Gain-scheduling model predictive control of a Fresnel collector field

Model predictive control strategies have been applied successfully when controlling solar plants. If the control algorithm uses a linear model associated only to an operating point, when the plant is working far from the design conditions, the performance of the controller may deteriorate.In this paper, a gain scheduling model predictive control strategy is designed for the Fresnel collector field located at the Escuela Superior de Ingenieros de Sevilla. Simulation results are provided comparing the proposed strategy with another linear MPC controller showing a better performance. Furthermore, two real tests are presented showing the effectiveness of the proposed strategy.     

Robust model predictive control for a nanofluid based solar thermal power plant

Among the several technologies for solar energy recovery, parabolic solar collectors have emerged as one of the most promising due to their performance, which can be enhanced if nanofluids are employed as heat transfer fluids instead of the traditional alternatives. The inherent time-dependent behavior of solar radiation profiles forces the solar thermal plants to be operated aided with controllers able to reject these strong disturbances. While traditional controllers can be employed for this aim, more advanced techniques such as Model Predictive Control are suggested since this optimal-control based method can be tuned to minimize operating costs, among some other features. The main objective of this work is to implement an MPC controller to a nanofluid-based solar thermal power plant in order to evaluate its performance to reject disturbances on the solar radiation profile in an efficient manner. An off-line nonlinear programming optimization was deployed so we could compare the response of the on-line MPC implementation on a strict enough basis. Furthermore, the performance of MPC controllers is affected by how well does the modeling of the system is able to stick to reality, thus, it is important to test if the controller is robust enough to deal with uncertainty that might be introduced as modeling errors. Results indicate that MPC controllers are suitable for their implementation on these kinds of power plants since they steer the system to achieve desired conditions by smoothly manipulating the decision variable, even in the scenarios where a substantial cascade-effect modeling error was imposed in the parameters of the nanofluid.     

Grey box modelling for model predictive control of a heating process

This paper presents a rational modelling procedure of a pilot heating process by using the grey box modelling method. A simplified nonlinear continuous model, based on the conservation of energy, is formed and unknown parameters of the model are estimated by using measured data from an experiment with the process. The model is expanded with a wider model structure by testing formulated hypothesis about the process. The model is also expanded in an engineering way by considering the shape of the residuals. During the model expansion the Likelihood ratio test is applied for falsification tests. The study uses the continuous model for both estimating the states of the process and controlling the system. A continuous-discrete extended Kalman filter estimates the model states and time varying disturbances. The model predictive controller is based on the continuous process model, but the optimisation of the control performance index is made at discrete sampling instances. The control law compensates for changing temperature references and compensate for varying load situations. Besides using the model for control purposes the case demonstrate the possibility of using the grey box modelling technique to estimate physical process parameters such as the thermal diffusivity of the process.     

Reference trajectory tuning of model predictive control

An approach to minimize tuning effort of nominal Model Predictive Control algorithms is proposed. The algorithm dynamically calculates output set points to accommodate user-defined output importance, which is more intuitive than selecting values for the MPC weighing matrices. Instead of tuning the weights on the outputs deviations from their set points, weights on the input values and input increments, which are the usual tuning parameters of MPC, the desired output control performance of the MPC can be specified by performance factors. The proposed method extends the existing methods that consider a reference trajectory for the output tracking to the case of zone control and input targets. The proposed method also assumes that, as in most commercial MPC packages, the controller has two layers: a static layer and an extended dynamic layer. The method is illustrated by three case studies, contemplating both SISO and MIMO systems. It is observed that: the output set point tracking performance can be changed without modifying the MPC tuning weights, the approach is capable of achieving similar performance to conventional MPC tuned by multiobjective optimization techniques from the literature, with a fraction of computer effort, and it can be integrated with Real Time Optimization algorithms to control complex systems, always respecting output constraints.     

Constrained output feedback model predictive control for nonlinear systems

A constrained output feedback model predictive control approach for nonlinear systems is presented in this paper. The state variables are observed using an unscented Kalman filter, which offers some advantages over an extended Kalman filter. A nonlinear dynamic model of the system, considered in this investigation, is developed considering all possible effective elements. The model is then adaptively linearized along the prediction horizon using a state-dependent state space representation. In order to improve the performance of the control system as many linearized models as the number of prediction horizons are obtained at each sample time. The optimum results of the previous sample time are utilized for linearization at the current sample time. Subsequently, a linear quadratic objective function with constraints is formulated using the developed governing equations of the plant. The performance and effectiveness of the proposed control approach is validated both in simulation and through real-time experimentation using a constrained highly nonlinear aerodynamic test rig, a twin rotor MIMO system (TRMS).     

状态空间模型的双层结构预测控制算法

双层结构预测控制是指先进行设定值优化、再进行设定值跟踪的预测控制.在已有的双层结构动态矩阵控制的基础上,本文给出基于状态空间模型的双层结构预测控制算法.该算法基于干扰模型和新定义的开环预测值,给出了新的开环预测模块.该开环预测模块采用Kalman滤波方法得到操作变量、被控变量的开环动、稳态预测值.基于这些开环预测值,稳态目标计算模块的基本原理同双层结构动态矩阵控制,但是具体细节上遵循状态空间方法.动态控制模块基于稳态目标计算提供的操作变量、被控变量的稳态目标(设定值),采用二次规划算法计算控制作用.仿真算例证实了该算法的有效性.     

Feedforward model predictive control

This paper examines the role played by feedforward in model predictive control (MPC). We contrast feedforward with preview action. The latter is standard in model predictive control, whereas feedforward has been rarely, if ever, used in contemporary formulations of MPC. We argue that feedforward can significantly improve performance in the presence of measurement noise and certain types of model uncertainty.     

On optimality of nonlinear model predictive control

In this note the optimality property of nonlinear model predictive control (MPC) is analyzed. It is well known that the MPC approximates arbitrarily well the infinite horizon (IH) controller as the optimization horizon increases. Hence, it makes sense to suppose that the performance of the MPC is a not decreasing function of the optimization horizon. This work, by means of a counterexample, shows that the previous conjecture is fallacious, even for simple linear systems.     

Multiobjective model predictive control

This paper proposes a novel model predictive control (MPC) scheme based on multiobjective optimization. At each sampling time, the MPC control action is chosen among the set of Pareto optimal solutions based on a time-varying, state-dependent decision criterion. Compared to standard single-objective MPC formulations, such a criterion allows one to take into account several, often irreconcilable, control specifications, such as high bandwidth (closed-loop promptness) when the state vector is far away from the equilibrium and low bandwidth (good noise rejection properties) near the equilibrium. After recasting the optimization problem associated with the multiobjective MPC controller as a multiparametric multiobjective linear or quadratic program, we show that it is possible to compute each Pareto optimal solution as an explicit piecewise affine function of the state vector and of the vector of weights to be assigned to the different objectives in order to get that particular Pareto optimal solution. Furthermore, we provide conditions for selecting Pareto optimal solutions so that the MPC control loop is asymptotically stable, and show the effectiveness of the approach in simulation examples.     

Unscented Kalman filter based nonlinear model predictive control of a LDPE autoclave reactor

This paper presents a multivariable nonlinear model predictive control (NMPC) scheme for the regulation of a low-density polyethylene (LDPE) autoclave reactor. A detailed mechanistic process model developed previously was used to describe the dynamics of the LDPE reactor and the properties of the polymer product. Closed-loop simulations are used to demonstrate the disturbance rejection and tracking performance of the NMPC algorithm for control of reactor temperature and weight-averaged molecular weight (WAMW). In addition, the effect of parametric uncertainty in the kinetic rate constants of the LDPE reactor model on closed-loop performance is discussed. The unscented Kalman filtering (UKF) algorithm is employed to estimate plant states and disturbances. All control simulations were performed under conditions of noisy process measurements and structural plant–model mismatch. Where appropriate, the performance of the NMPC algorithm is contrasted with that of linear model predictive control (LMPC). It is shown that for this application the closed-loop performance of the UKF based NMPC scheme is very good and is superior to that of the linear predictive controller.     

Cascade control of a distributed collector solar field

This paper reports experimental results on the cascade control of a distributed collector solar field. The control problem consists of keeping constant the field outlet oil temperature by acting on the circulating oil flow used for heat transfer. In the inner loop an adaptive model based predictive controller exploiting the information conveyed by accessible disturbances (radiation changes and inlet oil temperature) is used, while in the outer loop a PID is employed. The need for adaptive control arises from the time varying behaviour of the plant. Due to the generality of the methods employed, the experience reported is relevant to a wide class of industrial processes.     

Adaptive model predictive control for a class of constrained linear systems based on the comparison model

This paper proposes an adaptive model predictive control (MPC) algorithm for a class of constrained linear systems, which estimates system parameters on-line and produces the control input satisfying input/state constraints for possible parameter estimation errors. The key idea is to combine the robust MPC method based on the comparison model with an adaptive parameter estimation method suitable for MPC. To this end, first, a new parameter update method based on the moving horizon estimation is proposed, which allows to predict an estimation error bound over the prediction horizon. Second, an adaptive MPC algorithm is developed by combining the on-line parameter estimation with an MPC method based on the comparison model, suitably modified to cope with the time-varying case. This method guarantees feasibility and stability of the closed-loop system in the presence of state/input constraints. A numerical example is given to demonstrate its effectiveness.     

Feedback linearization control for a distributed solar collector field

This article describes the application of a feedback linearization technique for control of a distributed solar collector field using the energy from solar radiation to heat a fluid. The control target is to track an outlet temperature reference by manipulating the fluid flow rate through the solar field, while attenuating the effect of disturbances (mainly radiation and inlet temperature). The proposed control scheme is very easy to implement, as it uses a numerical approximation of the transport delay and a modification of the classical control scheme to improve startup in such a way that results compared with other control structures under similar conditions are improved while preserving short commissioning times. Experiments in the real plant are also described, demonstrating how operation can be started up efficiently.     

Linear programming and model predictive control

The practicality of model predictive control (MPC) is partially limited by the ability to solve optimization problems in real time. This requirement limits the viability of MPC as a control strategy for large scale processes. One strategy for improving the computational performance is to formulate MPC using a linear program. While the linear programming formulation seems appealing from a numerical standpoint, the controller does not necessarily yield good closed-loop performance. In this work, we explore MPC with an l₁ performance criterion. We demonstrate how the non-smoothness of the objective function may yield either dead-beat or idle control performance.     

Reduced complexity adaptive nonlinear control of a distributed collector solar field

An approach to the control of a distributed collector solar field relying on feedback linearization, Lyapunov based adaptation and a simplified plant model is presented. The control objective consists of manipulating the oil flow so that the outlet oil temperature is regulated around a given setpoint. For dealing with plant nonlinearities and external disturbances, a nonlinear transformation is performed on the accessible variables such that the transformed system behaves as an integrator, to which linear control techniques are then applied. Since the transformation depends on an unknown parameter, an adaptation law is designed so as to minimize a Lyapunov function for the whole system's state. For the sake of control synthesis a simplified plant model which retains the bilinear nonlinearity is employed. The resulting control law has the same control structure of the one yielding exact input-output linearization but assumes a different placement of a temperature sensor. In order to justify this procedure, plant internal dynamics is studied. Experimental results obtained in the actual field are presented.     

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.     

Least-restrictive move-blocking model predictive control

Move-blocking lowers the computational complexity of model predictive control (MPC) problems by reducing the number of optimization variables. However, this may render states close to constraints infeasible. Thus move-blocking generally results in control laws that are restrictive; the controller domains may be unacceptably and unnecessarily small. Furthermore, different move-blocking strategies may result in controller domains of different sizes, all other factors being equal. In this paper an approach is proposed to design move-blocking MPC control laws that are least-restrictive, i.e. the controller domain is equal to the maximum controlled invariant set. The domains of different move-blocking controllers are then by design equal to each other. This allows comparison of differing move-blocking strategies based on cost performance only, without needing to consider domain size also. Thus this paper is a step towards being able to derive optimal move-blocking MPC control laws.     

Constrained multivariable control of a distillation column using a simplified model predictive control algorithm

Distillation columns are important process units in petroleum refining and need to be maintained close to optimum operating conditions because of economic incentives. Model predictive control has been used for control of these units. However, the constrained optimization problem involved in the control has generally been solved in practice in a piece-meal fashion. To solve the problem without decomposition, the use of a linear programming (LP) formulation using a simplified model predictive control algorithm has been suggested in the literature. In this paper, the LP approach is applied for control of an industrial distillation column. The approach involved a very small size optimization problem and required very modest computational resources. The control algorithm eliminated the large cycling in the product composition that was present using SISO controllers. This resulted in a 2.5% increase in production rate, a 0.5% increase in product recovery, and a significant increase in profit.     

Robust model predictive control using tubes

A form of feedback model predictive control (MPC) that overcomes disadvantages of conventional MPC but which has manageable computational complexity is presented. The optimal control problem, solved on-line, yields a ‘tube’ and an associated piecewise affine control law that maintains the controlled trajectories in the tube despite uncertainty; computational complexity is linear (rather than exponential) in horizon length. Asymptotic stability of the controlled system is established.     

Learning-based tuning of supervisory model predictive control for drinking water networks

This paper presents a constrained Model Predictive Control (MPC) strategy enriched with soft-control techniques as neural networks and fuzzy logic, to incorporate self-tuning capabilities and reliability aspects for the management of drinking water networks (DWNs). The control system architecture consists in a multilayer controller with three hierarchical layers: learning and planning layer, supervision and adaptation layer, and feedback control layer. Results of applying the proposed approach to the Barcelona DWN show that the quasi-explicit nature of the proposed adaptive predictive controller leads to improve the computational time, especially when the complexity of the problem structure can vary while tuning the receding horizons.