Performance assessment of single-loop industrial controllers

The most common metric for controller performance assessment is a comparison of the process output variance to that which would have been obtained if some optimal controller had been applied to the process over the same time frame. Usually this optimal controller is a minimum variance controller, as a metric based on this controller requires a minimum of process knowledge and no plant tests. While minimum variance controllers by definition contain an accurate disturbance model, industrial controllers contain a simple fixed disturbance model, which may or may not be an accurate representation of the actual disturbance. Shown in this paper is the effect that this simple disturbance model has on performance indices, and methodologies for controller performance assessment that accounts for this simple model. In addition, a performance metric for non-deadtime-compensated (i.e., PID) controllers is shown.     

Performance assessment and retuning of PID controllers for integral processes

In this paper we propose a methodology for the performance assessment of a PID controller applied to an integral process and for the retuning of the parameters in case the obtained response is not satisfactory. The technique addresses both set-point and load disturbance step responses. Simulation and experimental results obtained with a laboratory scale equipment show the effectiveness of the methodology.     

基于混合制排队模型的SDN控制器性能评估研究

软件定义网络SDN将逻辑控制与数据转发相分离,提高了网络的灵活性和可编程能力,成为近年来未来网络领域的研究热点。SDN在实际应用部署时将面临控制器性能瓶颈的挑战,因而有必要理解SDN控制器的性能特性。为此,首先对SDN控制器中Packet-In消息的到达过程和处理时间进行分析,进而基于排队论提出了一种容量有限的SDN控制器性能评估模型M/M/1/m,推导得出了该模型的性能参数,包括:平均等待队长、平均等待时间、平均队列长度和平均逗留时间。最后,采用控制器性能测试工具Cbench对该模型进行了实验评估。实验结果表明:相对于现有其它模型,该模型的估计时延更接近于实际测量时延,可更精确地描述SDN控制器的性能。     

PID控制器的性能监控与评估

为了解决目前工业系统中普遍使用的PID控制器由于工况变化等原因引起的系统发生时变而导致所在回路PID控制器性能可能下降的问题,本文提出了一种专门针对PID控制器进行性能评估、优化及监控的方法,即:PID循环评估优化算法。该算法利用系统闭环输入输出数据,使用基于MVC(minimum variance control)的PID最小方差准则,来对PID控制器的性能进行评估,并且计算出在最小方差意义下最优PID控制器参数;评估过程结果与现实系统输出方差进行比较,做为PID参数在线优化的判断依据,当现实系统性能低于某一标准的时候对控制器进行优化处理。在整个算法中,通过输入输出数据的处理与判断,利用评估优化后的PID参数对系统进行控制,并再次回到最初的输入输出数据的处理和判断过程,实现在控制过程中的系统性能监控。本文的计算机仿真试验验证了该方法的有效性,由图可看出,系统发生渐变和突变后,当输出方差超过了程序限定的标准时,在1 300秒内系统能自动评估并施行优化而达到稳定。该循环评估优化算法现实了在对系统进行性能评估监控的同时,能按照一定条件作为标准对系统的PID参数进行优化,最终使得系统具有自我监控评估和自我优化的能力...     

Performance evaluation of two industrial MPC controllers

This paper presents case studies of the performance evaluation of two industrial multivariate model predictive control (MPC) based controllers at the Mitsubishi chemical complex in Mizushima, Japan: (1) a 6-output, 6-input para-xylene (PX) production process with six measured disturbance variables that are used for feedforward control; and (2) a multivariate MPC controller for a 6-output, 5-input poly-propylene splitter column with two measured disturbances. A generalized predictive controller-based MPC algorithm has been implemented on the PX process. Data from the PX unit before and after the MPC implementation are analyzed to obtain and compare several different measures of multivariate controller performance. The second case study is concerned with performance assessment of a commercial MPC controller on a propylene splitter. A discussion on the diagnosis of poor performance for the second MPC application suggests significant model-plant-mismatch under varying load conditions and highlights the role of constraints.     

Dampening controllers via a Riccati equation approach

An algorithm is presented which computes a state feedback for a standard linear system which not only stabilizes, but also dampens the closed-loop system dynamics. In other words, a feedback gain matrix is computed such that the eigenvalues of the closed-loop state matrix are within the region of the left half-plane where the magnitude of the real part of each eigenvalue is greater than that of the imaginary part, This may be accomplished by solving a damped algebraic Riccati equation and a degenerate Riccati equation. The solution to these equations are computed using numerically robust algorithms, Damped Riccati equations are unusual in that they may be formulated as an invariant subspace problem of a related periodic Hamiltonian system. This periodic Hamiltonian system induces two damped Riccati equations: one with a symmetric solution and another with a skew symmetric solution. These two solutions result in two different state feedbacks, both of which dampen the system dynamics, but produce different closed-loop eigenvalues, thus giving the controller designer greater freedom in choosing a desired feedback     

Eigenvalue assignment via uncertain state feedback controllers

In this paper, we propose a method for eigenvalue assignment using linear control systems containing uncertain elements. Uncertain systems are systems described by state equations which depend on uncertain parameters. In this paper, uncertainty is modeled with interval numbers. The proposed method assigns prescribed eigenvalues to a state feedback control system. Also, we introduce two interval operations to be used in our method use them. Some numerical experiments are presented to illustrate the effectiveness of the proposed method.     

Design of robust model-based controllers via parametric programming

In this paper a method is presented for deriving the explicit robust model-based optimal control law for constrained linear dynamic systems. The controller is derived off-line via parametric programming before any actual process implementation takes place. The proposed control scheme guarantees feasible operation in the presence of bounded input uncertainties by (i) explicitly incorporating in the controller design stage a set of feasibility constraints and (ii) minimizing the nominal performance, or the expectation of the performance over the uncertainty space. An extension of the method to problems involving target point tracking in the presence of persistent disturbances is also discussed. The general concept is illustrated with two examples.     

Stabilization of decentralized control systems via time-varying controllers

In the design of decentralized control systems it is well known that the existence of unstable fixed modes prevents us from stabilizing it via linear time-invariant local controllers. In this note, we show that such systems might be stabilizable via time-varying controllers. In particular, a design method using sample and hold is proposed.     

Performance of periodically time-varying controllers for sampleddata control

Analyzes performance of periodically time-varying sampled data controllers for L_p deterministic and uniform disturbance rejection. For a given linear periodic sampled data controller controlling a linear time-invariant continuous-time plant, it is shown that a linear time-invariant controller can be found to give better L _p sampled data control than the time-varying controller. The performance analysis is in time domain using convexity properties of the L_p signal space     

Performance assessment using a model predictive control benchmark

Model predictive control (MPC) technology has been widely implemented throughout the petroleum, chemical, metallurgical and pulp and paper industries over the past three decades. The focus of this paper is the assessment of single-input, single-output MPC schemes against a new performance standard. The proposed MPC benchmark is shown to be useful both as a model diagnostic and as a tuning guide during commissioning. A formal assessment procedure is presented which emphasizes the use of routine operating data plus knowledge of the deadtime to determine when it becomes worthwhile to invest in re-identification of the plant dynamics and re-installation of the MPC application.     

Optimal feedback scheduling of model predictive controllers

Model predictive control （MPC） could not be reliably applied to real-time control systems because its computation time is not well defined. Implemented as anytime algorithm, MPC task allows computation time to be traded for control performance, thus obtaining the predictability in time. Optimal feedback scheduling （FS-CBS） of a set of MPC tasks is presented to maximize the global control performance subject to limited processor time. Each MPC task is assigned with a constant bandwidth server （CBS）, whose reserved processor time is adjusted dynamically. The constraints in the FS- CBS guarantee scheduler of the total task set and stability of each component. The FS-CBS is shown robust against the variation of execution time of MPC tasks at runtime. Simulation results illustrate its effectiveness.     

The pole placement problem via PI feedback controllers

In this paper we study the pole placement problem using generalized PI controllers of a fixed lag k as compensators. We derive a new strong sufficiency condition which guarantees the arbitrary pole assignability of a given system having m inputs p outputs and McMillan degree n. This sufficiency condition misses the theoretical best possible necessary condition by one degree of freedom. The proof of the main result can be used to derive a numerical procedure. This numerical procedure is however very sensitive in the parameters and further research is required to investigate the conditions under which sensitivity occurs and whether the solution can be made more robust in this regard.     

基于历史性能基准的模型预测控制性能监控

针对实际工业过程中希望只利用过程的日常运行数据对控制系统进行监控的情况,提出了1种用历史性能基准对预测控制系统进行性能评估、监控以及分析的方法.利用运行状态良好的1段历史数据计算出历史性能基准,并将历史性能基准与实际性能的比值用于控制器性能的实时监控.根据历史性能指标的残差监控检测出性能变化时,进一步通过历史数据协方差监控及广义特征值分析,区分出性能显著变差或变好的方向和子空间.为现场工程师提供性能变化的一些原因,用于系统维护.最后通过Shell重油分馏塔仿真证明该方法可以获得很好的评估与监控结果.     

新型增益调度变结构控制器的性能比较研究

为了提高变结构控制系统的控制效率,从节省控制能耗、消除颤振、快速进入滑动模态、获取稳定滑动模态等基本要求出发,将变结构控制器设计成具有增益调度控制器参数的增益调度变结构控制器,并提出了增益调度变结构控制器的设计方法.通过选择不同的调度变量、调度变量函数以及调度变量的变化范围,给出6种不同的增益调度变结构控制器,并进行了仿真研究,以比较其控制性能.     

Performance comparison between PID and dead-time compensating controllers

This paper is intended to answer the question: ‘‘When can a simple dead-time compensator be expected to perform better than a PID?'. The performance criterion used is the integrated absolute error (IAE). It is compared for PI and PID controllers and a simple dead-time compensator (DTC) when a step load disturbance is applied at the plant input. Both stable and integrating processes are considered. For a fair comparison the controllers should provide equal robustness in some sense. Here, as a measure of robustness, the _∞ norm of the sum of the absolute values of the sensitivity function and the complementary sensitivity function is used. Performance of the DTC's is given also as a function of dead-time margin (D_M).     

Performance improvement of robust controllers for polynomially uncertain systems

This paper is concerned with the high-performance robust control of discrete-time linear time-invariant (LTI) systems with semi-algebraic uncertainty regions. It is assumed that a robustly stabilizing static controller is given whose gain depends polynomially on the uncertain variables. The problem of tuning this parameter-dependent gain with respect to a prescribed quadratic cost function is formulated as a sum-of-squares (SOS) optimization. This method leads to a near-optimal controller whose performance is better than that of the initial controller. It is shown that the results derived in the present work encompass the ones obtained in a recent paper. The efficacy of the results is elucidated by an example.     

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.     

Iterative feedback tuning for internal model controllers

In this paper, the applicability of iterative feedback tuning (IFT) to internal model controllers (IMCs) and smith predictors is examined. IFT is a model-free gradient descent controller tuning tool; refer to Hjalmarsson et al. (IEEE Control Systems Mag. 18 (1998) 26) and Hjalmarsson et al. (Proceedings of the Conference on Decision and Control, Orlando, FL, 1994, pp. 1735) for further details. It is shown that the IFT algorithm can be modified to tune IMCs and, more in particular, Smith predictors. The main difference with the original algorithm is that the cost gradient is obtained by doing four experiments (two recycling experiments) instead of three (one recycling experiment) for conventional controllers.     

Synthesis of sliding-mode controllers for nonlinear systems via extended linearization

In this article, a general synthesis method is proposed for the design of discontinuous feedback strategies leading to asymptotically stabilizing sliding regimes. The method is applicable to the class of nonlinear dynamical systems possessing constant equilibrium points. A family of nonlinear stabilizing sliding manifolds, parametrized by generic desired equilibrium point, is specified on the basis of the extended linearization approach. Some examples including simulations are presented for illustrative purposes. Editor: S. Zak