矩阵等于期望的对角矩阵来实现解耦,同时改进的辨识算法可进行在线辨识控制器的参数实现同步自适应解耦。通过以CARMA为多变量控制模型,采用该方法进行仿真有效的解决了多变量之间的耦合性。结果表明该方法能够适应相应的变化,跟踪性能较好,且具备良好的解耦能力,进而保证了闭环系统的稳定性,从而验证了此方法能够效提高控制系统的稳定性和鲁棒性。     

高阶时滞对象的预测PI(D)控制

利用频率域模型降阶理论,提出了高阶时滞对象的预测PI(D)控制器两种设计方法.一种方法是直接将高阶滞后对象在频率域内降阶为低阶滞后对象,针对低阶滞后对象设计预测PI(D)控制器;另一种方法是按照规定的性能指标设计控制器,并将该控制器在频率域内降阶为具有预测PI(D)控制器的结构形式.这两种方法设计的控制器均具有结构简单、可调参数少、参数调节方便的特点.仿真表明:在模型失配的情况下,此两类预测PI(D)控制器仍然具有良好的控制性能和鲁棒稳定性能.     

Closed form tuning equations for model predictive control of first-order plus fractional dead time models

Many industrial processes can be effectively described with first-order plus fractional dead time models. In the case of plants with a large dead time relative to the time constant, approximations in discretizing the time delay can adversely affect the performance and if the sample time is enforced by system requirements, the fractional nature of the delay should be considered. In this paper, an analytical approach to model predictive control tuning for stable and unstable first-order plus dead time models with fractional delay is presented. The existing tuning methods are based on trial and error or numerical optimization approaches and the available closed form equations are limited to plants with integer delays. In this paper, an analytical approach is adopted and the issues of closed loop stability and achievable performance are addressed. Finally, simulation results are used to show the effectiveness of the proposed tuning strategy.     

Closed-loop stable model predictive control of integrating systems with dead time

Model predictive control (MPC) applications in the process industry usually deal with process systems that show time delays (dead times) between the system inputs and outputs. Also, in many industrial applications of MPC, integrating outputs resulting from liquid level control or recycle streams need to be considered as controlled outputs. Conventional MPC packages can be applied to time-delay systems but stability of the closed loop system will depend on the tuning parameters of the controller and cannot be guaranteed even in the nominal case. In this work, a state space model based on the analytical step response model is extended to the case of integrating time systems with time delays. This model is applied to the development of two versions of a nominally stable MPC, which is designed to the practical scenario in which one has targets for some of the inputs and/or outputs that may be unreachable and zone control (or interval tracking) for the remaining outputs. The controller is tested through simulation of a multivariable industrial reactor system.     

On-line tuning strategy for model predictive controllers

This paper presents an intuitive on-line tuning strategy for linear model predictive control (MPC) algorithms. The tuning strategy is based on the linear approximation between the closed-loop predicted output and the MPC tuning parameters. By direct utilization of the sensitivity expressions for the closed-loop response with respect to the MPC tuning parameters, new values of the tuning parameters can be found to steer the MPC feedback response inside predefined time-domain performance specifications. Hence, the algorithm is cast as a simple constrained least squares optimization problem which has a straightforward solution. The simplicity of this strategy makes it more practical for on-line implementation. Effectiveness of the proposed strategy is tested on two simulated examples. One is a linear model for a three-product distillation column and the second is a non-linear model for a CSTR. The effectiveness of the proposed tuning method is compared to an exiting offline tuning method and showed superior performance.     

Multi-objective performance optimisation for model predictive control by goal attainment

This article proposes an approach for performance tuning of model predictive control (MPC) using goal-attainment optimisation of the cost function weighting matrices. The approach is developed for three formulations of the control problem: (i) minimal and (ii) non-minimal design based on the same cost function and (iii) a non-minimal MPC approach with an explicit integral-of-error state variable and modified cost function. This approach is based on earlier research into multi-objective optimisation for proportional-integral-plus control systems. Simulation experiments for a 3-input, 3-output Shell heavy oil fractionator model illustrate the feasibility of MPC goal attainment for multivariable decoupling and attainment of a specific output response. For this example, the integral-of-error state variable offers improved design flexibility and hence, when it is combined with the proposed tuning method, yields an improved closed-loop response in comparison to minimal MPC.     

Robust tuning for machine-directional predictive control of MIMO paper-making processes

This paper solves the controller tuning problem of machine-directional predictive control for multiple-input–multiple-output (MIMO) paper-making processes represented as superposition of first-order-plus-dead-time (FOPDT) components with uncertain model parameters. A user-friendly multi-variable tuning problem is formulated based on user-specified time domain specifications and then simplified based on the structure of the closed-loop system. Based on the simplified tuning problem and a proposed performance evaluation technique, a fast multi-variable tuning technique is developed by ignoring the constraints of the MPC. In addition, a technique to predict the computation time of the tuning algorithm is proposed. The efficiency of the proposed method is verified through Honeywell real time simulator platform with a MIMO paper-making process obtained from real data from an industrial site.     

Constrained linear quadratic regulation

The paper is a contribution to the theory of the infinite-horizon linear quadratic regulator (LQR) problem subject to inequality constraints on the inputs and states, extending an approach first proposed by Sznaier and Damborg (1987). A solution algorithm is presented, which requires solving a finite number of finite-dimensional positive definite quadratic programs. The constrained LQR outlined does not feature the undesirable mismatch between open-loop and closed-loop nominal system trajectories, which is present in the other popular forms of model predictive control (MPC) that can be implemented with a finite quadratic programming algorithm. The constrained LQR is shown to be both optimal and stabilizing. The solution algorithm is guaranteed to terminate in finite time with a computational cost that has a reasonable upper bound compared to the minimal cost for computing the optimal solution. Inherent to the approach is the removal of a tuning parameter, the control horizon, which is present in other MPC approaches and for which no reliable tuning guidelines are available. Two examples are presented that compare constrained LQR and two other popular forms of MPC. The examples demonstrate that constrained LQR achieves significantly better performance than the other forms of MPC on some plants, and the computational cost is not prohibitive for online implementation     

An analytical tuning approach to multivariable model predictive controllers

Multivariable model predictive control is a widely used advanced process control methodology, where handling delays and constraints are its key features. However, successful implementation of model predictive control requires an appropriate tuning of the controller parameters. This paper proposes an analytical tuning approach to multivariable model predictive controllers. The considered multivariable plants are square and consist of first-order plus dead time transfer functions. Most of the existing model predictive control tuning methods are based on trial and error or numerical approaches. In the case of no active constraints, closed loop transfer function matrices are derived and decoupling conditions are addressed. For control horizon of one, analytical tuning equations and achievable performances are obtained. Finally, simulation results are used to verify the effectiveness of the proposed tuning strategy.     

Robust tuning of dead-time compensators for processes with anintegrator and long dead-time

Presents a simple criterion for tuning a dead time compensator for plants with an integrator and long dead time. The criterion is based on the definition of a closed-loop performance and considers that the model of the process is not precisely known. Using an estimation of the dead time and velocity gain of the plant, the proposed control law has only one tuning parameter that determines the closed-loop performance and robustness. By tuning this parameter it is possible to attain some robust performance specifications. In order to compare the proposed criterion with previous algorithms proposed in the literature, a comparative analysis of robustness is presented. Some simulation examples demonstrate the good properties of the proposed compensator     

Tuning SISO offset-free Model Predictive Control based on ARX models

In this paper, we present a tuning methodology for a simple offset-free SISO Model Predictive Controller (MPC) based on autoregressive models with exogenous inputs (ARX models). ARX models simplify system identification as they can be identified from data using convex optimization. Furthermore, the proposed controller is simple to tune as it has only one free tuning parameter. These two features are advantageous in predictive process control as they simplify industrial commissioning of MPC. Disturbance rejection and offset-free control is important in industrial process control. To achieve offset-free control in face of unknown disturbances or model-plant mismatch, integrators must be introduced in either the estimator or the regulator. Traditionally, offset-free control is achieved using Brownian disturbance models in the estimator. In this paper we achieve offset-free control by extending the noise model with a filter containing an integrator. This filter is a first order ARMA model. By simulation and analysis, we argue that it is independent of the parameterization of the underlying linear plant; while the tuning of traditional disturbance models is system dependent. Using this insight, we present MPC for SISO systems based on ARX models combined with the first order filter. We derive expressions for the closed-loop variance of the unconstrained MPC based on a state space representation in innovation form and use these expressions to develop a tuning procedure for the regulator. We establish formal equivalence between GPC and state space based off-set free MPC. By simulation we demonstrate this procedure for a third order system. The offset-free ARX MPC demonstrates satisfactory set point tracking and rejection of an unmeasured step disturbance for a simulated furnace with a long time delay.     

ILC strategy for progress improvement of economic performance in industrial model predictive control systems

A novel approach to progress improvement of the economic performance in model predictive control (MPC) systems is developed. The conventional LQG based economic performance design provides an estimation which cannot be done by the controller while the proposed approach can develop the design performance achievable by the controller. Its optimal performance is achieved by solving economic performance design (EPD) problem and optimizing the MPC performance iteratively in contrast to the original EPD which has nonlinear LQG curve relationship. Based on the current operating data from MPC, EPD is transformed into a linear programming problem. With the iterative learning control (ILC) strategy, EPD is solved at each trial to update the tuning parameter and the designed condition; then MPC is conducted in the condition guided by EPD. The ILC strategy is proposed to adjust the tuning parameter based on the sensitivity analysis. The convergence of EPD by the proposed ILC has also been proved. The strategy can be applied to industry processes to keep enhancing the performance and to obtain the achievable optimal EPD. The performance of the proposed method is illustrated via an SISO numerical system as well as an MIMO industry process.