Improving performance and stability of MPC relevant identification methods

Model Predictive Control (MPC) Relevant Identification (MRI) methods are a good option for identification, if there is model structure mismatch. Herein a new MRI method, named Enhanced Multistep Prediction Error Method (EMPEM), is proposed. EMPEM combines the best characteristics of others MRI methods in a single algorithm. It was developed to identify either closed-loop or open-loop systems; its convergence and stability make it perform better than the other presented methods. To show the advantages of EMPEM, a comparison is made against two other methods (one MRI and one PEM). The statistical analysis indicates that in the cases studied, the performance and the robustness of the new method is equal or better than the other ones.     

A nonlinear observer design for an activated sludge wastewater treatment process

This paper treats the problem of estimating simultaneously the state and the unknown inputs of a class of nonlinear discrete-time systems. An observer design method for nonlinear Lipschitz discrete-time systems is proposed. By assuming that the linear part of this class of systems is time-varying, the state estimation problem of nonlinear system is transformed into a state estimation problem for LPV system. The stability analysis is performed using a Lyapunov function that leads to the solvability of linear matrix inequalities (LMIs). Performances of the proposed observer are shown through the application to an activated sludge process model.     

Stochastic MPC with inequality stability constraints

Stochastic uncertainty is a common feature of many control engineering problems, and is also present in a wider class of applications, e.g. finance and sustainable development. Recent work proposed a constrained MPC approach that took explicit account of the distributions of uncertain model parameters but used terminal equality constraints to ensure stability. The present paper reformulates the problem in order to relax the stability constraints by invoking appropriate terminal inequalities. The application of the proposed strategy and its advantages over earlier work are illustrated by means of a numerical example.     

网路化双线性系统的预测控制优化算法研究

本文对一类离散时间双线性系统进行网络化预测控制研究.针对控制系统网络信道传输引起的前向通道和反馈通道时延问题,基于双线性系统结构特性提出2种逐步优化算法对非凸优化问题进行求解,进而得到未来时刻的预测控制序列.仿真实例说明所求预测控制序列可以主动补偿网络引起的时延问题,从而说明所提出预测控制算法的有效性.     

Min-max MPC using a tractable QP problem

Min-max model predictive controllers (MMMPC) suffer from a great computational burden that is often circumvented by using approximate solutions or upper bounds of the worst possible case of a performance index. This paper proposes a computationally efficient MMMPC control strategy in which a close approximation of the solution of the min-max problem is computed using a quadratic programming problem. The overall computational burden is much lower than that of the min-max problem and the resulting control is shown to have a guaranteed stability. A simulation example is given in the paper.     

Resource-aware MPC for constrained linear systems: Two rollout approaches

In systems with resource constraints, such as actuation limitations in sparse control applications or limited bandwidth in networked control systems, it is desirable to use control signals that are either sparse or sporadically changing in time. Motivated by these applications, in this paper we propose two resource-aware MPC schemes for discrete-time linear systems subject to state and input constraints. The two MPC schemes exploit ideas from rollout strategies to determine simultaneously the new (continuous) control inputs and the (discrete) time instants at which the control actions are updated. The first scheme provides performance guarantees by design, in the sense that it allows the user to select a desired suboptimal level of performance, where the degree of suboptimality provides a trade-off between the guaranteed closed-loop control performance on the one hand and the utilization of (communication/actuation) resources on the other hand. The second scheme provides a guaranteed (average) resource utilization, while cleverly allocating these resources in order to maximize the control performance. By means of numerical examples, we demonstrate the effectiveness of the proposed strategies.     

Modified reference tracking MPC for constrained linear systems

This article presents a model predictive control for tracking piecewise constant references with a new steady-state parametrisation. The modified algorithm is based on the artificial reference idea, but the number of decision variables is equal to the standard MPC for regulation. The proposed strategy is able to track admissible constant references with an admissible evolution. If the reference is not admissible, the system is steered to the closest admissible stationary point. A modified initialisation algorithm is proposed to recover the enlarged domain of attraction provided by related artificial reference-based strategies. Simulation examples are presented to illustrate the benefits of the proposed strategy.     

Generic distributed parameter model control of a biological nutrient removal (BNR) activated sludge process

This paper addresses nonlinear control of a class of distributed parameter systems by the generic distributed parameter model-based control (GDPMC) strategy. Case studies on a complex biological nutrient removal (BNR) activated sludge process for nitrogen and phosphorus removal show that the GDPMC strategy is applicable for controlling species of interest in specific bioreaction zones. The designs give much improved performances compared to well-tuned PI controllers in terms of the integral time absolute errors (ITAE). In a study on control of the entire BNR activated sludge plant, a multi-unit decentralised GDPMC strategy is shown to be robust to 25% plant-model mismatch in three sensitive and uncertain kinetic parameters. The advantages of the GDPMC strategy over lumped-model generic model control (GMC) are demonstrated in a comparative study on soluble phosphate control within the anaerobic zone of the plant.     

双线性系统的自校正控制

本文分别对确定和随机双线性系统,首次建立了大范围渐近收敛和稳定的自校正控制算法。该算法具有渐近最优的控制效果,且适用于非最小相位系统情况。仿真实验表明了该算法的有效性。     

MPC for continuous piecewise-affine systems

A large class of hybrid systems can be described by a max–min-plus-scaling (MMPS) model (i.e., using the operations maximization, minimization, addition and scalar multiplication). First, we show that continuous piecewise-affine systems are equivalent to MMPS systems. Next, we consider model predictive control (MPC) for these systems. In general, this leads to nonlinear, nonconvex optimization problems. We present a new MPC method for MMPS systems that is based on canonical forms for MMPS functions. In case the MPC constraints are linear constraints in the inputs only, this results in a sequence of linear optimization problems such that the MPC control can often be computed in a much more efficient way than by just applying nonlinear optimization as was done in previous work.     

Conditions for which linear MPC converges to the correct target

This paper considers the efficacy of disturbance models for ensuring offset-free control and the determination of the optimum feasible steady-state target within linear model predictive control (MPC). Previously proposed methods for steady-state target determination can address model error, disturbances, and output target changes when the desired steady state is feasible, but may fail to achieve a feasible target that is as close as possible to the desired steady-state target when the desired target is unreachable due to active constraints. Under certain conditions, the resulting ‘feasible steady-state target’ can converge to a point that is not as close as possible to the optimal feasible target. By considering the Karush–Kuhn–Tucker (KKT) conditions of optimality for the steady-state target optimizer, sufficient multi-variable conditions are established for which convergence to the optimal feasible target is guaranteed and, conversely, when convergence to a sub-optimal feasible target is expected.     

Comparison of input signals in subspace identification of multivariable ill-conditioned systems

Ill-conditioned processes often produce data of low quality for model identification in general, and for subspace identification in particular, because data vectors of different outputs are typically close to collinearity, being aligned in the “strong” direction. One of the solutions suggested in the literature is the use of appropriate input signals, usually called “rotated” inputs, which must excite sufficiently the process in the “weak” direction. In this paper open-loop (uncorrelated and rotated) random signals are compared against inputs generated in closed-loop operation, with the aim of finding the most appropriate ones to be used in multivariable subspace identification of ill-conditioned processes. Two multivariable ill-conditioned processes are investigated and as a result it is found that closed-loop identification gives superior models, both in the sense of lower error in the frequency response and in terms of higher performance when used to build a model predictive control system.     

MPC: Current practice and challenges

Linear Model Predictive Control (MPC) continues to be the technology of choice for constrained, multivariable control applications in the process industry. Successful deployment of MPC requires “getting right” multiple aspects of the control problem. This includes the design of the underlying regulatory controls, design of the MPC(s), test design for model identification, model development, and dealing with nonlinearities. Approaches and techniques that are successfully applied in practice are described, including the challenges involved in ensuring a successful MPC application. Academic contributions are highlighted and suggestions provided for improving MPC.     

Resource-aware MPC for constrained nonlinear systems: A self-triggered control approach

In systems with resource constraints, such as actuation limitations or limited communication bandwidth, it is desired to obtain control signals that are either sparse or sporadically changing in time to reduce resource utilization. In this paper, we propose a resource-aware self-triggered MPC strategy for discrete-time nonlinear systems subject to state and input constraints that has three important features: Firstly, significant reductions in resource utilization can be realized without modifying the cost function by input regularization or explicitly penalizing resource usage. Secondly, the control laws and triggering mechanisms are synthesized so that a priori chosen performance levels (in terms of the original cost function) are guaranteed by design next to asymptotic stability and constraint satisfaction. Thirdly, we address the co-design problem of jointly designing the feedback law and the triggering condition. By means of numerical examples, we show the effectiveness of this novel strategy.     

城市污水处理过程污泥膨胀识别与抑制综述

污泥膨胀是活性污泥法污水处理过程中常见的一类异常工况, 且具有严重危害性, 研究污泥膨胀的识别和抑制方法对城市污水处理过程正常运行意义重大. 本文主要针对城市污水处理过程中污泥膨胀的识别和抑制方法进行综述. 首先, 文章概述了城市污水处理过程, 介绍了污泥膨胀的概念、主要特点、类型和成因; 其次, 概述了基于微生物生理特征、机理模型、图像识别和数据驱动的污泥膨胀识别方法, 分析其发展现状并指出优缺点; 然后, 概述了基于过程调控和机理特征的污泥膨胀抑制方法, 分析其发展现状并对比优缺点; 最后, 总结全文, 指出了城市污水处理过程污泥膨胀识别和抑制面临的主要问题, 并对其研究趋势进行了展望.     

Enlarging the domain of attraction of MPC controllers

This paper presents a method for enlarging the domain of attraction of nonlinear model predictive control (MPC). The usual way of guaranteeing stability of nonlinear MPC is to add a terminal constraint and a terminal cost to the optimization problem such that the terminal region is a positively invariant set for the system and the terminal cost is an associated Lyapunov function. The domain of attraction of the controller depends on the size of the terminal region and the control horizon. By increasing the control horizon, the domain of attraction is enlarged but at the expense of a greater computational burden, while increasing the terminal region produces an enlargement without an extra cost.In this paper, the MPC formulation with terminal cost and constraint is modified, replacing the terminal constraint by a contractive terminal constraint. This constraint is given by a sequence of sets computed off-line that is based on the positively invariant set. Each set of this sequence does not need to be an invariant set and can be computed by a procedure which provides an inner approximation to the one-step set. This property allows us to use one-step approximations with a trade off between accuracy and computational burden for the computation of the sequence. This strategy guarantees closed loop-stability ensuring the enlargement of the domain of attraction and the local optimality of the controller. Moreover, this idea can be directly translated to robust MPC.     

Fuzzy control of the activated sludge wastewater treatment process

The activated sludge process is a commonly used method for treating sewage and waste waters. It is characterised by a lack of relevant instrumentation, control goals that are not always clearly stated, the use of qualitative information in decision making and poorly understood basic biological behaviour mechanisms. In this brief paper we examine the behaviour of an experimental fuzzy control algorithm constructed to reflect actual operational practice. We conclude that this algorithm does rather well and that a fuzzy controller would be a useful and practical way of regulating the activated sludge process.     

Subspace identification of multivariable linear parameter-varying systems

A subspace identification method is discussed that deals with multivariable linear parameter-varying state-space systems with affine parameter dependence. It is shown that a major problem with subspace methods for this kind of system is the enormous dimension of the data matrices involved. To overcome the curse of dimensionality, we suggest using only the most dominant rows of the data matrices in estimating the model. An efficient selection algorithm is discussed that does not require the formation of the complete data matrices, but processes them row by row.     

Inferential control of product quality attributes—application to food cooking extrusion process

Reducing product quality variability is one of the most important issues for the process industry. As product quality attributes (PQAs) are often measured in a laboratory using off-line sensors, direct feedback control is not feasible unless expensive on-line sensors are used. Inferential control provides a means to the solution of this type of problem without the cost of expensive sensors. This paper reports a successful application of control of product quality attributes in a food cooking extruder. It covers the essential steps in achieving the control objective: (1) identifying the influential variables that can be measured on-line and have significant impact on the product quality attributes; (2) estimating a dynamic model between the influential variables and the PQAs for on-line prediction of product quality; (3) on-line feedback control using the influential variables. Experimental results demonstrate that the designed control system not only maintains the quality of the products but also automatically brings the PQAs to user's specification.