Disturbance modeling for offset-free linear model predictive control

An offset-free controller is one that drives controlled outputs to their desired targets at steady state. In the linear model predictive control (MPC) framework, offset-free control is usually achieved by adding step disturbances to the process model. The most widely-used industrial MPC implementations assume a constant output disturbance that can lead to sluggish rejection of disturbances that enter the process elsewhere. This paper presents a general disturbance model that accommodates unmeasured disturbances entering through the process input, state, or output. Conditions that guarantee detectability of the augmented system model are provided, and a steady-state target calculation is constructed to remove the effects of estimated disturbances. Conditions for which offset-free control is possible are stated for the combined estimator, steady-state target calculation, and dynamic controller. Simulation examples are provided to illustrate trade-offs in disturbance model design.     

Development and application of a model-plant mismatch expression for linear time-invariant systems

When a plant and its controller are sufficiently linear and time-invariant so that they can be represented by transfer functions, and this plant is under classical control (meaning the controller can also be represented by a transfer function), the model-plant mismatch (MPM) that often plagues industrial processes can be written as a closed-form expression. This includes a variety of controllers, among which the ubiquitous Proportional, Integral and Derivative (PID) controller. The MPM expression can then be used to identify a representative transfer function of the “true plant” from the currently available plant model. The MPM expression works for single-input single-output as well as multiple-input multiple-output systems. The closed-loop data required for application of the expression has to be sufficiently exciting. If significant disturbances perturb the plant their values need to be available. In this article the expression is applied to industrial data to show its applicability.     

Improved methodology and set-point design for diagnosis of model-plant mismatch in control loops using plant-model ratio

Performance of any model-based control scheme depends on the quality of model. When these schemes deliver poor loop performance due to model-plant mismatch (MPM), a detection of the same needs to be in place. A recently introduced plant model ratio (PMR) not only detects MPM but also facilitates a unique identification of the source of mismatch, namely, gain, dynamics (time constant) and delay mismatches. The prime objective of this work is to improve the PMR approach in a few key aspects, namely, estimation and experimental effort, and assessment procedure by taking a fresh perspective of PMR and conducting a detailed theoretical study of its signatures. A rigorous assessment procedure based on the theoretical properties of PMR is devised. Three threshold-based hypotheses tests are proposed for significance testing of PMR. A key contribution of this work is the design of set-point with minimal excitation for diagnosis of MPM, based on the features of PMR. The revised methodology is demonstrated and compared with the existing method through simulation examples. The study also demonstrates the potential of the proposed method in serving as a prelude to full/partial model re-identification.     

无偏模型预测控制综述

无偏(静差)模型预测控制(Model predictive control, MPC)的设计目标是使被控变量渐近地跟踪设定值, 这类控制方法直接关系到闭环系统的跟踪性能和抗扰性能.由于可以有效处理不可测扰动、模型失配等, 无偏MPC具有很强的工程应用价值, 但是在理论方面并没有得到充分重视.近30年来, 围绕无偏MPC的原理、分析和设计展开了一系列的研究工作, 并取得了系统性的研究成果.当前的一些研究结果大多分散在不同的参考文献中, 缺少全面的梳理和呈现.本文的主要工作包括回顾常见无偏控制方法, 综述当前无偏MPC的研究进展, 并探讨一些潜在的研究方向.     

Model predictive control: Recent developments and future promise

This paper recalls a few past achievements in Model Predictive Control, gives an overview of some current developments and suggests a few avenues for future research.     

Dynamic Output Feedback Robust MPC Using General Polyhedral State Bounds for the Polytopic Uncertain System With Bounded Disturbance

This paper considers the dynamic output feedback robust model predictive control (MPC) for a system with both polytopic model parametric uncertainty and bounded disturbance. For this topic, the techniques for handling the unknown true state are crucial, and the strict guarantee of the input/output/state constraints favors replacing the true state by its bound in the optimization problems. The previous utilized polyhedral bounds, constructed by virtue of the error signals which are some linear combinations of the true state, the estimated state and the output, are generalized, where a bias item is utilized. Based on this unified bounding approach, new techniques for handling the unknown true state are given for both the main and the auxiliary optimization problems. As before, the main optimization problem calculates the control law parameters conditionally, and the auxiliary optimization problem determines the time to refresh these parameters. By applying the proposed method, the augmented state of the closed‐loop system is guaranteed to converge to the neighborhood of the equilibrium point. A numerical example is given to illustrate the effectiveness of the new method.     

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.     

积分过程预测控制的稳态分析及反馈校正

多变量积分过程的控制,一直是预测控制理论研究与应用过程中的难点问题.现有的研究成果更多的关注于算法的实现上,而很少关注理论依据.本文从积分过程的控制输入平衡关系出发,利用线性代数方程组解的相容性原理,得到了一个适用于判断多变量积分过程设定点是否可达的判据,可以作为算法能否实现多变量积分过程无静差控制的理论依据.同时分析了传统算法无法在存在模型失配情况下对积分过程进行优化与控制的原因,利用补偿因子重新设计反馈校正环节,使改进后的算法能够实现存在模型失配过程的优化与控制,并通过仿真验证了本文提出的结论.     

基于互相关分析的模型失配性能评价与监视

为了对预测控制中的模型失配问题进行性能评价与监视,基于互相关分析理论,通过引入操纵变量激励信号,分析其与预测偏差之间的互相关性来确定传递函数矩阵的失配问题,然后将模型失配问题转化为互相关系数在置信区间上的分布问题.结合各个通道互相关函数仿真图来直观监视模型失配与否,从而对其进行性能评价.将此方法成功运用到Wood-Be...     

Constrained anti-disturbance control for a quadrotor based on differential flatness

The classical control design based on linearised model is widely used in practice even to those inherently nonlinear systems. Although linear design techniques are relatively mature and enjoy the simple structure in implementations, they can be prone to misbehaviour and failure when the system state is far away from the operating point. To avoid the drawbacks and exploit the advantages of linear design methods while tackling the system nonlinearity, a hybrid control structure is developed in this paper. First, the model predictive control is used to impose states and inputs constraints on the linearised model, which makes the linearisation satisfy the small-perturbation requirement and reduces the bound of linearisation error. On the other hand, a combination of disturbance observer-based control and H_∞ control, called composite hierarchical anti-disturbance control, is constructed for the linear model to provide robustness against multiple disturbances. The constrained reference states and inputs generated by the outer-loop model predictive controller are asymptotically tracked by the inner-loop composite anti-disturbance controller. To demonstrate the performance of the proposed framework, a case study on quadrotor is conducted.     

Comparison of nonlinear control design techniques on a model of the Caltech ducted fan

In this paper we compare different nonlinear control design methods by applying them to the planar model of a ducted fan engine. The methods used range from Jacobian linearization of the nonlinear plant and designing an LQR controller, to using model predictive control and linear parameter varying methods. The controller design can be divided into two steps. The first step requires the derivation of a control Lyapunov function (CLF), while the second involves using an existing CLF to generate a controller. The main premise of this paper is that by combining the best of these two phases, it is possible to find controllers that achieve superior performance when compared to those that apply each phase independently. All of the results are compared to the optimal solution which is approximated by solving a trajectory optimization problem with a sufficiently large time horizon.     

A hierarchical distributed model predictive control approach to irrigation canals: A risk mitigation perspective

This paper presents a hierarchical distributed model predictive control approach applied to irrigation canal planning from the point of view of risk mitigation. Two levels in optimization are presented. At the lower level, a distributed model predictive controller optimizes the operation by manipulating flows and gate openings in order to follow the water level set-points. The higher level implements a risk management strategy based on the execution of mitigation actions if risk occurrences are expected. Risk factors such as unexpected changes in demand, failures in operation or maintenance costs are considered in the optimization. Decision variables are mitigation actions which reduce risk impacts that may affect the system. This work shows how model predictive control can be used as a decision tool which takes into account different types of risks affecting the operation of irrigation canals.