CN112526879A - Parameter determination method, device, control method, system and medium for temperature control system - Google Patents
Parameter determination method, device, control method, system and medium for temperature control system Download PDFInfo
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Abstract
The application provides a control parameter determining method and device for a temperature control system, a temperature control method, the temperature control system and a computer readable storage medium.
Description
Technical Field
The present disclosure relates to the field of temperature control technologies, and in particular, to a method and an apparatus for determining control parameters of a temperature control system, a temperature control method, a temperature control system, and a computer-readable storage medium.
Background
Temperature control is an indispensable ring in modern life, industrial production and agricultural production, and the most important function of the temperature control is to regulate the temperature of indoor environment. In a traditional temperature control system with a PID controller (proportion-integral-derivative controller, proportion P, integral I and derivative D), parameters of the PID controller are fixed values, and a parameter optimization method is complex and has poor control effect, so that the indoor environment temperature fluctuation is large and the error is large, the temperature is unstable, the production environment cannot reach the standard, and the customer experience is poor.
In view of the above problems, no effective solution has been proposed.
Disclosure of Invention
In view of the above, the present application provides a method and an apparatus for determining control parameters for a temperature control system, a temperature control method, a temperature control system, and a computer readable storage medium, which are used for determining optimal control parameters of a PID controller based on an acquired expected temperature and an actual temperature by using an intelligent algorithm with a global optimization characteristic, so as to solve the problems of large temperature control fluctuation, large error, and instability of the conventional temperature control system, and improve the control effect.
According to one aspect of the present application, there is provided a control parameter determination method for a temperature control system having a PID controller, the method comprising:
acquiring a desired temperature and an actual temperature;
and determining the optimal control parameters of the PID controller by adopting an intelligent algorithm with global optimization characteristics based on the acquired expected temperature and the acquired actual temperature, so that the PID controller can use the determined optimal control parameters to execute temperature control.
Optionally, the intelligent algorithm comprises a bat algorithm.
Optionally, determining the optimal control parameter of the PID controller includes:
passing a predetermined operation on an error of the desired temperature and the actual temperature as an objective function of the bat algorithm;
and taking the reciprocal of the target function as a fitness function of the bat algorithm, and taking a three-dimensional vector solution with the maximum fitness as an optimal control parameter of the PID controller.
Optionally, the error between the desired temperature and the actual temperature is used as an objective function of the bat algorithm through a predetermined operation, including:
multiplying an absolute value of the error by a time integral as the objective function.
Optionally, taking a three-dimensional vector solution with the maximum fitness as the optimal control parameter of the PID controller, including: and taking the three-dimensional vector solution with the maximum fitness as the optimal values of the proportional parameter, the integral parameter and the differential parameter of the PID controller.
Optionally, a bat population of the bat algorithm is initialized using a random distribution method or a k-means clustering method.
According to yet another aspect of the present invention, there is provided a control parameter determination apparatus for a temperature control system having a PID controller, the apparatus comprising:
a data acquisition unit for acquiring a desired temperature and an actual temperature;
and the parameter determining unit is used for determining the optimal control parameter of the PID controller by adopting an intelligent algorithm with global optimization characteristics based on the expected temperature and the actual temperature acquired by the data acquiring unit so that the PID controller can use the determined optimal control parameter to execute temperature control.
Optionally, the intelligent algorithm comprises a bat algorithm.
Optionally, determining the optimal control parameter of the PID controller includes:
passing a predetermined operation on an error of the desired temperature and the actual temperature as an objective function of the bat algorithm;
and taking the reciprocal of the target function as a fitness function of the bat algorithm, and taking a three-dimensional vector solution with the maximum fitness as an optimal control parameter of the PID controller.
Optionally, the error between the desired temperature and the actual temperature is used as an objective function of the bat algorithm through a predetermined operation, including:
multiplying an absolute value of the error by a time integral as the objective function.
Optionally, taking a three-dimensional vector solution with the maximum fitness as the optimal control parameter of the PID controller, including: and taking the three-dimensional vector solution with the maximum fitness as the optimal values of the proportional parameter, the integral parameter and the differential parameter of the PID controller.
Optionally, a bat population of the bat algorithm is initialized using a random distribution method or a k-means clustering method.
According to yet another aspect of the present application, there is provided a temperature control method for a temperature control system having a PID controller, the method comprising:
acquiring a desired temperature and an actual temperature;
determining optimal control parameters of the PID controller by adopting an intelligent algorithm with global optimization characteristics based on the acquired expected temperature and the actual temperature;
the PID controller performs temperature control using the determined optimum control parameter.
According to yet another aspect of the present application, a temperature control system includes:
a PID controller and control parameter determining means as described previously;
the PID controller performs temperature control using the optimum control parameter determined by the control parameter determining means.
According to yet another aspect of the present application, a temperature control system includes: at least one processor, and a memory communicatively coupled to the at least one processor; wherein the memory stores instructions executable by the at least one processor, and the at least one processor executes the control parameter determination method of the present application by executing the instructions stored by the memory.
According to yet another aspect of the present application, a computer-readable storage medium having stored thereon computer instructions which, when run on a computer, cause the computer to perform the control parameter determination method of the claims.
According to the control parameter determining method, the control parameter determining device, the temperature control method, the temperature control system and the computer readable storage medium for the temperature control system, the optimal control parameters of the PID controller are determined by adopting an intelligent algorithm with global optimization characteristics based on the acquired expected temperature and the actual temperature, the problems of large control temperature fluctuation, large error and instability of the traditional temperature control system are solved, the control effect is improved, the temperature control system has good adaptivity and robustness, and the environment temperature is guaranteed to be maintained at the appropriate temperature in life and production.
The foregoing description is only an overview of the technical solutions of the present application, and in order to make the technical solutions of the present application more clear and clear, and to implement the technical solutions according to the content of the description, the following detailed description is made with reference to the preferred embodiments of the present application and the accompanying drawings.
Drawings
The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate an embodiment of the invention and, together with the description, serve to explain the invention and not to limit the invention. In the drawings:
FIG. 1 illustrates a schematic view of an embodiment of a temperature control system of the present application;
FIG. 2 illustrates a schematic diagram of an embodiment of a control parameter determining device for a temperature control system of the present application;
FIG. 3 illustrates a schematic diagram of an embodiment of a flow of a bat algorithm for a temperature control system of the present application;
FIG. 4 illustrates a schematic diagram of an embodiment of the present application for initializing a bat population using a random distribution method;
FIG. 5 illustrates a schematic diagram of an embodiment of the present application for initializing bat populations using a k-means clustering method;
FIG. 6 is a schematic diagram illustrating one embodiment of a control parameter determination method for a temperature control system according to the present application;
FIG. 7 illustrates a schematic diagram of an embodiment of a temperature control method for a temperature control system of the present application.
Detailed Description
In order to make the objects, technical solutions and advantages of the present application more apparent, the technical solutions of the present application will be described in detail and completely with reference to the following specific embodiments of the present application and the accompanying drawings. It should be apparent that the described embodiments are only some of the embodiments of the present application, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present application.
FIG. 1 shows a schematic view of an embodiment of a temperature control system of the present application.
As shown, the temperature control system 1 includes a PID controller 11 and a control parameter determination device 12.
The temperature control system 1 is any system for temperature control, such as a home air conditioning system or a central air conditioning system.
The PID controller is a common feedback loop component in industrial control application, consists of a proportional unit P, an integral unit I and a derivative unit D, and is a widely applied and technically mature controller. The basic idea of PID control is to combine three parameters of proportional, integral and differential (Kp, Ki, Kd) of deviation by linearity to form a controller, and to control the controlled object, and when PID control is adopted, the quality of system control depends on the setting of the three parameters. The output of the PID controller can be changed by adjusting the size of the Kp, Ki and Kd parameters, and the PID controller output acts on a controlled object, so that the response speed, overshoot, stability and precision of the system can be adjusted.
The PID controller 11 performs temperature control using the optimum control parameter determined by the control parameter determining means 12.
Fig. 2 shows a schematic diagram of an embodiment of a control parameter determining device for a temperature control system of the present application.
As shown in the figure, the control parameter determination device 12 includes a data acquisition unit 121 and a parameter determination unit 122.
A data acquisition unit 121 for acquiring the desired temperature and the actual temperature.
As an example, when the weather is hot, the user sets the target temperature of the air conditioning system, i.e., the desired temperature, to be 26 degrees and the current actual temperature measured by the air conditioning system to be 30 degrees by a temperature setting device, such as a wall controller, a remote control application, a home appliance control applet, or the like. The data acquiring unit 121 is used to acquire the desired temperature being 26 degrees and the actual temperature being 30 degrees, for example, the data acquiring unit 121 may obtain the actual temperature by reading data of the sensor, may obtain the desired temperature by reading the desired temperature setting module, and may also obtain the desired temperature and the actual temperature by directly reading system parameters, but is not limited thereto. When the acquired expected temperature is lower than the actual temperature, the air conditioning system needs to be cooled at the moment, so that the frequency of a compressor of the air conditioning system needs to be increased, but if the frequency of the compressor is too high, the actual temperature is much lower than 26 ℃ after a certain time, the frequency of the compressor needs to be reduced at the moment, and the proportional, integral and differential parameters of the PID controller play a role in adjusting the increased or reduced frequency at the moment. Therefore, in the process of temperature reduction or temperature rise of the temperature control system, the three parameters of the PID controller Kp, Ki and Kd are used for controlling the 'strength' of temperature reduction or temperature rise. However, the parameters of the traditional PID controller are usually fixed values, the parameter optimization method is complicated, the control effect is poor, and the indoor environment temperature fluctuation is large and the error is large, so that the temperature is unstable, the production environment cannot reach the standard, and the customer experience is poor.
Therefore, the parameter determining unit 122 of the present application is adopted to optimize the control parameters of the PID controller, so that the temperature control of the air conditioning system is faster, smoother, more stable and more adaptive.
The parameter determining unit 122 determines an optimal control parameter of the PID controller of the temperature control system by using an intelligent algorithm with a global optimization characteristic based on the expected temperature and the actual temperature acquired by the data acquiring unit 121, so that the PID controller performs temperature control using the determined optimal control parameter.
The intelligent algorithms with global optimization characteristics include a plurality of algorithms, such as a particle swarm algorithm, a genetic algorithm, a simulated annealing algorithm, a differential evolution algorithm, an artificial fish swarm algorithm, an artificial bee swarm algorithm, an artificial bat algorithm, a fruit fly optimization algorithm, and the like.
BA (Bat Algorithm), a bat algorithm, a group intelligent optimization algorithm, a novel optimization algorithm which is inspired by the behavior that bats adopt echo positioning to prey, is a heuristic intelligent search algorithm, has the advantages of simple model, high convergence speed, few parameters and the like, is suitable for solving the unconstrained optimization problem, and has good inherent advantages for optimizing the PID parameter problem. Therefore, the bat algorithm is exemplarily applied to the temperature control system, and the control parameters are optimized by utilizing the global optimizing characteristic of the bat algorithm.
The BA has the basic principle that the value of the bat position in the space is used as the solution of an objective function, then the corresponding fitness value is calculated according to the solution and the objective function, the bat individual is moved by simulating the bat predation process, if the bat individual is closer to food after being moved (namely the fitness value is larger), the bat position is updated, otherwise, the bat position is not updated.
In the present application, a temperature error (i.e., deviation) is calculated from a desired temperature e (t) and an actual temperature y (t), where e (t) is r (t) -y (t), and the PID controller outputs u (t) as:
where t is time, representing the sampling period of the PID controller. Which is parameter dependent, the sampling period will influence the actual temperature value.
Then, as can be seen from the above formula, the error of the desired temperature from the actual temperature can be made to be an objective function of the bat algorithm by a predetermined operation.
One implementation may be to multiply the absolute value of the temperature error by the time integral as an objective function J of the bat algorithm:
the smaller the value of J, the smaller the error and the better the control, i.e. the smaller the value of J, the larger the fitness value, so the fitness function g is taken as:
then, in the solution space range, a group of solutions with the maximum fitness g is found to be the optimal solutions.
The position of the bat in the bat algorithm is the solution to be found, and the position of the bat is represented by a three-dimensional vector, so that in the application, the proportional parameter, the integral parameter and the differential parameter of the PID controller can form the three-dimensional vector as the position of the bat, namely the solution of the bat algorithm
Finding out the optimal solution, namely finding out the optimal control parameters Kp, Ki and Kd of the PID controller.
FIG. 3 shows a schematic diagram of an embodiment of a flow of a bat algorithm for a temperature control system of the present application.
As shown in the figure, the control parameter determination device 12 includes a data acquisition unit 121 and a parameter determination unit 122.
And S1, initializing bat population parameters.
First randomly initializing the bat position in a solution space
Speed of rotation
Bat position
Is a three-dimensional vector [ Kp, Ki, Kd]I.e. by
As one implementation, Kp ∈ [0.01,10], Ki ∈ [0.01,10], Kd ∈ [0,10 ]; velocity v ∈ [ -0.5,0.5 ]; the population size N is 40, namely the bat number i belongs to [1,40], the iteration number M is 1000, namely the algebra z belongs to [0,999 ].
The bat population of the bat algorithm can be initialized by a random distribution method or a k-means clustering method.
And S2, calculating the optimal individual in the current population.
And calculating the fitness value of each individual in the current population, and finding out the optimal bat position X.
And S3, updating the individual frequency, position and speed.
The frequency, the position and the speed of the bats are updated, and the updating result is obtained by the following formula:
fi＝fmin+(fmax-fmin)β (1)
wherein beta is a random number on [0,1 ].
fiThe sound frequency f emitted by the batmaxAnd fminFor maximum and minimum values of the frequency, the frequency variation range can be adjusted according to the actual situation, e.g. frequency fmax＝2,fmin＝0。
The bat is positioned in
At a speed of
z is an algebra, z-1 is a previous generation, and i is a bat number.
The bat can continuously update the loudness of the sound wave in the process of approaching to the prey
Frequency of sum
The closer to the prey, the smaller the loudness and the greater the frequency. As one implementation, initial loudness
Take [1,2 ]]Random number of (2), initial frequency ri 0Take [0,0.05 ]]The random number of (2).
The position of the next generation bat is obtained through the above steps S1, S2, S3
S4, judging the random number rand1>ri？
riThe frequency of the ith bat. Generate a [0,1]]Random number rand1, if rand1>riStep S5 is executed.
And S5, obtaining a local new solution through the formula (5).
Selecting the optimal bat individual X obtained in the step S2 as SoldObtaining a local new solution by a random walk method, as shown in formula (5), wherein epsilon is [ -1,1]Random number of (A)zThe current population average loudness.
xnew＝xold+εAz (5)
S6, judging the random number rand2<Ai？
AiRepresenting the loudness of the ith bat. Generate a [0,1]]Random number rand2, if rand2<AiStep S7 is executed.
S7, judgment XnewIs the fitness value of?
At this time XnewIf the fitness value of the objective function is better than X in the previous stepoldThen step S8 is executed.
S8, receiving a new solution Xnew。
I.e. the new solution replaces the original optimal position.
And adjusting loudness and frequency according to:
ri z＝r0[1-exp(-γ×t)] (6)
as one implementation, the loudness and frequency adjustment coefficient α is 0.9.
And sequencing all the individual fitness values in the current population, and finding the highest X of the fitness values.
And searching a local new solution near the optimal bat position through the steps S4-S8, and replacing the original optimal position with the new solution if the fitness of the new solution is higher.
And S9, repeating the step S2-8 until the precision condition is met or the maximum iteration number is reached, wherein the result is the global optimal solution, namely the X with the highest fitness value is found, namely the optimal control parameters [ Kp, Ki and Kd ] are found, and outputting the result.
Optionally, steps S3' are added between steps S3-S4 as follows:
the bat of the next generation is mutated with the mutation probability of
Wherein P isc1＝0.2，Pc20.1, g' is the fitness value of the individual, gavgIs the mean value of the population fitness value of this generation, gmaxThe position of the bat is varied for the maximum fitness value of the generation group, and the variation formula is as follows:
wherein N (0,1) is a standard Gaussian distribution;
and calculating the fitness value of each bat, and finding out the X with the maximum fitness value to replace the X originally used in the step S2 in the steps S4-S8. Therefore, the efficiency and the precision of finding the optimal solution are further improved.
Compared with the traditional PID controller, the PID controller with BA optimized parameters has the advantages of strong robustness, high precision, high convergence speed and the like.
In step S1, if the initial population is initialized using the random distribution method, it may fall into a local optimal solution, then preferably, as mentioned above, the bat initial population may be initialized using a k-means clustering algorithm.
The k-means clustering algorithm is a clustering analysis algorithm for iterative solution, has the characteristics of simple calculation, dynamic clustering, strong self-adaptive capacity and the like, has wide application fields, and can obtain a good clustering result particularly when solving the problem that mode distribution presents in-class clustering, wherein in the invention, the k-means clustering algorithm enables the initial population distribution to be more uniform, the solution speed and the convergence speed to be faster, and the specific process is as follows:
dividing N bat individuals into K groups, and randomly selecting K individuals as initial clustering centers.
Calculating the distance between each individual and the cluster center, and assigning each individual to the cluster center closest to the individual.
And thirdly, recalculating the central point of the cluster, and taking the central point as a new cluster center.
And fourthly, repeating the steps 2 and 3 until the change of the clustering center is smaller than a set value, wherein the K central points are the initial bat individuals.
Fig. 4 shows a schematic diagram of an embodiment of the present application for initializing a bat population using a random distribution method.
Fig. 5 shows a schematic diagram of an embodiment of the present application for initializing bat populations using a k-means clustering method.
As shown in the figure, the initial population distributed by the k-means clustering algorithm is more uniform than the initial population distributed randomly, so that the diversity of understanding is improved, and the local optimal solution is not easy to fall into.
The present application further includes a control parameter determining method corresponding to the control parameter determining apparatus, and fig. 6 is a schematic diagram illustrating an embodiment of the control parameter determining method for a temperature control system according to the present application.
Step S121, acquiring an expected temperature and an actual temperature;
and step S122, based on the acquired expected temperature and the actual temperature, adopting an intelligent algorithm with global optimization characteristics to determine the optimal control parameters of the PID controller, so that the PID controller can use the determined optimal control parameters to execute temperature control.
Since the processes and functions implemented by the method of the present embodiment substantially correspond to the embodiments, principles and examples of the apparatus, reference may be made to the related descriptions in the embodiments without being detailed in the description of the present embodiment, which is not described herein again.
The present application further includes a temperature control method corresponding to the temperature control system, and fig. 7 is a schematic diagram illustrating an embodiment of the temperature control method for the temperature control system according to the present application.
Step S11, acquiring an expected temperature and an actual temperature;
step S12, based on the obtained expected temperature and actual temperature, adopting an intelligent algorithm with global optimizing characteristics to determine the optimal control parameters of the PID controller;
in step S13, the PID controller performs temperature control using the determined optimum control parameter.
In conclusion, by using the solution of the present application, the optimal control parameters can be adjusted in real time in the sampling period of the PID controller, so as to achieve a better temperature control effect.
Since the processing and functions implemented by the method of the present embodiment substantially correspond to the embodiments, principles and examples of the system, reference may be made to the related descriptions in the embodiments without being detailed in the description of the present embodiment, which is not described herein again.
The present application further includes a temperature control system comprising at least one processor, and a memory communicatively coupled to the at least one processor; the memory stores instructions executable by the at least one processor, and the at least one processor executes the temperature control method according to the embodiment of the invention by executing the instructions stored in the memory.
Based on the same inventive concept, an embodiment of the present invention further provides a computer-readable storage medium, where computer instructions are stored, and when the computer instructions are executed on a computer, the computer is caused to execute the debugging method of the air conditioner motor according to the embodiment of the present invention.
As will be appreciated by one skilled in the art, embodiments of the present invention may be provided as a method, system, or computer program product. Accordingly, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present invention may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present invention is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
It will be apparent to those skilled in the art that various changes and modifications may be made in the present invention without departing from the spirit and scope of the invention. Thus, if such modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include such modifications and variations.
It should be noted that the embodiments and features of the embodiments may be combined with each other without conflict. Any simple modification, equivalent change and modification of the above embodiments according to the technical spirit of the present invention still fall within the scope of the technical solution of the present invention.
Claims (16)
1. A control parameter determination method for a temperature control system having a PID controller, the method comprising:
acquiring a desired temperature and an actual temperature;
and determining the optimal control parameters of the PID controller by adopting an intelligent algorithm with global optimization characteristics based on the acquired expected temperature and the acquired actual temperature, so that the PID controller can use the determined optimal control parameters to execute temperature control.
2. The method of claim 1, wherein:
the intelligent algorithm comprises a bat algorithm.
3. The method of claim 2, wherein: determining optimal control parameters of the PID controller, including:
passing a predetermined operation on an error of the desired temperature and the actual temperature as an objective function of the bat algorithm;
and taking the reciprocal of the target function as a fitness function of the bat algorithm, and taking a three-dimensional vector solution with the maximum fitness as an optimal control parameter of the PID controller.
4. The method of claim 3, wherein: passing a predetermined operation on an error of the desired temperature and the actual temperature as an objective function of the bat algorithm, comprising:
multiplying an absolute value of the error by a time integral as the objective function.
5. The method according to claim 3, wherein the optimal control parameter of the PID controller is a three-dimensional vector solution with maximum fitness, and the method comprises the following steps: and taking the three-dimensional vector solution with the maximum fitness as the optimal values of the proportional parameter, the integral parameter and the differential parameter of the PID controller.
6. The method of claim 1, wherein:
and initializing the bat population of the bat algorithm by utilizing a random distribution method or a k-means clustering method.
7. A control parameter determination apparatus for a temperature control system having a PID controller, the apparatus comprising:
a data acquisition unit for acquiring a desired temperature and an actual temperature;
and the parameter determining unit is used for determining the optimal control parameter of the PID controller by adopting an intelligent algorithm with global optimization characteristics based on the expected temperature and the actual temperature acquired by the data acquiring unit so that the PID controller can use the determined optimal control parameter to execute temperature control.
8. The apparatus of claim 7, wherein:
the intelligent algorithm comprises a bat algorithm.
9. The apparatus of claim 8, wherein determining optimal control parameters for the PID controller comprises:
passing a predetermined operation on an error of the desired temperature and the actual temperature as an objective function of the bat algorithm;
and taking the reciprocal of the target function as a fitness function of the bat algorithm, and taking a three-dimensional vector solution with the maximum fitness as an optimal control parameter of the PID controller.
10. The apparatus of claim 9, wherein:
passing a predetermined operation on an error of the desired temperature and the actual temperature as an objective function of the bat algorithm, comprising:
multiplying an absolute value of the error by a time integral as the objective function.
11. The apparatus of claim 9, wherein the three-dimensional vector solution with the largest fitness is used as the optimal control parameter of the PID controller, and comprises:
and taking the three-dimensional vector solution with the maximum fitness as a proportional parameter, an integral parameter and a differential parameter of the PID controller.
12. The apparatus of claim 7, wherein:
and initializing the bat population of the bat algorithm by utilizing a random distribution method or a k-means clustering method.
13. A temperature control method for a temperature control system having a PID controller, the method comprising:
acquiring a desired temperature and an actual temperature;
determining optimal control parameters of the PID controller by adopting an intelligent algorithm with global optimization characteristics based on the acquired expected temperature and the actual temperature;
the PID controller performs temperature control using the determined optimum control parameter.
14. A temperature control system, comprising:
a PID controller and control parameter determining means as claimed in any one of claims 7 to 12;
the PID controller performs temperature control using the optimum control parameter determined by the control parameter determining means.
15. A temperature control system, comprising: at least one processor, and a memory communicatively coupled to the at least one processor; wherein the memory stores instructions executable by the at least one processor to perform the method of any one of claims 1 to 6 by executing the instructions stored by the memory.
16. A computer-readable storage medium having stored thereon computer instructions which, when executed on a computer, cause the computer to perform the method of any one of claims 1 to 6.
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