CN114296489B - RBF-PID (radial basis function-proportion integration differentiation) municipal solid waste incineration process hearth temperature control method based on event triggering - Google Patents
RBF-PID (radial basis function-proportion integration differentiation) municipal solid waste incineration process hearth temperature control method based on event triggering Download PDFInfo
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Abstract
A RBF-PID (radial basis function-proportion integration differentiation) municipal solid waste incineration process hearth temperature control method based on event triggering belongs to the field of municipal solid waste incineration and aims at the problems of low manual control precision of hearth temperature and frequent updating of a controller. Firstly, updating RBF network parameters on line through a gradient descent algorithm and a recursive least square algorithm, and simultaneously introducing the square of a momentum factor and a momentum term of the parameters to update controller parameters; then, an event trigger condition based on a fixed threshold value is designed to serve as a controller updating condition, an RBF-PID controller based on event trigger is established, accurate control over the temperature of the hearth is achieved, the problem that manual control accuracy of the temperature of the hearth in the urban solid waste incineration process is not high is solved, and theoretical support and technical guarantee are provided for safe and stable operation of the urban solid waste incineration process.
Description
Technical Field
The invention belongs to the field of urban solid waste incineration.
Background
A large amount of solid wastes not only pollute the atmosphere, water and soil, but also seriously affect the quality of urban ecological environment, and threaten the physical health of human beings and the sustainable development of society. Therefore, how to effectively treat municipal solid waste has become an increasingly urgent problem. Particularly, in the process of creating a civilized city in China, the problems of how to improve the environmental awareness of people, how to strengthen the management level of municipal solid waste, how to improve the treatment level of municipal solid waste and the like become an important research hotspot.
The urban solid waste incineration technology is widely applied worldwide as a new technology for harmless, quantitative-reduction and resource solid waste treatment. The effective control of the hearth temperature is the key for improving the solid waste treatment efficiency, inhibiting the discharge of pollutants and realizing the safe and stable operation of the urban solid waste incineration process. However, the incineration process of the municipal solid wastes is a complex physical and chemical reaction process and has the characteristics of nonlinearity, instability and large time variation. Meanwhile, solid waste components are easily influenced by factors such as climate and region, and show certain periodic change along with season change, so that the difficulty of controlling the temperature of the hearth is increased. At present, the urban solid waste incineration plants in China still mainly adopt manual control in actual operation, and hysteresis and subjectivity exist, so that the temperature control precision of a hearth is low. Moreover, manual operation is frequent, and the abrasion to the actuator is large. Therefore, whether the control is quickly and effectively controlled within a reasonable range has important practical significance.
In recent years, the PID controller is widely applied to industrial production by virtue of the advantages of simple algorithm and easy realization, and the application ratio is up to 90%. However, the traditional PID controller is complex in parameter selection and difficult to manually adjust. And the RBF-PID controller can effectively improve the defects of the conventional PID controller, and can perform online adaptive adjustment on parameters to realize accurate control. In addition, the event trigger control can well solve the problem of frequent updating of the controller and reduce the abrasion of the actuator. Therefore, the invention provides the RBF-PID urban solid waste incineration process furnace temperature control method based on event triggering, the furnace temperature is accurately controlled by adjusting the primary air volume, and the method has important practical significance for improving the solid waste incineration treatment capacity and inhibiting the emission of pollutants.
Disclosure of Invention
The invention provides a method for controlling the temperature of a hearth in an urban solid waste incineration process based on event triggering, which aims at solving the problems of low manual control precision of the temperature of the hearth and frequent updating of a controller. Firstly, updating RBF network parameters on line through a gradient descent algorithm and a recursive least square algorithm, and simultaneously introducing the square of a momentum factor and a momentum term of the parameters to update controller parameters; then, an event trigger condition based on a fixed threshold value is designed to serve as a controller updating condition, an RBF-PID controller based on event trigger is established, accurate control over the temperature of the hearth is achieved, the problem that manual control accuracy of the temperature of the hearth in the urban solid waste incineration process is not high is solved, and theoretical support and technical guarantee are provided for safe and stable operation of the urban solid waste incineration process.
An event-triggered RBF-PID (radial basis function-proportion integration differentiation) method for controlling the temperature of a hearth in a municipal solid waste incineration process comprises the following steps:
step 1: initialization parameters
Initializing controller parameters including the number of neurons in a hidden layer of the RBF network, the center of a Gaussian function, the width and an output weight; PID controller parameters and fixed event triggered thresholds;
step 2: calculating controller inputs
Calculating the tracking error e (k) of the hearth temperature at the current moment and the error variation ec (k) of the hearth temperature, and calculating as follows:
e(k)＝y d (k)-y(k) (1)
ec(k)＝e(k)-e(k-1) (2)
in the formula: e (k) and e (k-1) respectively represent the furnace temperature control errors at the k moment and the k-1 moment; ec (k) represents a furnace temperature error change amount at time k; y is d (k) And y (k) represents the expected value of the furnace temperature in the control process at the moment k and the actual output value of the control system;
and step 3: computing controller output
The controller adopts incremental PID, and the controller output is:
u(k)＝u(k-1)+Δu(k) (3)
wherein u (k) and u (k-1) represent the controller outputs at time k and time k-1, respectively; Δ u (k) is an increment of the control amount at time k, and is calculated as follows:
Δu(k)＝K p [e(k)-e(k-1)]+K i e(k)+K d [e(k)-2e(k-1)+e(k-2)] (4)
in the formula, K p 、K i 、K d Is a PID controller parameter; e (k), e (k-1) and e (k-2) respectively represent the tracking errors at the time k, the time k-1 and the time k-2;
and 4, step 4: judging the event trigger condition, if the event trigger is satisfied, updating the control quantity
The event trigger conditions are designed as follows:
k t+1 ＝{|Δu(k)|≥M} (6)
wherein M is a set event trigger threshold; u (k) t ) Is the actual control quantity under the t trigger sequence, which will be kept from the previous trigger sequence until the next trigger sequence is updated to u (k) t+1 ) (ii) a Δ u (k) is a control amount increment at time k; k is a radical of t Represents the time value under the t trigger sequence; k is a radical of t+1 Represents the time value under the t +1 trigger sequence;
and 5: calculating RBF network output y at current k moment m (k)
The RBF network mainly comprises an input layer, a hidden layer and an output layer, and the calculation mode is as follows:
gaussian function of hidden layer of RBF network is
Where x is the input vector, h j (x) Gaussian function value representing the jth neuron of the hidden layer when the input is x, c j And σ j Respectively hiding the center and the width of the Gaussian function of the jth neuron of the layer, wherein m is the number of neurons of the hidden layer.
The RBF network output is calculated as follows:
in the formula w j (k) For the jth network output weight at time k, y m (k) Is the output value of the RBF network at the k moment, and m is the number h of hidden layer neurons j (x) Representing the gaussian function value of the jth neuron of the hidden layer when the input is x.
Step 6: computing
Formula w j (k) For the jth network output weight at time k, h j (k) Gaussian function value for the jth neuron of the hidden layer at time k, c j (k) And σ j (k) Respectively representing the center and the width of the j-th neuron Gaussian function of the hidden layer at the k moment m (k) The output value of the RBF network at the moment k, m is the number of neurons in an implicit layer, and delta u (k) is the increment of the control quantity at the moment k;
and 7: method for calculating PID controller parameter increment by adopting gradient descent method
Using the square error function as the performance index:
in the formula: e (k) represents a performance index at time k; e (k) represents the furnace temperature control error at the time k; y is d (k) Y (k) represents the expected value of the furnace temperature at the time k in the control process and the actual output value of the control system;
and dynamically adjusting the parameter increment of the PID controller by adopting a gradient descent method, and calculating as follows:
wherein e (k) is,e (k-1) and e (k-2) respectively represent the tracking errors at the k moment, the k-1 moment and the k-2 moment; Δ K p (k)、ΔK i (k)、ΔK d (k) PID parameter increment at k moment; y is m (k) RBF network output at the time of k; eta p 、η i 、η d Learning rates of proportional, integral and differential parameters respectively; e (k) represents a performance index at time k;
and 8: updating PID controller parameters
K p (k)＝K p (k-1)+ΔK p (k)+α C 2 (K p (k-1)-K p (k-2)) (14)
K i (k)＝K i (k-1)+ΔK i (k)+α C 2 (K i (k-1)-K i (k-2)) (15)
K d (k)＝K d (k-1)+ΔK d (k)+α C 2 (K d (k-1)-K d (k-2)) (16)
In the formula K p (k)、K p (K-1) and K p (k-2) respectively representing proportional parameters of the k time, the k-1 time and the k-2 time; k i (k)、K i (K-1) and K i (k-2) respectively representing integral parameters at the k moment, the k-1 moment and the k-2 moment; k d (k)、K d (K-1) and K d (k-2) differential parameters at time k, time k-1 and time k-2, respectively; alpha is alpha C Is a momentum factor; Δ K p (k)、ΔK i (k)、ΔK d (k) PID parameter increment at the k moment;
and step 9: adjusting RBF network parameters, namely the center, the width and the network weight of a Gaussian function;
defining the performance index of the identifier as:
wherein y (k) represents the actual output value of the furnace temperature at the k moment in the control process; y is m (k) RBF network output for k time;
step 9.1: center and width update
Where eta is a learning rate, eta is an element [0,1 ]](ii) a J (k) is a performance index at the time k; h is j (x) Gaussian function value representing the jth neuron of the hidden layer when the input is x, c j (k) And σ j (k) Respectively representing the center and the width of the j-th neuron Gaussian function of the hidden layer at the k moment; x is an input vector; y (k) represents an actual output value of the furnace temperature in the control process at the time k; y is m (k) RBF network output value at k moment; w is a j (k) The weight is output for the jth network at time k.
Step 9.2: weight value updating
The recursive least squares algorithm is used here, and the formula is as follows:
in the formula: k (k), P (k) respectively represent the recursive least square parameter value at the time k, and I is an identity matrix; w (k) is the network output weight at time k; h (k) is the hidden layer output value at the time k; h is T (k) Transposing the output of the hidden layer for time k.
Compared with the prior art, the invention has the following obvious advantages and beneficial effects:
(1) the self-adaptive adjustment of the RBF-PID controller parameters based on event triggering can ensure that the temperature of the hearth can quickly respond to a set value, has certain advantages in the aspects of control precision and control performance, enables the controller to track the set value of the temperature of the hearth in time, and has higher control precision.
(2) The experimental result based on the hearth temperature shows that the RBF-PID controller based on the event trigger has the characteristics of high control precision, high response speed and less controller updating times.
Drawings
FIG. 1RBF Structure drawing
FIG. 2 parameter K p Is adjusted curve
FIG. 3 parameter K i Is adjusted curve
FIG. 4 parameter K d Is adjusted curve
FIG. 5 furnace temperature control Effect
FIG. 6 furnace temperature control error
FIG. 7 controller update times
FIG. 8 event trigger time intervals
Detailed Description
The method is characterized in that operation data under typical working conditions of several days are collected from a certain solid waste incineration company Limited in Beijing, and the sampling time is 2 s. Through preliminary screening, 500 groups of data of 6 months and 11 days in 2019 are finally selected and used for the fixed set value and variable set value experiments of the hearth temperature.
The event-triggered RBF-PID (radial basis function-proportion integration differentiation) furnace temperature control in the urban solid waste incineration process comprises the following steps:
step 1: initializing an RBF network, designing a network structure to be 3-6-1, initializing controller parameters, setting a Gaussian function center value c to be 30 × ones (3,6), setting a Gaussian function width value b to be 36.5 × ones (3,6), and outputting a weight w to be 30 × ones (3, 6); eta learning rate eta is 0.01; where ones (3,6) represents an identity matrix of three rows and six columns.
Step 2: initializing controller parameters, momentum factor alpha C 0.8; learning rate eta p ＝0.05、η i ＝0.1、η d 0.08; the constant value is kept in the control process.
And 3, step 3: setting an event trigger threshold M, wherein M is 0.2, and keeping a constant value in the control process;
and 4, step 4: updating RBF network parameters by using equations (16) - (22); if all data are completely operated, namely the simulation time k is 500, stopping updating the network parameters;
and 5: calculating controller parameters by using the expressions (1) to (15), and stopping updating the controller parameters when the simulation time k is 500; the results of the furnace temperature control are shown in fig. 2-8;
aiming at the problems of low control precision of the hearth temperature and frequent updating of the controller, the RBF-PID controller based on event triggering is provided. The self-adaptive adjustment of the RBF-PID controller parameters based on event triggering can ensure that the temperature of the hearth can quickly and stably follow a set value, has the control effects of high dynamic response speed, small overshoot and good stability, ensures that the controller can timely track the set value of the temperature of the hearth, and has higher control precision. Meanwhile, the controller based on the event trigger mechanism updates the controller only when the condition is triggered, so that the updating times of the controller can be effectively reduced. The triggering condition designed by the invention can effectively reduce the updating times of the controller and reduce the execution burden of the controller while ensuring the control effect. The method of the invention provides beneficial reference and correction for operators in the aspect of real-time control of the temperature of the hearth.
Claims (1)
1. A RBF-PID (radial basis function-proportion integration differentiation) municipal solid waste incineration process furnace temperature control method based on event triggering is characterized by comprising the following steps:
step 1: initialization parameters
Initializing controller parameters including the number of neurons in a hidden layer of the RBF network, the center of a Gaussian function, the width and an output weight; PID controller parameters and fixed event triggered thresholds;
step 2: calculating controller inputs
Calculating the tracking error e (k) of the hearth temperature at the current moment and the error variation ec (k) of the hearth temperature, and calculating as follows:
e(k)＝y d (k)-y(k) (1)
ec(k)＝e(k)-e(k-1) (2)
in the formula: e (k) and e (k-1) respectively representControlling the temperature of the hearth at the k moment and the k-1 moment; ec (k) represents a furnace temperature error change amount at time k; y is d (k) And y (k) represents the expected value of the furnace temperature in the control process at the moment k and the actual output value of the control system;
and step 3: computing controller output
The controller adopts incremental PID, and the controller output is:
u(k)＝u(k-1)+Δu(k) (3)
wherein u (k) and u (k-1) represent the controller outputs at time k and time k-1, respectively; Δ u (k) is an increment of the control amount at time k, and is calculated as follows:
Δu(k)＝K p [e(k)-e(k-1)]+K i e(k)+K d [e(k)-2e(k-1)+e(k-2)] (4)
in the formula, K p 、K i 、K d Is a PID controller parameter; e (k), e (k-1) and e (k-2) respectively represent the tracking errors at the time k, the time k-1 and the time k-2;
and 4, step 4: judging event trigger condition, if meeting event trigger, updating control quantity
The event trigger conditions are designed as follows:
k t+1 ＝{|Δu(k)|≥M} (6)
wherein M is a set event trigger threshold; u (k) t ) Is the actual control quantity under the t trigger sequence, which will be kept from the previous trigger sequence until the next trigger sequence is updated to u (k) t+1 ) (ii) a Δ u (k) is a control amount increment at time k; k is a radical of t Represents the time value under the t trigger sequence; k is a radical of formula t+1 Represents the time value under the t +1 trigger sequence;
and 5: calculating RBF network output y at current k moment m (k)
The RBF network mainly comprises an input layer, a hidden layer and an output layer, and the calculation mode is as follows:
gaussian function of hidden layer of RBF network is
Where x is the input vector, h j (x) Gaussian function value representing the jth neuron of the hidden layer when the input is x, c j And σ j Respectively hiding the center and the width of a Gaussian function of the jth neuron of the layer, wherein m is the number of neurons of the hidden layer;
the RBF network output is calculated as follows:
in the formula w j (k) For the jth network output weight at time k, y m (k) Is the output value of the RBF network at the k moment, and m is the number h of the hidden layer neurons j (x) Representing a Gaussian function value of a jth neuron of a hidden layer when the input is x;
step 6: computing
Formula w j (k) For the jth network output weight at time k, h j (k) Gaussian function value for the jth neuron of the hidden layer at time k, c j (k) And σ j (k) Respectively representing the center and the width of the j-th neuron Gaussian function of the hidden layer at the k moment m (k) The output value of the RBF network at the time k, m is the number of neurons of the hidden layer, and delta u (k) is the increment of the control quantity at the time k;
and 7: method for calculating PID controller parameter increment by adopting gradient descent method
Using the square error function as the performance index:
in the formula: e (k) represents a performance index at time k; e (k) represents the furnace temperature control error at the time k; y is d (k) Y (k) represents the expected value of the furnace temperature at the time k in the control process and the actual output value of the control system;
and (3) dynamically adjusting the PID controller parameter increment by adopting a gradient descent method, and calculating as follows:
wherein e (k), e (k-1) and e (k-2) represent tracking errors at time k, time k-1 and time k-2, respectively; Δ K p (k)、ΔK i (k)、ΔK d (k) Is PID parameter increment at the k moment; y is m (k) RBF network output at the time of k; eta p 、η i 、η d Learning rates of proportional, integral and differential parameters respectively; e (k) represents a performance index at time k;
and 8: updating PID controller parameters
K p (k)＝K p (k-1)+ΔK p (k)+α C 2 (K p (k-1)-K p (k-2)) (14)
K i (k)＝K i (k-1)+ΔK i (k)+α C 2 (K i (k-1)-K i (k-2)) (15)
K d (k)＝K d (k-1)+ΔK d (k)+α C 2 (K d (k-1)-K d (k-2)) (16)
In the formula K p (k)、K p (K-1) and K p (k-2) respectively representing proportional parameters of the k time, the k-1 time and the k-2 time; k i (k)、K i (K-1) and K i (k-2) respectively representing integral parameters at the time k, the time k-1 and the time k-2; k d (k)、K d (K-1) and K d (k-2) differential parameters indicating a k time, a k-1 time and a k-2 time, respectively; alpha is alpha C Is a momentum factor; Δ K p (k)、ΔK i (k)、ΔK d (k) PID parameter increment at the k moment;
and step 9: adjusting RBF network parameters, namely the center, the width and the network weight of a Gaussian function;
defining the performance index of the recognizer as:
wherein y (k) represents the actual output value of the furnace temperature at the k moment in the control process; y is m (k) RBF network output at the time of k;
step 9.1: center and width update
Where eta is a learning rate, eta is an element [0,1 ]](ii) a J (k) is a performance index at the time k; h is j (x) Gaussian function value representing the jth neuron of the hidden layer when the input is x, c j (k) And σ j (k) Respectively representing the center and the width of the j-th neuron Gaussian function of the hidden layer at the k moment; x is an input vector; y (k) represents an actual output value of the furnace temperature in the control process at the time k; y is m (k) RBF network output value at k moment; w is a j (k) Outputting the weight for the jth network at the moment k;
step 9.2: weight value updating
Using a recursive least squares algorithm, the formula is as follows:
in the formula: k (k), P (k) respectively represent the recursive least square parameter value at the time k, and I is an identity matrix; w (k) is the network output weight at time k; h (k) is the hidden layer output value at the time k; h is T (k) Transposing the output of the hidden layer for time k.
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