Adaptive UKF-based model predictive control of a Fresnel collector field

One of the ways to improve the efficiency of solar energy plants is by using advanced control and optimization algorithms. In particular, model predictive control strategies have been applied successfully in their control.The control objective of this kind of plant is to regulate the solar field outlet temperature around a desired set-point. Due to the highly nonlinear dynamics of these plants, a simple linear controller with fixed parameters is not able to cope with the changing dynamics and the multiple disturbance sources affecting the field.In this paper, an adaptative model predictive control strategy is designed for a Fresnel collector field belonging to the solar cooling plant installed at the Escuela Superior de Ingenieros in Sevilla. The controller changes the linear model used to predict the future evolution of the system with respect to the operating point.Since only the inlet and outlet temperatures of the heat transfer fluid are measurable, the intermediate temperatures have to be estimated. An unscented Kalman filter is used as a state estimator. It estimates metal-fluid temperature profiles and effective solar radiation.Simulation results are provided comparing the proposed strategy with a PID + feedforward series controller showing better performance. The controller is also compared to a gain scheduling generalized predictive controller (GS-GPC) which has previously been tested at the actual plant with a very good performance. The proposed strategy outperforms these two strategies.Furthermore, two real tests are presented. These tests show that the proposed controller achieves adequate set-point tracking in spite of strong disturbances.     

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.     

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.     

A switching control strategy applied to a solar collector field

This work presents a new switching control procedure that has been chosen to deal with the changes in plant dynamics. Several control systems composed of IMC-based PID controllers and feedforward compensators are designed for each operation region and a continuous switching mechanism for the overall control system is defined. Experimental tests which have been performed in a distributed collector field of a solar air cooling system, are presented showing promising results for the proposed strategy.     

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.     

Generation of optimal schedules for metro lines using model predictive control

This paper presents a new methodology for computation of optimal train schedules in metro lines using a linear-programming-based model predictive control formulation. The train traffic model is comprised of dynamic equations describing the evolution of train headways and train passenger loads along the metro line, considering the time variation of the passenger demand and all relevant safety and operational constraints for practical use of the generated schedule. The performance index is a weighted sum of convex piecewise-linear functions for directly or indirectly modelling the waiting time of passengers at stations, onboard passenger comfort, train trip duration and number of trains in service. The proposed methodology is computationally very efficient and can generate optimal schedules for a whole day operation as well as schedules for transition between two separate time periods with known schedules. The use and performance of the proposed methodology is illustrated by an application to a metro line similar to the North-South line of São Paulo Underground.     

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.     

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.     

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.     

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.     

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.     

A hybrid model predictive control strategy for nonlinear plant-wide control

A plant-wide control strategy based on integrating linear model predictive control (LMPC) and nonlinear model predictive control (NMPC) is proposed. The hybrid method is applicable to plants that can be decomposed into approximately linear subsystems and highly nonlinear subsystems that interact via mass and energy flows. LMPC is applied to the linear subsystems and NMPC is applied to the nonlinear subsystems. A simple controller coordination strategy that counteracts interaction effects is proposed for the case of one linear subsystem and one nonlinear subsystem. A reactor/separator process with recycle is used to compare the hybrid method to conventional LMPC and NMPC techniques.     

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.     

Period-robust repetitive model predictive control

Repetitive model predictive control (RMPC) incorporates the idea of repetitive control (RC) into the basic formulation of model predictive control (MPC) to enable the user to take full advantage of the constraint handling, multivariable control features of MPC in controlling a periodic process. The RMPC achieves perfect asymptotic setpoint tracking/disturbance rejection in periodic processes, provided that the period length used in the control formulation matches the actual period of the reference/disturbance signal exactly. Even a small mismatch between the actual period of the process and the controller period can deteriorate the RMPCs performance significantly. The period mismatch can occur either from an inaccurate estimation of the actual frequency of disturbance due to resolution limit or from trying to force the controller period to be an integer multiple of the sampling time. For such cases, an extension of RMPC called “period-robust” repetitive model predictive control (pr-RMPC) is proposed. It is based on the idea of using weighted, multiple memory loops in RC, such that small changes in period length do not diminish the tracking/rejection properties by much. Simulation results show that, in case of a slight period mismatch, pr-RMPC achieves significant improvement over the standard RMPC in rejecting periodic disturbances.     

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.     

Generalized terminal state constraint for model predictive control

A terminal state equality constraint for Model Predictive Control (MPC) laws is investigated, where the terminal state/input pair is not fixed a priori but it is a free variable in the optimization. The approach, named “generalized” terminal state constraint, can be used for both tracking MPC (i.e. when the objective is to track a given steady state) and economic MPC (i.e. when the objective is to minimize a cost function which does not necessarily attains its minimum at a steady state). It is shown that the proposed technique provides, in general, a larger feasibility set with respect to the existing approaches, given the same prediction horizon. Moreover, a new receding horizon strategy is introduced, exploiting the generalized terminal state constraint. Under mild assumptions, the new strategy is guaranteed to converge in finite time, with arbitrarily good accuracy, to an MPC law with an optimally-chosen terminal state constraint, while still enjoying a larger feasibility set. The features of the new technique are illustrated by an inverted pendulum example in both the tracking and the economic contexts.     

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.     

Coalitional model predictive control of an irrigation canal

We present a hierarchical control scheme for large-scale systems whose components can exchange information through a data network. The main goal of the supervisory layer is to find the best compromise between control performance and communicational costs by actively modifying the network topology. The actions taken at the supervisory layer alter the control agents’ knowledge of the complete system, and the set of agents with which they can communicate. Each group of linked subsystems, or coalition, is independently controlled through a decentralized model predictive control (MPC) scheme, managed at the bottom layer. Hard constraints on the inputs are imposed, while soft constraints on the states are considered to avoid feasibility issues. The performance of the proposed control scheme is validated on a model of the Dez irrigation canal, implemented on the accurate simulator for water systems SOBEK. Finally, the results are compared with those obtained using a centralized MPC controller.     

Cyber-security in networked and distributed model predictive control

Distributed model predictive control (DMPC) schemes have become a popular choice for networked control problems. Under this approach, local controllers use a model to predict its subsystem behavior during a certain horizon so as to find the sequence of inputs that optimizes its evolution according to a given criterion. Some convenient features of this method are the explicit handling of constraints and the exchange of information between controllers to coordinate their actuation and minimize undesired mutual interactions. However, we find that schemes have been developed naively, presenting flaws and vulnerabilities that malicious entities can exploit to gain leverage in cyber-attacks. The goal of this work is to raise awareness about this issue by reviewing the vulnerabilities of DMPC methods and surveying defense mechanisms. Finally, several examples are given to indicate how these defense mechanisms can be implemented in DMPC controllers.