Self-optimizing Control Research Articles

Maximum sustainable yield from interacting fish stocks in an uncertain world: two policy choices and underlying trade-offs

The case of fisheries management illustrates how the inherent structural instability of ecosystems can have deep-running policy implications. We contrast ten types of management plans to achieve maximum sustainable yields (MSY) from multiple stocks and compare their effectiveness based on a management strategy evaluation (MSE) that uses complex food webs in its operating model. Plans that target specific stock sizes ($B_{\text{MSY}}$) consistently led to higher yields than plans targeting specific fishing pressures ($F_{\text{MSY}}$). A new self-optimising control rule, introduced here for its robustness to structural instability, led to intermediate yields. Most plans outperformed single-species management plans with pressure targets set without considering multispecies interactions. However, more refined plans to "maximise the yield from each stock separately", in the sense of a Nash equilibrium, produced total yields comparable to plans aiming to maximise total harvested biomass, and were more robust to structural instability. Our analyses highlight trade-offs between yields, amenability to negotiations, pressures on biodiversity, and continuity with current approaches in the European context. Based on these results, we recommend directions for developments of EU fisheries policy.

The Importance of Nominal Operating Point Selection in Self-Optimizing Control

A self-optimizing control (SOC) structure is when we can achieve an acceptable loss with constant setpoints for controlled variables. In the original paper (Skogestad, J. Process Control, 2000, 10 (5), 487–507), the operating point is selected first and then the controlled variables, using the optimal values for nominal disturbance as setpoints. In this work, the importance of nominal operating point selection is evaluated, showing that setpoints obtained by optimization along the disturbance region can provide a better self-optimizing structure. A simultaneous procedure is proposed where controlled variables are selected together with the nominal operating point. Despite the more expensive optimization procedure, this new policy leads to a better controlled variables set. This is corroborated by a reactor–distillation case study and a cumene unit case study where the operating point selected decreases significantly the worst-case and mean losses for the process.

Process control of the advanced flash stripper for CO2 solvent regeneration

The advanced flash stripper (AFS) is an intensified process design for CO2 solvent regeneration in amine scrubbing. This work identified self-optimizing controlled variables for the energy recovery bypass flowrates of the AFS, as well as a controller configuration for the steam extraction flowrate. Two self-optimizing variables were selected using a high-fidelity steady state process model: the temperature difference at the top of the stripper packing and the temperature difference on the hot end of the stripper overhead heat exchanger. Ranges of possible off-design conditions for the rich loading, absorber temperature, rich flowrate, and flash tank operating temperature were evaluated, and the worst case heat duty for CO2 stripping of the self-optimizing control scheme was within 1% of the true system optimum. A low-order dynamic model was used to test the proposed self-optimizing control strategy and showed no significant control loop interactions in the closed-loop response. Cascade control, where the inner loop controlled the steam heater effluent temperature and the outer loop controlled the flash tank temperature, was found to have favorable dynamic performance compared to a non-cascaded structure with uncontrolled flash tank temperature.

Self-Optimizing Control of a Two-Stage Refrigeration Cycle

The application of self-optimizing control theory to a two-stage refrigeration cycle was investigated. Defining the cost function as the economical trade-off between the power consumption and the evaporator outlet temperatures, it was found that the optimal point of operation leaves two unconstrained degrees of freedom for implementing a self-optimizing control structure. We consider two cases: (1) where the self-optimizing control structure is designed to optimally reject only physical process disturbances, and (2) where the control structure in addition handles changes in the economic parameters of the cost function. The control structure is able to keep the process close to optimal despite disturbances and changes in the product prices, and thus makes a supervisory real-time optimization (RTO) layer unnecessary.

Subset Measurement Selection for Globally Self-Optimizing Control of Tennessee Eastman Process

The concept of globally optimal controlled variable selection has recently been proposed to improve self-optimizing control performance of traditional local approaches. However, the associated measurement subset selection problem has not be studied. In this paper, we consider the measurement subset selection problem for globally self-optimizing control (gSOC) of Tennessee Eastman (TE) process. The TE process contains substantial measurements and had been studied for SOC with controlled variables selected from individual measurements through exhaustive search. This process has been revisited with improved performance recently through a retrofit approach of gSOC. To extend the improvement further, the measurement subset selection problem for gSOC is considered in this work and solved through a modification of an existing partially bidirectional branch and bound (PB3) algorithm originally developed for local SOC. The modified PB3 algorithm efficiently identifies the best measurement candidates among the full set which obtains the globally minimal economic loss. Dynamic simulations are conducted to demonstrate the optimality of proposed results.

A Decentralized Hierarchical Control Structure and Self-Optimizing Control Strategy for F-P Type DGs in Islanded Microgrids

A decentralized and self-optimizing control strategy is proposed for the frequency-power droop type distributed generators (DGs). The main characteristics of the proposed control strategy are the following: 1) it is hierarchical and fully decentralized, i.e., the functions of primary, secondary and tertiary frequency control can be realized locally, with the microgrid centralized controller making communication networks unnecessary and 2) it can make DGs share loads according to the equal incremental principle. Simulation results verify the effectiveness of the proposed control strategy.

Null-space method for optimal operation of transient processes

We consider batch process optimization and robust implementation of optimal control policies. The dynamic optimization of such processes is in most cases model based, and therefore subject to uncertainties. This may lead to sub-optimal control trajectories with significant economical losses. In this paper we extended the concept of self-optimizing control for the optimal operation of transient processes. The main idea is to find a function of the measurements whose trajectory is optimally invariant to disturbances, and then track the trajectory using standard feedback controllers. Doing so results in near-optimal economic operation in spite of varying disturbances without the need for re-optimization. We show that the invariant trajectories can be computed as linear combinations of the measurement vector, where the combination matrix is easily obtained from optimal sensitivities. We illustrate the application of the proposed method in a semi-batch reactor case study.

Simulation of Variable-Pitch Control for Direct Drive Permanent Magnet Synchronous Wind Turbine

当风力机运行在高风速区域时，捕获的风能超过了发电机组额定运行范围，因此，本文采用调节桨距角的方式维持发电机功率输出在额定值附近。首先介绍了变桨型风力机的特点和结构；接着针对风力发电系统非线性强的特点，提出采用模糊控制的策略实现桨距角的变换。通过分析模糊控制原理，设计自优化模糊PID控制器，并建立变桨控制仿真模型，完成与传统PID调节的对比分析。 When the wind turbines work in the high speed region, they capture more wind energy than ge-nerating units rated operating range. Therefore, in this paper, the way of adjusting the pitch angle was used to maintain generator power output in the vicinity of the rating. First of all, the paper introduces the characteristics and structure of variable-pitch wind turbine; then according to the strong nonlinear characteristics of wind power generation system, the fuzzy control strategy to realize the transformation of the pitch was proposed. By analyzing the principle of fuzzy control, the self-optimizing fuzzy PID controller is designed, and the simulation model of variable pitch control is established. And the comparison of the traditional PID regulation is accomplished.

Global Approximation of Self-Optimizing Controlled Variables with Average Loss Minimization

Self-optimizing control (SOC) constitutes an important class of control strategies for real-time optimization (RTO) of chemical plants, by means of selecting appropriate controlled variables (CVs). Within the scope of SOC, this paper develops a CV selection methodology for a global solution which aims to minimize the average economic loss across the entire operation space. A major characteristic making the new scheme different from existing ones is that each uncertain scenario is independently considered in the new solution without relying on a linearized model, which was necessary in existing local SOC methods. Although global CV selection has been formulated as a nonlinear programming (NLP) problem, a tractable numerical algorithm for a rigorous solution is not available. In this work, a number of measures are introduced to ease the challenge. First, we suggest representing the economic loss as a quadratic function against the controlled variables through Taylor expansion, such that the average loss bec...

Self-optimizing control structure design in oxy-fuel circulating fluidized bed combustion

A wealth of control designs and experience are available for traditional air combustion in circulating fluidized bed (CFB) boilers. For the novel process of oxy combustion (for facilitated CO2 capture) input gas compositions and flows can be adjusted independently, which decouples fluidization and oxygen carrying tasks and introduces new degrees of freedom and alternatives for control. The self-optimizing control approach (as formulated by Skogestad and colleagues in the 2000s) was used with steady-state approximations of a validated dynamic model for a pilot-size CFB combustor to study how the added degrees of freedom should be used. Instead of centralized online optimization of setpoints, self-optimizing control searches for a set of controlled variables which can be kept at constant setpoints despite disturbances and measurement errors, resulting in performance with acceptable steady-state loss. Results for air firing support method validity by suggesting the common practice in control; keeping power, flue gas O2 and primary air/fuel feed ratio constant. For oxy firing, various control structures could satisfactorily compensate for studied disturbances and errors. Results suggest direct oxidant O2% control or simpler feed-forward solutions in line with current industrial CFB control, or alternatively using the added degrees of freedom for controlling variables such as furnace temperatures. Differences in, e.g. controllability, dynamic performance and implementation cost are relevant in further studies. The results serve as a first step in oxy-CFB control studies, suggesting candidate structures for dynamic analysis.

Extremum seeking control for efficient operation of hybrid ground source heat pump system

The Hybrid Ground Source Heat Pump (GSHP) systems combine the renewable geothermal energy and cooling tower for rejecting the cooling load, which is often adopted for high cooling demand. Model based control can be limited due to variations in ambient conditions, ground-loop heat exchanger (GHE) and equipment characteristics, cost and reliability of sensors. A self-optimizing control scheme is proposed for efficient operation of the hybrid GSHP based on Extremum Seeking Control (ESC), with feedback of the total power consumption and the control inputs of the relative flow rate of cooling tower and the water pump speed. The cooling capacity of the heat pump regulates the evaporator leaving water at 7 °C. A Modelica based dynamic simulation model is developed for a Hybrid GSHP system, with the vertical GHE model adopted from Modelica Buildings Library. The transient heat transfer is implemented with a finite volume method inside and outside the borehole. The proposed ESC scheme is evaluated under the scenarios of fixed cooling load, ramp change in the evaporator inlet water temperature, diurnal sinusoidal cycle of air wet-bulb temperature, and realistic ambient and cooling load condition. Simulation results show the proposed ESC strategy effectively achieves nearly optimal efficiency without the need for plant model.

Integrating self-optimizing control and real-time optimization using zone control MPC

The combination of real-time optimization (RTO) and model predictive control (MPC) methodologies is widely used in the chemical and petrochemical industry to optimize continuous processes. However, often the setpoint updates computed by the RTO are not frequent enough to capture all disturbances. This leads to suboptimal process operation, because the system is not re-optimized after a disturbance, until it has reached its new (suboptimal) steady state. An efficient way to handle this issue is to include economic considerations in the design of the lower MPC layer. This is the main idea of self-optimizing control (SOC), where controlled variables are selected, such that keeping them constant results in near-optimal operation without requiring an RTO update. Thus, we argue that SOC is complementary to RTO, and we develop a new MPC strategy with zone control and SOC variable targets. In particular, we present an approach toward solving the problem of low-frequency setpoint updates, also when the active set changes. We demonstrate the performance of our approach in steady state and dynamic simulations, and compare it to a classic RTO/MPC combination. The results show that our approach improves the coordination between the RTO and MPC layers. As it gives better performance in between RTO executions, it also leads to a higher overall profit.

Model predictive control for the self-optimized operation in wastewater treatment plants: Analysis of dynamic issues

This paper describes a procedure to find the best controlled variables in an economic sense for the activated sludge process in a wastewater treatment plant, despite the large load disturbances. A novel dynamic analysis of the closed loop control of these variables has been performed, considering a nonlinear model predictive controller (NMPC) and a particular distributed NMPC-PI control structure where the PI is devoted to control the process active constraints and the NMPC the self-optimizing variables. The well-known self-optimizing control methodology has been applied, considering the most important measurements of the process. This methodology provides the optimum combination of measurements to keep constant with minimum economic loss. In order to avoid nonfeasible dynamic operation, a preselection of the measurements has been performed, based on the nonlinear model of the process and evaluating the possibility of keeping their values constant in the presence of typical disturbances.

Dual-loop self-optimizing robust control of wind power generation with Doubly-Fed Induction Generator

This paper presents a self-optimizing robust control scheme that can maximize the power generation for a variable speed wind turbine with Doubly-Fed Induction Generator (DFIG) operated in Region 2. A dual-loop control structure is proposed to synergize the conversion from aerodynamic power to rotor power and the conversion from rotor power to the electrical power. The outer loop is an Extremum Seeking Control (ESC) based generator torque regulation via the electric power feedback. The ESC can search for the optimal generator torque constant to maximize the rotor power without wind measurement or accurate knowledge of power map. The inner loop is a vector-control based scheme that can both regulate the generator torque requested by the ESC and also maximize the conversion from the rotor power to grid power. An ℋ∞ controller is synthesized for maximizing, with performance specifications defined based upon the spectrum of the rotor power obtained by the ESC. Also, the controller is designed to be robust against the variations of some generator parameters. The proposed control strategy is validated via simulation study based on the synergy of several software packages including the TurbSim and FAST developed by NREL, Simulink and SimPowerSystems.

Enhanced-efficiency operating variables selection for vapor compression refrigeration cycle system

In this paper, a novel enhanced-efficiency selection of operating variables based on self-optimizing control (SOC) method for the vapor compression refrigeration cycle (VCC) system is proposed. An objective function is proposed to maximize the energy efficiency of the VCC system while meeting with the demand of indoor thermal comfort. With the detailed analysis of operating variables, three unconstrained degrees of freedom are selected among all the candidate operating variables. Then two SOC methods are applied to determine the optimal individual controlled variables (CVs) and measurement combinations as CVs. The model predictive control (MPC) method based controllers and PID controllers are designed for different sets of CVs, and the experimental results indicate that the proposed selection of CVs can achieve a good trade-off between optimal (or near optimal) stable operation and enhanced-efficiency of the synthesized control structure.

Self-optimizing control of air-source heat pump with multivariable extremum seeking

The air-source heat pump (ASHP) is widely adopted for cooling and heating of residential and commercial buildings. The performance of ASHP can be controlled by several operating variables, such as compressor capacity, condenser fan speed, evaporator fan speed and suction superheat. In practice, the system characteristics can be varied significantly by the variations in ambient condition, operation setpoint, internal thermal load and equipment degradation, which makes it difficult to obtain accurate plant models. As consequence, the model based control strategies for ASHP could limit the achievable energy efficiency. Model-free self-optimizing control strategies are thus more preferable. In this study, a multi-input extremum seeking control (ESC) scheme is proposed for both heating and cooling operation of ASHP. The zone temperature is assumed to be regulated by the compressor capacity, while the expansion valve opening is used to regulate the suction superheat at the given setpoint. The total power consumption of the compressor, the condenser fan and the evaporator fan is measured as input to the ESC, while the ESC controls the evaporator fan speed, the condenser fan speed and the suction superheat setpoint. The proposed scheme is evaluated with a Modelica based dynamic simulation model of ASHP under both cooling and heating modes of operation. Simulation results show the effectiveness of the proposed scheme to achieve the maximum achievable efficiency in a nearly model-free manner.

A generic methodology for the optimisation of sewer systems using stochastic programming and self-optimizing control

The design of sewer system control is a complex task given the large size of the sewer networks, the transient dynamics of the water flow and the stochastic nature of rainfall. This contribution presents a generic methodology for the design of a self-optimising controller in sewer systems. Such controller is aimed at keeping the system close to the optimal performance, thanks to an optimal selection of controlled variables. The definition of an optimal performance was carried out by a two-stage optimisation (stochastic and deterministic) to take into account both the overflow during the current rain event as well as the expected overflow given the probability of a future rain event. The methodology is successfully applied to design an optimising control strategy for a subcatchment area in Copenhagen. The results are promising and expected to contribute to the advance of the operation and control problem of sewer systems.

Extremum seeking control of COP optimization for air-source transcritical CO2 heat pump water heater system

Abstract Air-source transcritical CO2 heat pump systems have found attractive applications in automobile air conditioning, regional heating and commercial water heating systems. The coefficient of performance (COP) of such systems is affected by several operational variables, such as ambient temperatures, water outlet temperature, and discharge pressure. For practical operation, it is desirable to maintain the maximum achievable efficiency or COP of such systems in real time. However, performance of model based control/optimization strategies can be quite limited by the difficulty in acquiring accurate system models due to system nonlinearity, large variations in ambient conditions and thermal load, as well as equipment variation and degradation. In this study, a self-optimizing control scheme is proposed to maximize the COP in real time by using the extremum seeking control (ESC) strategy. ESC is a class of self-optimizing control strategy that can search for the unknown or slowly varying optimum input with respect to certain performance index, which is effectively a dynamic realization of the gradient search based on a dither-demodulation scheme. For the air-source transcritical CO2 heat-pump water heater, the discharge pressure setpoint is taken as the input to the ESC controller, while the system COP is taken as the performance index, i.e. the feedback signal for the extremum seeking process. To evaluate the proposed ESC strategy, a Modelica based dynamic simulation model is developed for the plant to perform the simulation study. Simulations are conducted for several scenarios: a fixed operation condition, change of the water outlet temperature setpoint, change of ambient condition, and changes of both the ambient temperature and water outlet temperature setpoint. For all simulation cases, the water inlet temperature is fixed at 12 °C, the ambient temperature is assumed to range from −15 °C to −35 °C, while the water outlet temperature ranges from 55 °C to 80 °C. Simulation results show that ESC is able to search and even track both fixed and slowly varying optimum COP without need for system model. Significant recovery of energy efficiency can thus be obtained for practical operation of such systems in a nearly model-free fashion.

Optimal Operation of a Three-Product Dividing-Wall Column with Self-Optimizing Control Structure Design

This paper deals with optimal operation of a three-product Dividing-Wall Column (DWC). The main idea is to design a control structure, through a systematic procedure for plantwide control, with an objective to achieve desired product purities with the minimum use of energy. Exact local method is used to find the best controlled variables as single measurement or combination of measurements based on the idea of self-optimizing control. It concluded that it is possible to have better self-optimizing properties by controlling linear combinations of measurements than by controlling conventional individual measurements. Dynamic validation showed that the proposed control structure with the aid of low-complexity simple PI controller stabilized the plant, rejected the effect of disturbances and made DWC to produce product with desired specifications.

Dynamic Self-Optimizing Control for Oil Reservoir Waterflooding

Waterflooding is a common oil recovery method where water is injected into the reservoir for increased productivity. Optimal operational strategy of waterflooding processes has to consider proceeds realized from produced oil and cost of productions including both injected and produced water. This is a dynamic optimization problem. The problem could be solved through numerical algorithms based on traditional optimal control theory which can provide only open-loop control solutions and rely on an accurate process model. However, reservoir properties are extremely uncertain, and hence open-loop solutions based on a nominal model are not suitable for applications with real reservoirs. Introduction of feedback into the optimization structure to counteract the effect of uncertainties has been proposed recently. In this work, a novel feedback optimization method for optimal waterflooding operation is presented. In the approach, appropriate controlled variables as combinations of measurement histories and manipulated variables are first derived through regression based on simulation data obtained from a nominal model. Then a feedback control law was represented as a linear function of measurement histories from the controlled variables obtained. Through a case study, it was shown that the feedback control solution proposed in this work was able to achieve a near-optimal operational profit with only 0.45% worse than that achieved through the true optimal control (with system's properties assumed to be known a priori), but 95.05% better than that obtained with the open-loop solution under uncertainties.