ES2345801A1 - Fractional order control system with programmed gain of water levels in main irrigation channels (Machine-translation by Google Translate, not legally binding) - Google Patents

Abstract

Fractional order control system with programmed gain of water levels in main irrigation channels that includes, at least: (a) a plurality of gates at the beginning (2) and end (3) of the channel section (1), a downstream water level sensor (5) located at the end of the channel section (1), an analog converter/digital (8), a digital/analog converter (10) and a motor (11) that moves the start gate (2) of the channel section (1); y (b) a water level sensor upstream (6) located at the end of the preceding section, a water level sensor downstream located at the beginning of the section (4), a gate position sensor (7) located in the gate upstream of the section and a fractional order controller with programmed gain (9) that generates the error signals e (kt) and control ufdli (kt). (Machine-translation by Google Translate, not legally binding)

Description

Fractional order control system with programmed gain of water levels in main channels of irrigation.

The purpose of the control system recommended by The present invention is to increase the robustness and effectiveness in the control of water levels in the sections of the channels main irrigation which are characterized by presenting large variations in all its dynamic parameters, such as gain, time constants and delays, by varying the download to through its upstream gates, so that, it increases the operability in the distribution of water in these sections, raise safety in the operation of the control system, as well as obtain a significant reduction in current water losses for exploitation concept. The present invention is framed in the technical sectors of hydraulics and agriculture, more specifically in relation to the control systems of water levels in main irrigation canals.

Background of the invention

Currently, there are different control systems that perform the downstream regulation of water levels in a section of a main irrigation canal. The PID controllers (proportional, integral and derivative) of these systems are generally tuned on the basis of the mathematical model that describes the nominal dynamic behavior of said section. However, when changing the hydraulic conditions of the section of the channel (for example, the discharge through its upstream gate) the parameters (gain and time delay) of the mathematical model that describes the dynamic behavior of said section experience a certain variation in relation to its nominal values, causing serious effects on the control of the water level in said section and consequently causing great losses of water in the canal. The PID controllers used in these systems do not have the robustness necessary to carry out an effective control of the water levels under conditions of variation in a certain range of the parameters that describe the dynamic behavior of the section of the channel ( vid Patentes SU362895, SU1135837, CA2450151 and US4349296).

Other control systems estimate online parameters describing dynamic behavior of the channel section (gain and time delay) and later readjust (re-tune) the parameters online of the controller using an adaptive algorithm. These systems are characterized by presenting structures and control algorithms very complex. They also have a global behavior (stability and / or robustness) highly sensitive to any error that it can be committed to reset the parameters of the controller, what often causes the total loss of the stability of the control system. To improve the stability of these systems, the controllers are designed with an algorithm of operation that produces a very slow readjustment of its parameters, which causes the control system to lose the ability to quickly follow abrupt variations in water levels that originate in the section of the channel. This leads to a low operability in the section of the channel and therefore to an increase in water losses throughout the canal (Patent CU21885).

To improve the robustness in the control of the distribution of water in the sections of the main irrigation channels characterized by presenting variable dynamic parameters (gain and time delay) there are systems that consider the application of a discrete fractional order controller ( FPID ) , which is named by the expression PI λ D \ (Patent ES2277757). These systems are more robust than control systems based on classic controllers ( PIDs ), because the PI ^ {\ lambda} D ^ {\ mu} controllers have two more tuning parameters than the PID controllers (the fractional order coefficients \ lambda and \ mu). The fractional order coefficients (\ lambda and \ mu) are used to comply with additional design specifications and achieve more robust control systems against the uncertainties of the processes, among which are the variations of their dynamic parameters. There are sections of main irrigation channels (such as the first section of the Imperial Canal of Aragon of the Hydrographic Confederation of the Ebro, Spain) in which the discharge varies through its gate upstream in the operating range ( Q_ {min} ( t ), Q_ {max} ( t )) originate large variations in all parameters (gain, time constants and time delay) that characterize the dynamic behavior of that section. In these cases, fractional order controllers do not make it possible to obtain a high effectiveness in the control, especially in the range of greater variations of said parameters, leading to large losses of water throughout the channel.

Description of the invention

To alleviate the problems mentioned above, presents the fractional order control system with profit programmed water levels in main irrigation canals, object of the present invention. Said system comprises, at less:

(a) a plurality of gates at the beginning and end of the channel section, a downstream water level sensor located at the end of the section, an analog / digital converter, a digital / analog converter and a motor that moves the gate beginning of the section;

(b) an upstream water level sensor located at the end of the preceding section, a water level sensor downstream located at the beginning of the section, a position sensor of gate located on the gate upstream of the section and a fractional order controller with programmed gain that generates error and control signals; and where, in addition,

said fractional order controller with programmed gain is comprised of n discrete FDI type fractional controllers ( DI \ lambda ), which are tuned for different sub-ranges of variation of the operation discharge through the gate upstream of the section and incorporating a block for calculating the current discharge through the gate upstream of the section, which makes it possible to connect the tuned DI ^ {\ lambda} i controller for the variation sub-range of the operation download to which the current download belongs.

Thanks to the system described in this way, the robustness and effectiveness in the control of water levels in the sections of the main irrigation canals is increased, characterized by large variations in all its dynamic parameters (gain, time constants and time delay) by varying the discharge through its upstream gates in the operating range ( Q_ {min} ( t ), Q_ {max} ( t )), in order to increase the operability in the distribution of water in these sections, to increase the safety in the operation of the control system, as well as to obtain a significant reduction in current water losses due to exploitation.

A controller is considered robust when:

(1) has a low sensitivity for the purpose of the plant (channel) that were not considered in the analysis phase and control system design (for example dynamic not modeled, disturbances, measurement noise, etc.);

(2) guarantees stable operation of the control system over the entire range of variations of the dynamic parameters of the plant (channel), and

(3) exhibit the desired behavior, complying with the design specifications, despite the presence of large uncertainties in the plant (large variations in dynamic parameters of the channel).

Brief description of the figures

Then it goes on to describe very brief a series of drawings that help to better understand the invention and that expressly relate to an embodiment of said invention presented as a non-limiting example of is:

Fig 1.- Schematically represents the configuration and control system elements object of the present invention

Fig 2.- Schematically represents the closed loop configuration of fractional order with programmed gain object of the present invention.

Preferred Embodiment of the Invention

Figure 1 shows the configuration and elements of the fractional order control system with gain computer-based programming of water levels in a stretch of A main irrigation canal. The section of the main irrigation canal 1, with gate 2 upstream (from the beginning) of the section and gate 3 downstream (of the end) of the section, it presents a level sensor of the downstream water 4 located at the beginning of the section, a sensor downstream water levels 5 located at the end of the section, a sensor of upstream water levels 6 located at the end of the section above and a gate position sensor 7 located in the gate upstream of the section.

The output signals of the water level sensors 4, 5 and 6 ( H_ {aabc} ( t ), H_ {aabf} ( t ), H_ {aar} ( t )) and the output signal of the position sensor of gate 7 ( a ( t )) by means of analog / digital converter A / D 8 are converted into discrete signals ( H_ {aabc} ( kT ), H_ {aabf} ( kT ), H_ {aar} ( kT ), a ( kT )). The fractional order controller with programmed gain ( FDIGP ) 9 enables the effective control of water levels in the channel section, generating the error signals e ( kT ) and control signals u FDI \ i ( kT ) in correspondence with a discrete FDI type fractional order control algorithm. The discrete control signal u FDI \ i ( kT ) is converted into a continuous signal u FDI \ i ( t ) by the digital / analog converter D / A 10, which represents a sampling device and data retention. The continuous control signal u FDI \ i ( t ) acts on the motor 11 of the gate 2 upstream of the section, causing displacements of said gate corresponding to the magnitude and sign of the error signal e ( kT ) . The displacements of gate 2 cause variations in the inlet discharge to the section, which are maintained as long as the error signal e ( kT ) does not equal zero.

Figure 2 shows the loop configuration of closed control of fractional order with programmed gain of water levels in a section of a main irrigation canal.

The calculation block of the discharge 12 on the basis of the signals H_ {aar} ( kT ), H_ {aabc} ( kT ) and a ( kT ) calculates the current discharge ( Q_ {j} ( t )) through the gate upstream of the section determines the variation subrange (Δ Q_ {j} ( t )) of the operating discharge ( Q_ {min} ( t ), Q_ {max} ( t )) to which said unloads and closes the contact of the DI controller ? tuned for said subrange.

The present invention in this embodiment refers to a new fractional order control system with programmed gain of water levels in a section of a main irrigation channel, which incorporates a computer (PC) as a fractional order controller with programmed gain ( FPIGP ). The inclusion of the computer greatly facilitates the implementation and execution of the fractional order control algorithm with programmed gain. The control of the water levels in the section of the channel is carried out in correspondence with the downstream regulation method with remote water level sensor (located at the end of the section).

As is known, as the discharge varies through the gate upstream of the section of the channel in the operating range ( Q_ {min} ( t ), Q_ {max} ( t )), the dynamic parameters (gain, constants) vary of time and time delay) of the section of the channel over a wide range. In this case, the mathematical model that describes the dynamic behavior of the variation of the water level downstream at the end of the section is described by the expression:

one

where:

ΔH_aabf ( t ) - variation of the water level downstream at the end of the section;

Δ u ( t ) - variation of the position of the gate upstream of the section;

K ( t ) - gain of the tranche;

T1 ( t ), T2 ( t ) - time constants;

\ tau ( t ) - time delay.

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The range of variation of the parameters Dynamic model equation [1] is represented by the expressions:

2

The fractional order controller with programmed gain ( FDIGP ) is comprised of n fractional order (integrative derivative) DI ( FDI ) controllers, which are called by the expression DI ^ {\ lambda} _ {i} , i =
1,2, ..., n . Each of these controllers is tuned for a certain sub-range of variation (\ Delta Q_ {i} ( t )) of the operation discharge ( Q_ {min} ( t ), Q_ {max} ( t )) a through the gate upstream of the section of the canal, where:

3

That is, the total range of the operation discharge ( Q_ {min} ( t ), Q_ {max} ( t )) through the upstream gate is subdivided into n sub-ranges of variations \ Delta Q_ {i} ( t ) smaller 100 for each of which a fractional order controller ( DI ^ {\ lambda} {i} , i = 1,2, ..., n ) is tuned on the basis of the actual variations experienced by the dynamic parameters of the channel section 101 1000 when the current discharge ( Q_ {i} ( t )) through the upstream gate is in the variation sub-range \ Delta Q_ {i} ( t ), where:

102

The fact of having a controller with programmed gain ( FDIGP ) made up of n controllers of fractional order ( DI ^ {\ lambda} {i} , i = 1,2, ..., n ) and tuning the parameters of Each of these controllers, based on a certain sub-range of variation of the dynamic parameters of the section of the channel, makes it possible to increase the robustness and effectiveness of the control system by varying the discharge throughout the entire operating range, as well as raising the safety in the operation of the control system.

The current download through the gate upstream of the section of the canal is determined by the expression:

4

where:

C d - gate discharge coefficient;

L - gate width;

a ( t ) - magnitude of gate opening;

H_ {aar} ( t ) - upstream water level;

H_ {aabc} ( t ) - water level downstream at the beginning of the section;

g - acceleration of the force of gravity.

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The control algorithm of each of the fractional order controllers ( DI <\ lambda} i ) in the time domain is represented by the equation:

5

where:

u FDI \ i ( t ) - control signal;

D r - integer-differential operator of non-integer order r ;

\ lambda_ {i} - arbitrary real number (0 \ leq \ lambda_ {i} \ leq 1);

K P \ i - coefficient of proportionality;

T d \ i - time constant;

e ( t ) - error signal between the controlled variable (downstream water level) and the reference signal.

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Equation 4 in the frequency domain is Represented by the following transfer function:

6

The magnitudes of the water levels downstream at the beginning and end of the section ( H_ {aab} ( t )) and upstream ( H_ {aar} ( t )), as well as the magnitude of opening of the upstream gate ( a ( t )) are captured by the respective water level sensors (SN) and by the gate position sensor (SPC) and transmitted to the analog / digital converter (A / D), which converts them into discrete signals ( H_ {aar} ( kT ), H_ {aabc} ( kT ), H_ {aabf} ( kT ), a ( kT )) for processing by the fractional order controller with programmed gain ( FDIGP ). The value of the downstream water level reference signal at the end of the channel section ( H_ {r, \ aabf} ( kT )) is registered and stored in the controller memory ( FDIGP ) and can be varied by operators corresponding to the operating regime of the channel.

The error signal is determined by the expression:

7

The signals H_ {aar} ( kT ), H_ {aabc} ( kT ) and a ( kT ) are processed by the controller download calculation block ( FDIGP ), which by equation 3 calculates the current discharge ( Q_ {j} ( t )) through the gate upstream of the section of the channel and determines to which of the sub-ranges of variations ( ΔQ_ {i} ( t )) does said discharge belong. Corresponding to the value obtained from the variation sub-range (\ Delta Q_ {i} ( t )) to which the current discharge ( Q_ {j} ( t )) belongs through the gate upstream of the section, the block Calculation of the discharge closes the contact of the controller DI ^ {i} , tuned for said sub-range (see Figure 2). In this way, the connected DI ^ {\ lambda} i processor processes the error signal e ( kT ) and generates the control signal ( u FDI \ i ( kT )), corresponding to the magnitude and sign of the error signal ( e ( kT )).

The control signal is generated through a discrete FDI control algorithm, which has the form:

8

where:

80 - discrete equivalent of the integer-differential operator of order not integer r ,
0 < r <1, which is determined by the following general formula:

9

T - sampling period.

Equation 8 represents a function of Rational transfer of discrete time of infinite order. A approach as a finite order rational function is obtained applying the continuous fraction expansion method (CFE). Using this method, equation 8 is expressed as:

10

where:

CFE { U } - denotes the expansion of continuous fractions of U ;

P ( z -1), Q ( z -1) - polynomials of degree p , q respectively.

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The discrete control signal ( u FDI \ i ( kT )) of the controller output ( FDIGP ) is converted into a continuous control signal ( u FDI \ i ( t )) by the digital / analog converter (D / A), which represents a sampling and data retention device.

The continuous control signal ( u FDI \ i ( t )) acts on the motor that moves the gate upstream of the section, causing a displacement of said gate in correspondence with the magnitude and sign of the error signal ( e ( kT )). In this way the current discharge is varied through the gate upstream of the channel section, until the error signal e ( kT ) is equal to zero.

From equation 7, it is observed that the DI <\ lambda} i controllers have 3 tuning parameters K P \ i, K I \ i and \ lambda_ {i}, which makes it possible to obtain a more effective tuning than in standard DI controllers (they only have two tuning parameters). The fact that the parameter \ lambda_ {i} is not integer, offers greater flexibility, as well as possibilities to obtain a better tuning of the controller in front of the variations of the dynamic parameters of the section of the channel.

Under the conditions of variations in a wide range of parameters (gain, time constants and time delay) that characterize the dynamic behavior of the section of the channel, the system does not need to readjust the controller parameters online, since it has n controllers of fractional order DI ^ \ lambda tuned for different sub-ranges of variation (? Q_ {i} ( t )) of the operation discharge ( Q_ {min} ( t ), Q_ {max} ( t )). This makes it possible to increase the robustness and effectiveness in the control of the water levels, as well as to increase the operability on the section and as a consequence reduce the water losses due to exploitation.

The fact that each of the DI ^ {\ lambda} i controllers is tuned for a smaller variation range of the parameters that characterize the dynamic behavior of the channel section decreases the effort in controlling said controllers. , which makes it possible to increase the safety in the operation of the control system.

The proposed system has a graphical environment that can be managed by users, which allows observing from the computer the control of water levels in the section of the channel, adjusting the parameters of the DI ^ {\ lambda} controllers i , communicate with the main control program, manually operate on the gate motor upstream of the channel section, enter new data and / or vary existing data (for example the value of the reference H_ { r, \ aabc} ( kT ), as well as knowing possible failures in the system.

The input data ( e ( kT ), H_ {r, \ aabc} ( kT ), H_ {aabc} ( kT ), H_ {aabf} ( kT ), H_ {aar} ( kT ), a ( kT ) and Q_ {j} ( kT )) and output ( u FDI \ i} ( kT )) of the control system, as well as the sub-range of variation (\ Delta Q_ {i} ( t ) of the current discharge ( Q_ {j} ( t )) are recorded and stored in files on the computer and can be reproduced by users through the computer application responsible for performing the data processing procedure.The output of this data is done through the USB port of the computer in digital format.

The proposed system has software that is part of this invention and that constitutes a part indissoluble of it. This software is made up of four intimately related modules: the first module It constitutes a graphical environment, which is managed by users to manage the fractional order control process with profit programmed water levels in a section of a main channel of irrigation. The second module develops the treatment tasks of data and control This module runs on the computer itself and is It relates to the graphic environment to interpret your orders. He third module deals with communication between the graphic environment and the data processing and control module. The fourth module develops control system supervision, offering following facilities: alarm generation against damage (possible or verified) in the system and suggesting the actions corresponding, detection of possible failures in the different devices that integrate the control system (computer, sensors, motor, gate, etc.), status determination software operation, etc.

Of everything described and by observing Figures 1 and 2, the advantages presented by the Fractional order control system with programmed gain that it is proposed, with respect to other preceding embodiments.

What is new in the proposed system is the inclusion of a fractional order controller with programmed gain, in which n fractional order controllers DI ^ {\ lambda} i tuned for different sub-ranges of variation ( ΔQ_ {i} ( t )) of the operation discharge ( Q_ {min} ( t ), Q_ {max} ( t )) through the gate upstream of the channel section, which implies a significant increase in robustness and effectiveness in the control, as well as in the operation on the section of the canal and as a consequence a reduction in the current losses of water and an increase in the safety of the control system; the incorporation into the controller of a block of calculation of the current discharge ( Q_ {j} ( t )) through the gate upstream of the section of the channel, which makes it possible to connect the controller DI ^ {\ lambda} _ {i} tuned for the variation sub-range (Δ Q_ {i} ( t )) to which said download belongs.

Claims (4)

1. Fractional order control system with programmed gain of water levels in main channels of irrigation comprising at least: (a) a plurality of gates at the beginning (2) and end (3) of the section of the channel (1), a water level sensor downstream (5) located at the end of the section of the canal (1), a analog / digital converter (8), a digital / analog converter (10) and an engine (11) that moves the start gate (2) of the channel section (1); characterized in that it also includes (b) an upstream water level sensor (6) located at the end of the preceding section, a downstream water level sensor located at the beginning of the section (4), a gate position sensor (7) located in the gate upstream of the section and a fractional order controller with programmed gain (9) that generates the error signals e ( kT ) and control signals u FDI \ i ( kT ); and where, in addition, the output signals ( H_ {aabc} ( t ), H_ {aabf} ( t ), H_ {aar} ( t )) of the water level sensors (4,5,6) and the sensor output signal of gate position (7) ( a ( t )) by means of the analog / digital converter A / D (8) are converted into discrete signals ( H_ {aabc} ( kT ), H_ {aabf} ( kT ), H_ {aar } ( kT ), a ( kT )); and where the fractional order controller with programmed gain (9) enables the effective control of the water levels in the section of the channel (1), generating the error signals e ( kT ) and control signals u FDI \ i} ( kT ) in correspondence with a discrete FDI type fractional order control algorithm; and where the discrete control signal u FDI \ i ( kT ) is converted into a continuous signal u FDI \ i ( t ) by the digital / analog converter D / A (10), which represents a sampling device and data retention; and where the continuous control signal u FDI \ i ( t ) acts on the motor (11) of the gate (2) upstream of the section, causing displacements of said gate corresponding to the magnitude and sign of the signal of error e ( kT ).

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2. Control system according to claim 1 wherein the displacements of the gate (2) cause variations in the discharge of input to the section, which are maintained as long as the error signal e ( kT ) does not equal zero. 3. Control system according to claims 1 and 2 wherein said fractional order controller with programmed gain (9) is comprised of n discrete FDI type fractional controllers ( DI \ lambda ), which are tuned to different sub-ranges of variation of the operation discharge through the gate upstream of the section. 4. Control system according to previous claims wherein the fractional order controller with programmed gain (9) comprises a block for calculating the current discharge (12) through the upstream gate (2) of the section, which makes it possible to connect the DI <i> \ lambda} tuned controller for the sub-range of variation of the operation discharge to which the current discharge belongs.