CN108287466B - Improved active disturbance rejection control method for high-order system - Google Patents
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Abstract
The invention provides an improved active disturbance rejection control method for a high-order system, and belongs to the technical field of automatic control. The method describes an actual controlled object by adopting a high-order system with first-order inertia links connected in series; compensating an input value of a last calculation step sequence of the high-order system through a compensation algorithm to obtain a compensation value of the current calculation step sequence; and performing ESO calculation on the output value of the current calculation step sequence of the high-order system and the compensation value of the current calculation step sequence to obtain a tracking value of the output value of the next calculation step sequence of the high-order system and a tracking value of a first derivative of the output value, further obtaining input values of two calculation step sequences of the high-order system, and simultaneously adjusting the variation of the executing mechanism in real time by the high-order system according to the calculation result. The method can also be applied to the implementation of an improved second-order active disturbance rejection control method for a high-order system. The invention can better give consideration to the tracking capability and the anti-interference capability of a closed-loop system and has good control quality.
Description
Technical Field
The invention belongs to the technical field of automatic control, and particularly relates to an improved active disturbance rejection control method for a high-order system.
Background
At present, the control strategies in industrial process control including chemical process, thermal process and the like still mainly adopt Proportional-Integral control (PI) and Proportional-Integral-Derivative control (PID), which are mainly due to the characteristics of simple and easy realization, multiple parameter setting methods and the like of the PI/PID. However, with the increasing demands on the economy and the control quality in the industrial production process, the PI/PID is difficult to meet the current control requirements. Active Disturbance Rejection Control (ADRC) technology is a Control method proposed by koro jingqing researchers in the chinese academy of sciences. At present, ADRC is successfully applied to actual fields of coal mill outlet air temperature control, hearth negative pressure control and the like, which lays a good foundation for the wide application of ADRC in industrial control.
The hot working process such as superheated steam temperature system, main steam pressure system, etc. has expressions such as
The system is a high-order system formed by serially connecting first-order inertia elements, wherein s, k, T and n are differential operators, gain coefficients, time constants and orders of the high-order system respectively, n is more than or equal to 3, and Y(s) and U(s) are output and input of the high-order system respectively. In a higher-order system, such as a main steam pressure system, the meaning of each parameter in the above formula is: the output Y(s) is the pressure output value of the main steam pressure system, the input U(s) is the coal feeding amount of the unit, the gain coefficient k is the amplification factor of the high-order system to the input value, the input value is the change amount of the main steam pressure corresponding to 1 ton of coal, and the time constant T is the time required by the system response to reach 63.2% of a steady-state value.
For the above high-order system, the implementation flow of the standard first-order ADRC method is shown in fig. 1, and includes the following steps:
1) the controlled actual industrial object is described by a high-order system formed by connecting first-order inertia links in series, and the mathematical expression is as follows:
wherein, the output Y(s) and the input U(s) of the high-order system are respectively represented by y () and u () in each calculation step sequence, which represents the calculation step sequence, s, k, T and n are respectively a differential operator, a gain coefficient, a time constant and an order of the identified high-order system, and n is more than or equal to 3; in the formula, a gain coefficient and a time constant are determined according to different controlled actual industrial objects, typically, for a main steam pressure loop of a thermal power generating unit, the gain coefficient is generally within the range of 0.01-0.1, and the time constant is generally within the range of 30-50;
2) the input value and the output value of the current calculation step sequence of the high-order system are respectively set as u () and y (), an Euler method is adopted for discretization in practical application to obtain the ADRC which can be realized digitally, and an Euler discretization algorithm adopted in the discretization process is as follows:
where the calculation step is indicated, h represents the sampling step,
represents the first derivative of the variable x;
the output value y (-1) of the step sequence calculated on the high-order system and the input value u (-1) of the step sequence calculated on the high-order system are calculated in real time by adopting an Extended State Observer (ESO) together to obtain a tracking value z of the output value y () of the current step sequence calculated on the high-order system1() And the tracking value z of the first derivative of the output value y2() Wherein z is2() Currently calculating an observed value of a step sequence for total disturbance borne by a high-order system;
z1() And z2() The calculation expression of (a) is as follows:
wherein, β1、β2And b0For calculating coefficients, representing a calculation step sequence, h represents a sampling step length;
3) the output set value r () of the current calculation step sequence and the tracking value z of the output value y () of the current calculation step sequence of the high-order system are obtained1() Is amplified by the difference of (k)pSubtracting the observed value z of the total disturbance after multiplication2() And the obtained results are amplified again
Multiplying the input value u (+1) of a high-order system serving as the next step sequence;
the mathematical expression of the input value u (+1) of the next higher-order system of calculation steps is as follows:
wherein k ispCalculating the coefficient, coefficient kpSelecting an appropriate value according to the control requirements;
4) and updating the input value of the current calculation step sequence of the high-order system to be u (+1), and controlling and adjusting the variable quantity of the actuating mechanism, such as the opening of a valve, the rotating speed of a pump and the like, in real time by the high-order system according to u (+ 1).
The implementation steps of the second-order ADRC and the first-order ADRC are basically the same, and the flow is shown in fig. 2, wherein steps 2) and 3) are changed according to the structure of the second-order ADRC; the method comprises the following steps:
1) the controlled actual industrial object is described by a high-order system formed by connecting first-order inertia links in series, and the mathematical expression is as follows:
wherein the output Y(s) and the input U(s) of the high-order system are respectively represented by y () and u () in each calculation step sequence, the calculation step sequences are represented, s, k, T and n are respectively a differential operator, a gain coefficient, a time constant and an order of the identified high-order system, and n is more than or equal to 3; in the formula, a gain coefficient and a time constant are determined according to different controlled actual industrial objects, typically, for a main steam pressure loop of a thermal power generating unit, the gain coefficient is generally within the range of 0.01-0.1, and the time constant is generally within the range of 30-50;
2) the input value of the current calculation step sequence and the output value of the current calculation step sequence of a high-order system are respectively set as u () and y (), an Euler method is adopted for discretization in practical application to obtain the ADRC which can be digitally realized, and an Euler discretization algorithm adopted in the discretization process is as follows:
where the calculation step is indicated, h represents the sampling step,
represents the first derivative of the variable x;
the output value y (-1) of the step sequence calculated on the high-order system and the input value u (-1) of the step sequence calculated on the high-order system are calculated in real time by adopting an Extended State Observer (ESO) together to obtain a tracking value z of the output value y () of the current step sequence calculated on the high-order system1() Tracking value z of the first derivative of the output value y ()2() And a tracking value z of the second derivative of the output value y +3() (ii) a Wherein z is3() Currently calculating an observed value of a step sequence for total disturbance borne by a high-order system;
z1()、z2() And z3() The calculation expression of (a) is as follows:
wherein, β1、β2And b0For calculating coefficients, the calculation step order is expressed, and h represents the sampling step size.
3) The output set value r () of the current calculation step sequence and the tracking value z of the output value y () of the current calculation step sequence of the high-order system are obtained1() Is amplified by the difference of (k)pThe tracking value z of the first derivative of the output value y () is subtracted after multiplication2() K of (a)dObserved value z of multiple sum total disturbance3(κ) re-amplification of the results obtained
After doubling, the input value u (+1) of the next high-order system for calculating the step order is obtained.
The mathematical calculation of the input value u (+1) of the next higher-order system for calculating the step order is as follows:
wherein k isp、kdTo calculate the coefficients. Coefficient kp、kdAn appropriate value is selected according to the control requirements.
4) And updating the current calculation step sequence input value of the high-order system to be u (+1), and controlling and adjusting the variable quantity of the actuating mechanism, such as the opening of a valve, the rotating speed of a pump and the like, in real time by the high-order system according to u (+ 1).
Existing first-order ADRC and second-order ADRC control high-order system
The tracking ability and the interference rejection can not be well considered, the interference rejection effect is poor when the tracking ability is strong, and the tracking effect is poor when the interference rejection is strong. In order to better consider the tracking capability and the anti-interference capability of the system, improve the control quality of the system and carry out high-order system
Research into the improvement of ADRC is necessary.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides an improved active disturbance rejection control method for a high-order system. The invention enables the closed-loop system to better take the tracking capability and the anti-interference capability into consideration, and provides better support for further popularizing the application of ADRC in industrial process control such as a chemical process, a thermal process and the like.
The invention provides an improved active disturbance rejection control method for a high-order system, which is characterized by comprising the following steps:
1) the controlled actual industrial object is described by a high-order system formed by connecting first-order inertia links in series, and the mathematical expression is as follows:
wherein, the output Y(s) and the input U(s) of the high-order system are respectively represented by y () and u () in each calculation step sequence, which represents the calculation step sequence, s, k, T and n are respectively a differential operator, a gain coefficient, a time constant and an order of the identified high-order system, and n is more than or equal to 3;
2) compensating the input value u (-1) of the last calculation step sequence of the high-order system selected in the step 1) through a compensation algorithm to obtain a compensation value u of the current calculation step sequencecp() (ii) a The mathematical expression of the compensation algorithm is as follows:
wherein the output U of the compensation algorithmcp(s) and input U(s) with u in each calculation stepcp() And u (-1) represents T1M is the time constant and order of the compensation algorithm respectively; the input of the compensation algorithm is a high-order system input value u (-1) of the last calculated step sequence, and the output is a compensation value u of the current step sequencecp()；T1∈[0.5T,1.5T]，m≤n；
3) The output value y () of the current calculation step sequence of the high-order system and the compensation value u of the current calculation step sequence obtained by the compensation algorithm are comparedcp() The ESO is jointly adopted to carry out real-time estimation and compensation calculation to obtain a tracking value z of an output value y (+1) of the next calculation step of the high-order system1(+1) and the tracking value z of the first derivative of the output value y (+1)2(+1) wherein z is2(+1) is an observed value of a next calculation step sequence under the total disturbance of the high-order system;
z1(+1) and z2The calculation expression of (+1) is as follows:
wherein, β1、β2And b0For calculating the coefficient, h represents the sampling step length;
4) the input set value r (+1) of the next calculation step sequence and the tracking value of the output value y (+1) of the next calculation step sequence of the high-order system are comparedz1Differential amplification of (+1) kpSubtracting the observed value z of the total disturbance after multiplication2(+1), the results obtained are reamplified
Taking the multiplied result as an input value u (+2) of a next two high-order systems for calculating the step sequence;
the mathematical expressions for the input values u (+2) of the next two higher-order systems for calculating the step order are as follows:
wherein k ispTo calculate the coefficients;
5) and updating the input value of the next calculation step sequence of the high-order system to be u (+2), and adjusting the variable quantity of the actuating mechanism in real time by the high-order system according to u (+ 2).
The invention provides an improved second-order active disturbance rejection control method for a high-order system, which is characterized by comprising the following steps:
1) the controlled actual industrial object is described by a high-order system formed by connecting first-order inertia links in series, and the mathematical expression is as follows:
wherein, the output Y(s) and the input U(s) of the high-order system are respectively represented by y () and u () in each calculation step sequence, which represents the calculation step sequence, s, k, T and n are respectively a differential operator, a gain coefficient, a time constant and an order of the identified high-order system, and n is more than or equal to 3;
2) compensating the input value u (-1) of the last calculation step sequence of the high-order system selected in the step 1) through a compensation algorithm to obtain a compensation value u of the current calculation step sequencecp() (ii) a The mathematical expression of the compensation algorithm is as follows:
wherein the content of the first and second substances,output U of the compensation algorithmcp(s) and the input U(s) are u(s) in each calculation stepcp() And u (-1), s, T1M is the time constant and order of the compensation algorithm respectively; the input of the compensation algorithm is a high-order system input value u (-1) of the last calculation step sequence, and the output is a compensation value u of the current calculation step sequencecp()；T1∈[0.5T,1.5T]，m≤n；
3) The output value y () of the current calculation step sequence of the high-order system and the compensation value u of the current calculation step sequence obtained by the compensation algorithm are comparedcp() The ESO is jointly adopted to carry out real-time estimation and compensation calculation to obtain a tracking value z of a next calculation step output value y (+1) of a high-order system1(+1), tracking value z of the first derivative of the output value y (+1)2(+1) and the tracking value z of the second derivative of the output value y (+1)3(+1) wherein z is3(+1) is an observed value of a next calculation step sequence under the total disturbance of the high-order system;
z1(+1)、z2(+1) and z3The calculation expression of (+1) is as follows:
wherein, β1、β2And b0For calculating the coefficient, h represents the sampling step length;
4) the input set value r (+1) of the next calculation step sequence and the tracking value z of the next calculation step sequence y (+1) of the high-order system are compared1Differential amplification of (+1) kpThe tracking value z of the first derivative of the output value y (+1) is subtracted after multiplication2K of (+1)dObserved value z of total disturbance of multiple sum system3(+1), the results obtained are reamplified
Taking the multiplied result as an input value u (+2) of a next two high-order systems for calculating the step sequence;
the mathematical expressions for the input values u (+2) of the next two higher-order systems for calculating the step order are as follows:
wherein k isp、kdTo calculate the coefficients;
5) and updating the next calculation step sequence input value of the high-order system to be u (+2), and adjusting the variation of the actuating mechanism by the high-order system according to u (+ 2).
The invention has the characteristics and beneficial effects that:
the invention provides an improved active disturbance rejection control method for a high-order system, which keeps the characteristics of simple and easy realization of ADRC; and the compensation algorithm can be designed by fully utilizing the information of the order n, the time constant T and the like of the high-order system; the improved ADRC can better give consideration to the tracking capability and the anti-interference capability of the system, so that the system has high tracking speed and strong anti-interference capability.
Drawings
FIG. 1 is a block diagram of a standard first-order ADRC control flow for a class of high-order systems.
FIG. 2 is a block diagram of a standard second-order ADRC control flow for a class of high-order systems.
Fig. 3 is a control flow diagram of an improved active disturbance rejection control method for a high-order system according to the present invention.
Fig. 4 is a control flow diagram of an improved second-order active disturbance rejection control method for a high-order system according to the present invention.
FIG. 5 is a graph of system output response to improve first order ADRC in simulation according to an embodiment of the present invention.
Fig. 6 is a graph showing the effect of the first-order ADRC improvement applied to the main steam pressure loop of the thermal power generating unit in the field.
FIG. 7 is a field application effect diagram of a PID in a main steam pressure loop of a thermal power generating unit.
Detailed Description
The invention provides an improved active disturbance rejection control method for a high-order system, which is further described in detail below with reference to the accompanying drawings and specific embodiments.
The flow of the improved active disturbance rejection control method for a high-order system provided by the invention is shown in fig. 3, and the method comprises the following steps:
1) the controlled actual industrial object is described by a high-order system formed by connecting first-order inertia links in series, and the mathematical expression is as follows:
wherein, the output Y(s) and the input U(s) of the high-order system are respectively represented by y () and u () in each calculation step sequence, which represents the calculation step sequence, s, k, T and n are respectively a differential operator, a gain coefficient, a time constant and an order of the identified high-order system, and n is more than or equal to 3; in the formula, a gain coefficient and a time constant are determined according to different controlled actual industrial objects, typically, for a main steam pressure loop of a thermal power generating unit, the gain coefficient is generally within the range of 0.01-0.1, and the time constant is generally within the range of 30-50;
2) compensating an input value u (-1) of the last calculation step sequence of the high-order system selected in the step 1) through a compensation algorithm, and obtaining a compensation value u of the current calculation step sequence through the compensation algorithm based on the order n and the time constant T of the high-order systemcp() (ii) a The mathematical expression of the compensation algorithm is as follows:
wherein the output U of the compensation algorithmcp(s) and input U(s) with u in each calculation stepcp() And u (-1) represents T1And m are the time constant and order of the compensation algorithm, respectively. The input of the compensation algorithm is a high-order system input value u (-1) of the last calculated step sequence, and the output is a compensation value u of the current step sequencecp(). And the time constant of the compensation algorithm is set to T1∈[0.5T,1.5T]，m≤n。
3) The input value and the output value of the current calculation step sequence of the high-order system are respectively set as u () and y (), an Euler method is adopted for discretization in practical application to obtain the ADRC which can be realized digitally, and an Euler discretization algorithm adopted in the discretization process is as follows:
where the calculation step is indicated, h represents the sampling step,
represents the first derivative of the variable x;
the output value y () of the current calculation step sequence of the high-order system and the compensation value u of the current calculation step sequence obtained by the compensation algorithm are comparedcp() An Extended State Observer (ESO) method is jointly adopted for real-time estimation and compensation calculation to obtain a tracking value z of an output value y (+1) of a next calculation step of a high-order system1(+1) and the tracking value z of the first derivative of the output value y (+1)2(+1) wherein z is2And the +1 is an observed value of the total disturbance of the high-order system in the current calculation step sequence.
z1(+1) and z2The calculation expression of (+1) is as follows:
wherein, β1、β2And b0The selection of the calculation coefficients is based on the dynamics of the higher order system, generally β1、β2The value of (A) is in the range of 0.01 to 2; b0Can be generally at
Within the range.
4) The input set value r (+1) of the next calculation step sequence and the tracking value z of the output value y (+1) of the next calculation step sequence of the high-order system are compared1Differential amplification of (+1) kpSubtracting the observed value z of the total disturbance after multiplication2(+1), the results obtained are reamplified
Multiplying as the next two calculation stepsThe input value u (+2) of the sequential high-order system.
The mathematical calculation of the input value u (+2) for the next two higher order systems that calculate the step order is as follows:
wherein k ispFor calculating the coefficients, coefficient kpAn appropriate value is selected according to the control requirements.
5) And updating the input value of the next calculation step of the high-order system to be u (+2), and adjusting the variable quantity of the actuating mechanism, such as the opening of a valve, the rotating speed of a pump and the like, in real time by the high-order system according to the u (+ 2).
And after the input value of the next calculation step sequence of the high-order system is updated to u (+2), the input value is used as the input quantity of the compensation algorithm to calculate the next period. And u (+2) is sent to the high-order system to realize the adjustment of the output value of the high-order system.
The implementation of the improved first-order active disturbance rejection control method for the high-order system can be completed according to the steps.
The flow of the improved second-order active disturbance rejection control method for a high-order system provided by the invention is shown in fig. 4, and the method comprises the following steps:
1) the controlled actual industrial object is described by a high-order system formed by connecting first-order inertia links in series, and the mathematical expression is as follows:
wherein, the output Y(s) and the input U(s) of the high-order system are respectively represented by y () and u () in each calculation step sequence, which represents the calculation step sequence, s, k, T and n are respectively a differential operator, a gain coefficient, a time constant and an order of the identified high-order system, and n is more than or equal to 3; in the formula, a gain coefficient and a time constant are determined according to different controlled actual industrial objects, typically, for a main steam pressure loop of a thermal power generating unit, the gain coefficient is generally within the range of 0.01-0.1, and the time constant is generally within the range of 30-50;
2) for step 1) The input value u (-1) of the last calculation step sequence of the selected high-order system is compensated through a compensation algorithm, and the compensation value u of the current calculation step sequence is obtained through the compensation algorithm based on the order n and the time constant T of the high-order systemcp(). The mathematical expression of the compensation algorithm is as follows:
wherein the output U of the compensation algorithmcp(s) and the input U(s) are u(s) in each calculation stepcp() And u (-1), T1And m are the time constant and order of the compensation algorithm, respectively. The input of the compensation algorithm is a high-order system input value u (-1) of the last calculation step sequence, and the output is a compensation value u of the current calculation step sequencecp(). And the time constant of the compensation algorithm is set to T1∈[0.5T,1.5T]，m≤n。
3) The input value and the output value of the current calculation step sequence of the high-order system are respectively set as u () and y (), an Euler method is adopted for discretization in practical application to obtain the ADRC which can be realized digitally, and an Euler discretization algorithm adopted in the discretization process is as follows:
where the calculation step is indicated, h represents the sampling step,
represents the first derivative of the variable x;
the output value y () of the current calculation step sequence of the high-order system and the compensation value u of the current calculation step sequence obtained by the compensation algorithm are comparedcp() An Extended State Observer (ESO) method is jointly adopted for real-time estimation and compensation calculation to obtain a tracking value z of a next calculation step output value y (+1) of a high-order system1(+1), tracking value z of the first derivative of the output value y (+1)2(+1) and the tracking value z of the second derivative of the output value y (+1)3(+1) wherein z is3(+1) is the next calculation step of total disturbance of the high-order systemObservation of sequences.
z1(+1)、z2(+1) and z3The calculation expression of (+1) is as follows:
wherein, β1、β2And b0The coefficients are selected based on the dynamics of the higher order system, generally β1、β2、β3The value of (A) is in the range of 0.01 to 2; b0Can be generally at
Within the range.
4) The input set value r (+1) of the next calculation step sequence and the tracking value z of the next calculation step sequence y (+1) of the high-order system are compared1Differential amplification of (+1) kpThe tracking value z of the first derivative of the output value y (+1) is subtracted after multiplication2K of (+1)dObserved value z of total disturbance of multiple sum system3(+1), the results obtained are reamplified
After doubling, the input value u (+2) of the next two high-order systems for calculating the step order is obtained.
The mathematical expressions for the input values u (+2) of the next two higher-order systems for calculating the step order are as follows:
wherein k isp、kdFor calculating the coefficients, coefficient kp、kdAn appropriate value is selected according to the control requirements.
5) And updating the next calculation step sequence input value of the high-order system to be u (+2), and adjusting the variable quantity of the actuating mechanism, such as the opening of a valve, the rotating speed of a pump and the like, by the high-order system according to u (+ 2).
And after the input value of the high-order system is updated to u (+2), the input value is used as the input quantity of the compensation algorithm to calculate the next period. And u (+2) is sent to the high-order system to realize the adjustment of the output value of the high-order system.
In contrast to the standard ADRC control block diagram shown in fig. 1 and 2, the present invention adds a compensation algorithm, which causes the input amount of the ESO to change: the input value u (-1) and the output value y (-1) of the high-order system are changed into the output value y (-1) of the high-order system and the output value u of the compensation algorithm by using the input value u (-1) and the output value y (-1) of the high-order system as input quantitiescpAs input amount (-1).
The technical advantages of the invention are illustrated by the following example, which takes the control of the main steam pressure in the thermal system as an example:
1) the main steam pressure control system is described by adopting a high-order system formed by connecting first-order inertia links in series, and the mathematical expression is as follows:
wherein, the output y(s) of the high-order system is the pressure output value of the main steam pressure control system, the input u(s) of the high-order system is the amount of coal fed by the unit, y(s) and u(s) are respectively represented by y () and u () in each calculation step, s, k, T and n are respectively a differential operator, a gain coefficient, a time constant and an order of the main steam pressure control system, in the embodiment, k is 0.028, T is 50 and n is 5.
2) Compensating the input value u (-1) of the last calculation step of the main steam pressure control system selected in the step 1) by a compensation algorithm, and obtaining the compensation value u of the current calculation step by the compensation algorithm based on the information of the order n-5, the time constant T-50 and the like of the main steam pressure control systemcp(). The mathematical expression of the compensation algorithm is as follows:
wherein the output U of the compensation algorithmcp(s) and input U(s) with u in each calculation stepcp() And u (-1) represents T1M are respectively compensationTime constant and order of the algorithm, T in this example150, m is 4. The input of the compensation algorithm is the input value u (-1) of the high-order system for calculating the step sequence at the last time, and the output is the compensation value u of the current step sequencecp()。
3) The output value y () of the current calculation step of the main steam pressure control system and the compensation value u of the current calculation step obtained by the compensation algorithmcp() An Extended State Observer (ESO) method is jointly adopted for real-time estimation and compensation calculation to obtain a tracking value z of an output value y (+1) of the next calculation step of the main steam pressure control system1(+1) and the tracking value z of the first derivative of the output value y (+1)2(+1) wherein z is2And the (+1) is an observed value of a next calculation step sequence under the total disturbance of the main steam pressure control system.
z1(+1) and z2The calculation expression of (+1) is as follows:
wherein, β1、β2And b0For calculating coefficients, representing the calculation step order, h represents the sample step size in this embodiment, β1＝0.6、β20.09 and b0＝0.016。
4) The input set value r (+1) of the next calculation step sequence and the tracking value z of the output value y (+1) of the next calculation step sequence of the main steam pressure control system are compared1Differential amplification of (+1) kpSubtracting the observed value z of the total disturbance after multiplication2(+1), the results obtained are reamplified
After doubling the input value u (+2) of the main steam pressure control system as the next two calculation steps.
The mathematical calculation of the input value u (+2) of the main steam pressure control system for the next two calculation steps is as follows:
wherein k ispTo calculate the coefficients, k in this examplepThe value is 0.018.
5) And updating the input value of the next calculation step sequence of the high-order system to be u (+2), and adjusting the coal feeding amount by the coal feeder according to u (+ 2).
After the input value of the main steam pressure control system is updated to u (+2), the next cycle is calculated as the input amount of the compensation algorithm. And u (+2) is sent to the main steam pressure control system to realize the pressure adjustment of the main steam pressure control system.
Fig. 5 is a comparison result of simulation performed according to the embodiment. The solid line is the simulation result of the improved ADRC provided by the invention, and the dot-dash line, the thick dotted line and the thin dotted line are the simulation results of the PI, the PID and the standard first-order ADRC respectively. The specific simulation process is as follows: and at the starting time of simulation, the system is at the steady-state time, the set value is changed from 0 to 0.5 at 1000s, the disturbance of the control quantity is carried out on the closed loop at 10000s, the disturbance is changed from 0 to-1, and the steady state is reached at 30000 s. According to simulation, the improved first-order ADRC can well take the tracking capability and the anti-interference capability of the system into consideration, has the advantages of higher tracking capability and stronger anti-interference capability, and improves the control quality of the system.
Fig. 6 and 7 are comparison graphs of field tests of the first-order ADRC and PID of the improvement on the main steam pressure loop of the thermal power generating unit respectively. The improved first-order ADRC Control algorithm is realized by configuring on a Distributed Control System (DCS) platform of a thermal power generating unit according to an improved first-order ADRC Control block diagram shown in fig. 3. The time lengths of fig. 6 and 7 are both one hour and the loads are compared for a 15MW drop. In fig. 6 (a), the solid line is the load set value, and the broken line is the actual load value, which indicates that the load is decreased by 15 MW; the solid line in fig. 6 (b) is the pressure set value, and the dotted line is the actual pressure value, so that it can be seen that the actual pressure value can well track the pressure set value under the condition that the load is reduced by 15MW, and the tracking without the static error is realized. In fig. 7 (a), the solid line is the load set value, and the broken line is the actual load value, which shows that the load is decreased by 15 MW; in fig. 7, (b) the solid line is the pressure set value, and the dotted line is the actual pressure value, it can be seen that there is a static difference of 0.3MPa between the actual pressure value and the pressure set value, and the actual pressure value cannot track the pressure set value well. Through the practical application on the spot, the invention is proved to obviously improve the tracking speed of the main steam control system, realize the tracking without the static error and improve the control quality of the system.
Claims (2)
1. An improved active disturbance rejection control method for a high-order system, comprising the steps of:
1) the controlled actual industrial object is described by a high-order system formed by connecting first-order inertia links in series, and the mathematical expression is as follows:
wherein, the output Y(s) and the input U(s) of the high-order system are respectively represented by y () and u () in each calculation step sequence, which represents the calculation step sequence, s, k, T and n are respectively a differential operator, a gain coefficient, a time constant and an order of the identified high-order system, and n is more than or equal to 3;
2) compensating the input value u (-1) of the last calculation step sequence of the high-order system selected in the step 1) through a compensation algorithm to obtain a compensation value u of the current calculation step sequencecp() (ii) a The mathematical expression of the compensation algorithm is as follows:
wherein the output U of the compensation algorithmcp(s) and input U(s) with u in each calculation stepcp() And u (-1) represents T1M is the time constant and order of the compensation algorithm respectively; the input of the compensation algorithm is a high-order system input value u (-1) of the last calculated step sequence, and the output is a compensation value u of the current step sequencecp()；T1∈[0.5T,1.5T]，m≤n；
3) The output value y () of the current calculation step sequence of the high-order system and the complement of the current calculation step sequence obtained by a compensation algorithm are comparedCompensation ucp() The ESO is jointly adopted to carry out real-time estimation and compensation calculation to obtain a tracking value z of an output value y (+1) of the next calculation step of the high-order system1(+1) and the tracking value z of the first derivative of the output value y (+1)2(+1) wherein z is2(+1) is an observed value of a next calculation step sequence under the total disturbance of the high-order system;
z1(+1) and z2The calculation expression of (+1) is as follows:
wherein, β1、β2And b0For calculating the coefficient, h represents the sampling step length;
4) the input set value r (+1) of the next calculation step sequence and the tracking value z of the output value y (+1) of the next calculation step sequence of the high-order system are compared1Differential amplification of (+1) kpSubtracting the observed value z of the total disturbance after multiplication2(+1), the results obtained are reamplified
Taking the multiplied result as an input value u (+2) of a next two high-order systems for calculating the step sequence;
the mathematical expressions for the input values u (+2) of the next two higher-order systems for calculating the step order are as follows:
wherein k ispTo calculate the coefficients;
5) and updating the input value of the next calculation step sequence of the high-order system to be u (+2), and adjusting the variable quantity of the actuating mechanism in real time by the high-order system according to u (+ 2).
2. An improved second-order active disturbance rejection control method for a class of high-order systems is characterized by comprising the following steps:
1) the controlled actual industrial object is described by a high-order system formed by connecting first-order inertia links in series, and the mathematical expression is as follows:
wherein, the output Y(s) and the input U(s) of the high-order system are respectively represented by y () and u () in each calculation step sequence, which represents the calculation step sequence, s, k, T and n are respectively a differential operator, a gain coefficient, a time constant and an order of the identified high-order system, and n is more than or equal to 3;
2) compensating the input value u (-1) of the last calculation step sequence of the high-order system selected in the step 1) through a compensation algorithm to obtain a compensation value u of the current calculation step sequencecp() (ii) a The mathematical expression of the compensation algorithm is as follows:
wherein the output U of the compensation algorithmcp(s) and the input U(s) are u(s) in each calculation stepcp() And u (-1), s, T1M is the time constant and order of the compensation algorithm respectively; the input of the compensation algorithm is a high-order system input value u (-1) of the last calculation step sequence, and the output is a compensation value u of the current calculation step sequencecp()；T1∈[0.5T,1.5T]，m≤n；
3) The output value y () of the current calculation step sequence of the high-order system and the compensation value u of the current calculation step sequence obtained by the compensation algorithm are comparedcp() The ESO is jointly adopted to carry out real-time estimation and compensation calculation to obtain a tracking value z of a next calculation step output value y (+1) of a high-order system1(+1), tracking value z of the first derivative of the output value y (+1)2(+1) and the tracking value z of the second derivative of the output value y (+1)3(+1) wherein z is3(+1) is an observed value of a next calculation step sequence under the total disturbance of the high-order system;
z1(+1)、z2(+1) and z3The calculation expression of (+1) is as follows:
wherein, β1、β2And b0For calculating the coefficient, h represents the sampling step length;
4) the input set value r (+1) of the next calculation step sequence and the tracking value z of the next calculation step sequence y (+1) of the high-order system are compared1Differential amplification of (+1) kpThe tracking value z of the first derivative of the output value y (+1) is subtracted after multiplication2K of (+1)dObserved value z of total disturbance of multiple sum system3(+1), the results obtained are reamplified
Taking the multiplied result as an input value u (+2) of a next two high-order systems for calculating the step sequence;
the mathematical expressions for the input values u (+2) of the next two higher-order systems for calculating the step order are as follows:
wherein k isp、kdTo calculate the coefficients;
5) and updating the next calculation step sequence input value of the high-order system to be u (+2), and adjusting the variation of the actuating mechanism by the high-order system according to u (+ 2).
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