Two approaches to significantly reduce ship model simulation times at Marin are presented. Combin... more Two approaches to significantly reduce ship model simulation times at Marin are presented. Combining them is shown to provide a most interesting and general perspective for improvement. One approach makes use of a highly simplified ship model that can be partly solved analytically. The other applies proper orthogonal decomposition (POD) to reduce the ship model currently used at Marin. POD is demonstrated using a model that is more convenient for presentation and implementation than the Marin ship model. Arguments are provided why POD is expected to also work for Marin ship simulations.
Drying processes are highly energy consuming and can lead to degradation of product quality. Opti... more Drying processes are highly energy consuming and can lead to degradation of product quality. Optimisation of a drying process is studied based on an extensive model, which combines a model on macro-scale with a distributed, nonlinear and stiff model on micro-scale. Using a multi objective function, optimal control trajectories are computed for different drying times and for two cases: a biotechnological and a food industry application of enzyme drying. The optimisation results indicate the existence of an optimal drying time, an increase in the profit and an improvement of the performance of the operation. Particularly, the optimisations reveal that spatial quality distributions need to be integrated in the optimisation procedure, either in the objective function or as a constraint, instead of the common practice of an average quality index. It even appears that the spatial quality distributions inside the material can be influenced by the trajectory of control variables.
UD factorisations of algorithms for optimal full and reduced-order output feedback control of dis... more UD factorisations of algorithms for optimal full and reduced-order output feedback control of discrete-time systems with white stochastic parameters have been published by us in two recent papers. Although all examples in both papers were successfully and correctly solved they all lacked a cross product in the quadratic cost function as well as a cross covariance between the additive white system and measurement noise. The UD factored algorithms published by us claimed to also solve problems including such a cross product and cross covariance. As is demonstrated in this technical communique they do not. We also demonstrate that when the parameters of the input and output matrix of the system are all deterministic, still allowing for stochastic parameters in the state matrix, the UD factored algorithms can be easily adapted to do so. If not the algorithms can also be adapted to do so but at the expense of an additional intermediate recovery of two of the four UD factored matrices dur...
A Kalman decomposition for linear time-varying discrete-time systems is introduced that detects t... more A Kalman decomposition for linear time-varying discrete-time systems is introduced that detects temporal uncontrollability/unreconstructability that is not detected by any of the four conventional Kalman decompositions. This new discrete-time Kalman decomposition is associated with j-step reachability and k-step observability. The system structure obtained from the Kalman decomposition may be interpreted as the temporal linear system structure. This paper reveals that the difference between controllability and reachability as well as reconstructability and observability is entirely due to changes of the temporal linear system structure. Finally this paper reveals how our Kalman decomposition relates to the conventional ones and how temporal discrete-time linear system properties relate to their well established non temporal counterparts.
Abstract. A wide range of various classical and modern control methods is classified from the poi... more Abstract. A wide range of various classical and modern control methods is classified from the point of view of required information and put in the context of optimization.
Abstract Two time-scale receding horizon optimal control (TTRHOC) of greenhouse cultivation is in... more Abstract Two time-scale receding horizon optimal control (TTRHOC) of greenhouse cultivation is investigated. Recent developments enable closure of the outer-loop of this control system because they facilitate on-line recomputation of the optimal control of the slow dynamics on a daily basis. This paper quantifies the benefits obtained from having an outer closed-loop that counteracts errors and changes concerning predictions of crop growth, long-term weather, revenues obtained from selling crops and costs to control greenhouse climate. As a special, important case LED lighting is considered which increases both crop growth and profit. Having an outer closed-loop is especially beneficial in this case.
A two time-scale, receding horizon, optimal controller for greenhouse lettuce cultivation is exte... more A two time-scale, receding horizon, optimal controller for greenhouse lettuce cultivation is extended with on-line parameter estimation to handle ill-known or time-varying parameters of the greenhouse-crop model. By means of simulations, the possible improvement of performance and reduction of constraint violation, introduced by this extension, are investigated. Moreover, uncommon issues in the adaptive controller design due to the two time-scales are considered and handled in this paper. The estimated parameters are selected based on their uncertainty and performance sensitivity. Using a recently developed very efficient algorithm, the selected parameters are checked for identifiability first. Finally the possibility of real-time implementation of the adaptive two time-scale receding horizon optimal controller is investigated.
Abstract The optimal control of greenhouse climate and crop cultivation is performed by two-time-... more Abstract The optimal control of greenhouse climate and crop cultivation is performed by two-time-scale decomposition. First the slow sub-problem is solved leading lo a seasonal pattern tor the crop adjoint variables associated to the assimilate buffer, and the fruit and leaf weights. The adjoint variables or co-states are then used to represent the marginal price of a unit of buffer, leaf and fruit in an on-line receding horizon control of the greenhouse climate. Comparing simulations using the dynamic co-slates to experimental results obtained with fixed co-states reveals that the on-line control is sensitive to the co-state trajectory. This suggests that it is advantageous to repeat the seasonal optimization from time to time to adjust to past weather and realized crop state.
Two approaches to significantly reduce ship model simulation times at Marin are presented. Combin... more Two approaches to significantly reduce ship model simulation times at Marin are presented. Combining them is shown to provide a most interesting and general perspective for improvement. One approach makes use of a highly simplified ship model that can be partly solved analytically. The other applies proper orthogonal decomposition (POD) to reduce the ship model currently used at Marin. POD is demonstrated using a model that is more convenient for presentation and implementation than the Marin ship model. Arguments are provided why POD is expected to also work for Marin ship simulations.
Drying processes are highly energy consuming and can lead to degradation of product quality. Opti... more Drying processes are highly energy consuming and can lead to degradation of product quality. Optimisation of a drying process is studied based on an extensive model, which combines a model on macro-scale with a distributed, nonlinear and stiff model on micro-scale. Using a multi objective function, optimal control trajectories are computed for different drying times and for two cases: a biotechnological and a food industry application of enzyme drying. The optimisation results indicate the existence of an optimal drying time, an increase in the profit and an improvement of the performance of the operation. Particularly, the optimisations reveal that spatial quality distributions need to be integrated in the optimisation procedure, either in the objective function or as a constraint, instead of the common practice of an average quality index. It even appears that the spatial quality distributions inside the material can be influenced by the trajectory of control variables.
UD factorisations of algorithms for optimal full and reduced-order output feedback control of dis... more UD factorisations of algorithms for optimal full and reduced-order output feedback control of discrete-time systems with white stochastic parameters have been published by us in two recent papers. Although all examples in both papers were successfully and correctly solved they all lacked a cross product in the quadratic cost function as well as a cross covariance between the additive white system and measurement noise. The UD factored algorithms published by us claimed to also solve problems including such a cross product and cross covariance. As is demonstrated in this technical communique they do not. We also demonstrate that when the parameters of the input and output matrix of the system are all deterministic, still allowing for stochastic parameters in the state matrix, the UD factored algorithms can be easily adapted to do so. If not the algorithms can also be adapted to do so but at the expense of an additional intermediate recovery of two of the four UD factored matrices dur...
A Kalman decomposition for linear time-varying discrete-time systems is introduced that detects t... more A Kalman decomposition for linear time-varying discrete-time systems is introduced that detects temporal uncontrollability/unreconstructability that is not detected by any of the four conventional Kalman decompositions. This new discrete-time Kalman decomposition is associated with j-step reachability and k-step observability. The system structure obtained from the Kalman decomposition may be interpreted as the temporal linear system structure. This paper reveals that the difference between controllability and reachability as well as reconstructability and observability is entirely due to changes of the temporal linear system structure. Finally this paper reveals how our Kalman decomposition relates to the conventional ones and how temporal discrete-time linear system properties relate to their well established non temporal counterparts.
Abstract. A wide range of various classical and modern control methods is classified from the poi... more Abstract. A wide range of various classical and modern control methods is classified from the point of view of required information and put in the context of optimization.
Abstract Two time-scale receding horizon optimal control (TTRHOC) of greenhouse cultivation is in... more Abstract Two time-scale receding horizon optimal control (TTRHOC) of greenhouse cultivation is investigated. Recent developments enable closure of the outer-loop of this control system because they facilitate on-line recomputation of the optimal control of the slow dynamics on a daily basis. This paper quantifies the benefits obtained from having an outer closed-loop that counteracts errors and changes concerning predictions of crop growth, long-term weather, revenues obtained from selling crops and costs to control greenhouse climate. As a special, important case LED lighting is considered which increases both crop growth and profit. Having an outer closed-loop is especially beneficial in this case.
A two time-scale, receding horizon, optimal controller for greenhouse lettuce cultivation is exte... more A two time-scale, receding horizon, optimal controller for greenhouse lettuce cultivation is extended with on-line parameter estimation to handle ill-known or time-varying parameters of the greenhouse-crop model. By means of simulations, the possible improvement of performance and reduction of constraint violation, introduced by this extension, are investigated. Moreover, uncommon issues in the adaptive controller design due to the two time-scales are considered and handled in this paper. The estimated parameters are selected based on their uncertainty and performance sensitivity. Using a recently developed very efficient algorithm, the selected parameters are checked for identifiability first. Finally the possibility of real-time implementation of the adaptive two time-scale receding horizon optimal controller is investigated.
Abstract The optimal control of greenhouse climate and crop cultivation is performed by two-time-... more Abstract The optimal control of greenhouse climate and crop cultivation is performed by two-time-scale decomposition. First the slow sub-problem is solved leading lo a seasonal pattern tor the crop adjoint variables associated to the assimilate buffer, and the fruit and leaf weights. The adjoint variables or co-states are then used to represent the marginal price of a unit of buffer, leaf and fruit in an on-line receding horizon control of the greenhouse climate. Comparing simulations using the dynamic co-slates to experimental results obtained with fixed co-states reveals that the on-line control is sensitive to the co-state trajectory. This suggests that it is advantageous to repeat the seasonal optimization from time to time to adjust to past weather and realized crop state.
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