A method for tracing the source of PID controller parameter degradation

Abstract

The present invention discloses a PID controller parameter degradation tracing method, including judging whether the system performance is degraded, whether the system is adjusted too fast or too slowly; for the loop of the controller being adjusted too fast, judging whether the loop has oscillation; if the loop being adjusted too fast has oscillation, using the in-phase and out-phase degree index based on the cross-correlation function to trace whether the cause of the PID controller degradation is dominated by excessively strong proportional action or excessively strong integral action; for the loop of the controller being adjusted too slowly, using the segmented curve fitting method based on the particle swarm optimization algorithm to fit the closed-loop pulse response sequence; calculating the decline amplitude index in the proportion-dominated area of ​​the obtained fitting curve, and calculating the decline time of the fitting curve at the same time, tracing whether the cause of the PID controller degradation is dominated by excessively weak proportional action or excessively weak integral action. The method of the present invention can timely discover and identify the defects of the control system and the loop, optimize the control system parameters, thereby improving the reliability and operation performance of the system.

Description

Technical Field

[0001] The invention belongs to the field of process industry control engineering, and in particular, relates to a PID controller parameter degradation tracing method. Background Art

[0002] There are hundreds of control loops in modern industrial process systems. These controllers have good performance in the early stage of the entire industrial process, but as time goes by, they will be affected by various factors, and the performance of the controllers will gradually deteriorate, eventually resulting in a large gap between the actual performance and the design requirements. According to statistics, about 60% of the controllers in industrial sites have performance defects, which will not only reduce product quality, increase operating costs, and increase equipment usage time, but may also cause safety problems.

[0003] In traditional industrial processes such as nuclear power, petroleum, and chemical industry, PID controllers are widely used, accounting for more than 90%. The quality of their control performance directly affects the regulation quality and the stability of the unit operation. PID controllers are designed according to certain performance benchmarks. As the operating time goes by, their control performance will decline and fail to meet the expected performance goals, resulting in a large gap between actual performance and expected requirements. In industrial processes, there are many poor performance loops, and the performance is generally poor. Excluding factors such as valve sticking, many of these loops are caused by improper control parameter settings.

[0004] Therefore, how to integrate the operating data of the control loop, trace the causes of PID controller degradation, and then guide the parameter setting of industrial field controllers has become an urgent need in today's control industry. Summary of the invention

[0005] The purpose of the present invention is to provide a PID controller parameter degradation tracing method in view of the deficiencies in the prior art.

[0006] The specific technical solutions adopted by the present invention are as follows:

[0007] The present invention provides a PID controller parameter degradation tracing method, which is as follows:

[0008] S1: Collect loop operation data, calculate the time series AR model of the PID control loop, calculate the closed-loop pulse response sequence and the closed-loop step response sequence, and use a method based on the regulation performance index to determine whether the system control performance is deteriorated; if the system control performance is not deteriorated, end the determination; if the system control performance is deteriorated, proceed to step S2;

[0009] S2: For the system with performance degradation, use the second-order closed-loop transfer function model SOPTD with time lag to fit the closed-loop step response sequence, and judge whether the system is adjusted too fast or too slow by the time constant τ and the damping ratio ζ; if the system is adjusted too fast, proceed to step S3; if the system is adjusted too slowly, proceed to steps S5 and S6;

[0010] S3: For the loop whose controller is adjusted too fast, use the improved oscillation detection index based on ACF to monitor whether the loop has oscillation; if the loop does not have oscillation, end the judgment; if the loop has oscillation, proceed to step S4;

[0011] S4: If there is oscillation in the loop that is tuned too fast, use the in-phase and out-of-phase degree index based on the cross-correlation function to trace the cause of PID controller degradation to whether it is dominated by excessive proportional action or excessive integral action;

[0012] S5: For the loop where the controller is tuned too slowly, the closed-loop impulse response sequence is fitted using a piecewise curve fitting method based on a particle swarm optimization algorithm to obtain a fitting curve;

[0013] S6: Calculate the decline index in the proportion-dominated area of ​​the fitting curve, compare it with 50%, and calculate the decline time of the fitting curve, compare it with the expected recovery time, and trace back to whether the cause of the degradation of the PID controller is dominated by the proportional action being too weak or the integral action being too weak.

[0014] Preferably, the step S1 is specifically as follows:

[0015] Collect the operating data of the PID control loop, the operating data includes system input data, system output data and controller output data; use the prediction error algorithm to calculate the time series AR model of the PID control loop; the prediction error algorithm is a one-step prediction error method combined with a final prediction error criterion, and the prediction error algorithm adopts the following model structure,

[0016] AR Model:

[0017] y(k)+a1y(k-1)+…+a n y(kn)=e(k)

[0018] Optimization goal:

[0019]

[0020] Where y represents the output value of the loop; y(k), y(k-1), …, y(kn) represent the output values ​​of the loop at time k, time (k-1), …, time (kn) respectively; e(k) represents the white noise value at time k; a1, …, a nThey represent the model parameters corresponding to different output values ​​at different times before time k; n is the number of preset time selections; θ represents the model parameter matrix, θ=[a1a2…a n ] T ; N represents the number of model parameters; is the one-step forecast value, which means the prediction of the system output value at time k at time (k-1). The specific form is shown in the following formula:

[0021] One-step forecast value:

[0022]

[0023] The output dataset [·] T represents transposition; the optimization objective is further transformed into the least squares proposition expressed by the following formula:

[0024]

[0025] After the AR model is calculated, it is converted into an MA model, and the first d terms are extracted to obtain the expected closed-loop model;

[0026] MA Model:

[0027] y t =(f0+f1q -1 +…+f d-1 q -d+1 +f d q -d +…+f n q -n +…)e t

[0028] Expected closed loop model:

[0029]

[0030] Where d is the system delay; q is the forward propagation operator, q -1 f(k)=f(k-1); α=exp(-t s / τ C ), t s is the sampling time, τ C is the expected response time; i is the parameter of MA model; e t is white noise;

[0031] The MA model is then used to calculate the closed-loop impulse response sequence and the closed-loop step response sequence;

[0032] Then, a method based on the adjustment performance index is used to determine whether the system performance is degraded, as follows:

[0033] Adjustment performance index:

[0034]

[0035] in represents the output variance of the expected closed-loop system, represents the output variance of the actual system, Represents the output variance of white noise, and the RPI value range is (0,1); if the RPI is less than 0.8, it is considered that the system control performance has deteriorated.

[0036] Preferably, the step S2 is specifically as follows:

[0037] For the system with degraded control performance, the following second-order closed-loop transfer function model with time lag SOPTD is used to fit the closed-loop step response sequence obtained in step S1;

[0038] SOPTD model:

[0039]

[0040] Among them, θ represents the time lag, s represents the complex variable;

[0041] Then, the time constant τ and the damping ratio ζ are used to determine whether the system is adjusted too fast or too slow.

[0042] Preferably, the improved oscillation detection index based on ACF in step S3

[0043]

[0044] In the above formula

[0045]

[0046] Among them, h1 is defined as the distance between the autocorrelation coefficient value and the zero coordinate axis when the time lag is 0, and h i It is defined as the continuous extreme value points of the curve in the autocorrelation diagram, and n is the number of extreme value points; when OsctIndex<0.25, it is considered that there is no oscillation in the loop; when 0.25≤OsctIndex<1, it is considered that there is oscillation in the loop.

[0047] Preferably, the step S4 is specifically as follows:

[0048] If the loop that is set too fast has oscillation, calculate the cross-correlation function between the controller output OP and the system output PV.

[0049] Cross-correlation function:

[0050] R op,pv (τ)=E{op(t)pv *(t-τ)}

[0051] Where E{·} means to find the expectation; τ is the time difference between the two signal values, called lag; * means complex conjugate; t means time;

[0052] After the cross-correlation function is obtained, the in-phase and out-of-phase degree index is calculated; the in-phase and out-of-phase degree index includes the in-phase time index Δτ and the in-phase degree index Δρ;

[0053] In-Phase Time Index:

[0054]

[0055] In-phase index:

[0056]

[0057] where τ left and τ right are the first zero crossing points on the left and right sides of the cross-correlation function curve when the time lag τ = 0, R0 represents the cross-correlation function value corresponding to the time lag τ = 0, and R max represents the extreme point of the cross-correlation function closest to the τ = 0 axis;

[0058] like and The reason for the degradation of the PID controller is that the proportional action is too dominant; if and The reason for the degradation of the PID controller is that the proportional and integral effects are both too strong and dominate together; if and The reason for the degradation of the PID controller is that the integral action is too dominant.

[0059] Preferably, the step S5 is specifically as follows:

[0060] The segmented curve is

[0061]

[0062] The optimization goal is

[0063]

[0064] Among them, k and q are the parameters of the first straight line, a and b are the parameters of the second curve, and t θ is the system delay, t P is the turning time, f(t P ) indicates that t P is the residual sum of squares at the turning point;

[0065] Write the piecewise curve in matrix form

[0066] Φθ=Y,

[0067] in

[0068]

[0069] The residual sum of squares is

[0070]

[0071] The parameter estimates based on least squares are

[0072]

[0073] Best turning point The particle swarm optimization algorithm is used to calculate the update formula of the speed and position of each particle in the population as follows:

[0074]

[0075] in Represents the speed of the individual at the kth iteration, that is, the direction and size of parameter update; represents the individual optimal solution; represents the optimal solution of the group; represents the individual position, and the objective function corresponding to the position is fitness; w is the inertia weight, c1 and c2 are both learning factors, and r1 and r2 are random numbers in the interval [0,1];

[0076] According to the best turning point Get the fitting curve

[0077]

[0078] Preferably, step S6 is specifically as follows:

[0079] The proportional dominant region of the obtained fitting curve is where t θ is the system delay, To calculate the best turning point, the decline index m is calculated by the following formula:

[0080] Decline index:

[0081]

[0082] The obtained m value is compared with 50%, and the pulse half-value time t taken for the pulse response value to drop to 50% of the initial moment is calculated. k ,

[0083] Pulse half-value time:

[0084]

[0085] in represents the closed-loop impulse response value at time t, It represents the function of finding the corresponding time when the closed-loop impulse response value is known;

[0086] The obtained t k Value and Compare and then calculate the falling time of the fitting curve; the falling time refers to the time from t θ Starting from time t, the closed-loop pulse response value drops to t θ Moment The time taken; the fall time is calculated by the following formula,

[0087] Fall time:

[0088]

[0089] Compare the resulting fall time with the expected recovery time;

[0090] If m≤50% or Then the reason for the deterioration of the PID controller is that the proportion is too weak to dominate;

[0091] If m ≥ 50% and At the same time fall >2τ C , then the reason for the degradation of the PID controller is that the integral is too weakly dominated.

[0092] Compared with the prior art, the present invention has the following beneficial effects:

[0093] 1) The PID controller parameter degradation tracing method for a PID control loop of the present invention makes up for the deficiency that the traditional method cannot perform PID controller parameter degradation tracing.

[0094] 2) The PID controller parameter degradation tracing method of the present invention is simple to implement and has low environmental dependence.

[0095] 3) The principle of the method for tracing the degradation of PID controller parameters of the present invention is concise and clear, easy to implement on a computer, and very flexible, and can better meet the requirements of performance evaluation of actual industrial control loops. BRIEF DESCRIPTION OF THE DRAWINGS

[0096] Figure 1 This is the flow chart of the PID controller parameter degradation traceability solution.

[0097] Figure 2 It is the cross-correlation function curve diagram in Example 1. DETAILED DESCRIPTION

[0098] The present invention is further described and illustrated below in conjunction with the accompanying drawings and specific embodiments. The technical features of each embodiment of the present invention can be combined accordingly without conflicting with each other.

[0099] The present invention provides a method for tracing the source of PID controller parameter degradation, the flow chart of which is as follows: Figure 1 As shown in the figure, the process includes obtaining loop operation data, calculating the time series AR model of the control loop, calculating the regulation performance index RPI, judging the speed of controller tuning, oscillation detection, segmented curve fitting, and finally tracing back the cause of PID controller degradation. This method collects the operation data of the PID control loop and calculates the time series AR model of the closed-loop control system. Then, the closed-loop pulse response sequence and step response sequence of the time series AR model are calculated, and the method based on the regulation performance index is used to determine whether the system performance is degraded. For the degraded system, the closed-loop step response is fitted using the second-order closed-loop transfer function model with time lag, and τ and ζ are used to determine whether the system is tuned too fast or too slow. In the case of too fast controller tuning, the improved oscillation detection index based on ACF is used to monitor whether the loop has oscillation. For the loop with oscillation, the in-phase and out-of-phase index based on the cross-correlation function is used to locate the cause of poor controller performance. In the case of too slow controller tuning, the segmented curve fitting method based on the particle swarm optimization algorithm is used to fit the closed-loop pulse response sequence, and then the pulse response drop index in the proportional dominant area and the actual system drop time are combined to locate the cause of poor controller performance.

[0100] The method of the present invention will be described in detail below.

[0101] S1: Collect loop operation data, calculate the time series AR model of the PID control loop, calculate the closed-loop impulse response sequence and the closed-loop step response sequence, and use the method based on the adjustment performance index to determine whether the system control performance is degraded. If the system control performance is not degraded, then end the judgment; if the system control performance is degraded, proceed to step S2.

[0102] Step S1 is specifically as follows:

[0103] Collect the operating data of the PID control loop, which includes system input data, system output data and controller output data. The system in the present invention refers to the control loop. The prediction error algorithm is used to calculate the time series AR model of the PID control loop. The prediction error algorithm is a one-step prediction error method combined with the final prediction error criterion. The prediction error algorithm adopts the following model structure:

[0104] AR Model:

[0105] y(k)+a1y(k-1)+…+a n y(kn)=e(k)

[0106] Optimization goal:

[0107]

[0108] Where y represents the output value of the loop; y(k), y(k-1), …, y(kn) represent the output values ​​of the loop at time k, time (k-1), …, time (kn) respectively; e(k) represents the white noise value at time k; a1, …, a n They represent the model parameters corresponding to different output values ​​at different times before time k; n is the number of preset time selections; θ represents the model parameter matrix, θ=[a1a2…a n ] T ; N represents the number of model parameters; is the one-step forecast value, which means the prediction of the system output value at time k at time (k-1). The specific form is shown in the following formula:

[0109] One-step forecast value:

[0110]

[0111] The output dataset [·] T represents transpose; the optimization objective is further transformed into the least squares proposition expressed by the following formula

[0112]

[0113] After the AR model is calculated, it is converted into an MA model, and the first d terms are extracted to obtain the expected closed-loop model;

[0114] MA Model:

[0115] y t =(f0+f1q -1 +…+f d-1 q -d+1 +f d q -d +…+f n q -n +…)e t

[0116] Expected closed loop model:

[0117]

[0118] Where d is the system delay; q is the forward propagation operator, q -1 f(k)=f(k-1); α=exp(-t s / τ C ), t sis the sampling time, τ C is the expected response time; i is the parameter of MA model; e t is white noise.

[0119] The MA model is then used to calculate the closed-loop impulse response sequence and the closed-loop step response sequence;

[0120] Then, a method based on the Regulation Performance Index (RPI) is used to determine whether the system performance has deteriorated, as follows:

[0121] Adjustment performance index:

[0122]

[0123] in represents the output variance of the expected closed-loop system, represents the output variance of the actual system, Represents the output variance of white noise. The RPI value range is (0,1). The closer the RPI is to 1, the better the loop control performance. If the RPI is less than 0.8, it is considered that the system control performance has deteriorated.

[0124] S2: For systems with degraded performance, use the second-order closed-loop transfer function model with time lag (SOPTD) to fit the closed-loop step response sequence, and use the time constant τ and the damping ratio ζ to determine whether the system is adjusted too fast or too slow; if the system is adjusted too fast, proceed to step S3; if the system is adjusted too slowly, proceed to steps S5 and S6.

[0125] Step S2 is specifically as follows:

[0126] For the system with degraded control performance, the following second-order closed-loop transfer function model with time lag (SOPTD) is used to fit the closed-loop step response sequence obtained in step S1;

[0127] SOPTD model:

[0128]

[0129] Among them, θ represents the time lag, s represents the complex variable;

[0130] Then, the time constant τ and the damping ratio ζ are used to determine whether the system is adjusted too fast or too slow.

[0131] S3: For the loop whose controller is adjusted too fast, use the improved oscillation detection index based on ACF to monitor whether the loop has oscillation; if the loop does not have oscillation, end the judgment; if the loop does have oscillation, proceed to step S4.

[0132] In step S3, the improved oscillation detection index based on ACF is

[0133]

[0134] In the above formula

[0135]

[0136] Among them, h1 is defined as the distance between the autocorrelation coefficient value and the zero coordinate axis when the time lag is 0, and h i It is defined as the continuous extreme value points of the curve in the autocorrelation diagram, and n is the number of extreme value points; when OsctIndex<0.25, it is considered that there is no oscillation in the loop; when 0.25≤OsctIndex<1, it is considered that there is oscillation in the loop.

[0137] S4: If there is oscillation in the loop that is tuned too fast, use the in-phase and out-of-phase degree index based on the cross-correlation function to trace the cause of the PID controller degradation to see whether it is dominated by the excessive proportional action or the excessive integral action.

[0138] Step S4 is specifically as follows:

[0139] If the loop is tuned too fast and oscillates, calculate the cross-correlation function between the controller output (OP) and the system output (PV).

[0140] Cross-correlation function:

[0141] R op,pv (τ)=E{op(t)pv * (t-τ)}

[0142] Where E{·} means to find the expectation; τ is the time difference between the two signal values, called lag; * means complex conjugate; t means time;

[0143] After the cross-correlation function is obtained, the in-phase and out-of-phase degree index is calculated; the in-phase and out-of-phase degree index includes the in-phase time index Δτ and the in-phase degree index Δρ;

[0144] In-Phase Time Index:

[0145]

[0146] In-phase index:

[0147]

[0148] where τ left and τ right are the first zero crossing points on the left and right sides of the cross-correlation function curve when the time lag τ = 0, R0 represents the cross-correlation function value corresponding to the time lag τ = 0, and R maxIt represents the extreme point of the cross-correlation function closest to the τ=0 axis; then the cause of the degradation of the PID controller is traced back by combining Δτ and Δρ, as follows:

[0149] like and The reason for the degradation of the PID controller is that the proportional action is too dominant; if and The reason for the degradation of the PID controller is that the proportional and integral effects are both too strong and dominate together; if and The reason for the degradation of the PID controller is that the integral action is too dominant.

[0150] S5: For the loop where the controller is tuned too slowly, the closed-loop impulse response sequence is fitted using a piecewise curve fitting method based on a particle swarm optimization algorithm to obtain a fitting curve.

[0151] Step S5 is specifically as follows:

[0152] The segmented curve is

[0153]

[0154] The optimization goal is

[0155]

[0156] Among them, k and q are the parameters of the first straight line, a and b are the parameters of the second curve, and t θ is the system delay, t P is the turning time, f(t P ) indicates that t P is the residual sum of squares at the turning point;

[0157] Write the piecewise curve in matrix form

[0158] Φθ=Y,

[0159] in

[0160]

[0161] Then the residual sum of squares is

[0162]

[0163] The parameter estimates based on least squares are

[0164]

[0165] Best turning point The particle swarm optimization algorithm is used to calculate the update formula of the speed and position of each particle in the population as follows:

[0166]

[0167] in Represents the speed of the individual at the kth iteration, that is, the direction and size of parameter update; represents the individual optimal solution; represents the optimal solution of the group; represents the individual position, and the objective function corresponding to the position is fitness; w is the inertia weight, c1 and c2 are both learning factors, and r1 and r2 are random numbers in the interval [0,1].

[0168] According to the best turning point Get the final fitting curve

[0169]

[0170] S6: Calculate the decline index in the proportion-dominated area of ​​the fitting curve, compare it with 50%, and calculate the decline time of the fitting curve, compare it with the expected recovery time, and trace back to whether the cause of the degradation of the PID controller is dominated by the proportional action being too weak or the integral action being too weak.

[0171] That is, calculate the decline index m in the proportion-dominant region of the fitting curve, compare it with 50%, and calculate the pulse half-value time t taken for the pulse response value to drop to 50% of the initial moment k ,and By comparison, the fall time of the fitting curve is calculated and compared with the expected recovery time, so as to trace back the cause of the PID controller degradation, whether it is dominated by the weak proportional action or the weak integral action.

[0172] Step S6 is specifically as follows:

[0173] The proportional dominant region of the obtained fitting curve is where t θ is the system delay, To calculate the best turning point, the decline index m is calculated by the following formula:

[0174] Decline index:

[0175]

[0176] Compare the obtained m value with 50%, and calculate the pulse half-value time t taken for the pulse response value to drop to 50% of the initial moment k ,

[0177] Pulse half-value time:

[0178]

[0179] in represents the closed-loop impulse response value at time t, It represents the function of finding the corresponding time when the closed-loop impulse response value is known;

[0180] The obtained t k Value and Compare and then calculate the fall time of the fitting curve; the fall time refers to the time from t θ Starting from time t, the closed-loop pulse response value drops to t θ Moment The time taken; the fall time is calculated by the following formula,

[0181] Fall time:

[0182]

[0183] Compare the resulting fall time with the expected recovery time;

[0184] If m≤50% or Then the reason for the deterioration of the PID controller is that the proportion is too weak to dominate;

[0185] If m ≥ 50% and At the same time fall >2τ C , then the reason for the degradation of the PID controller is that the integral is too weakly dominated.

[0186] Example 1

[0187] Taking the liquid level control loop of a chemical plant in Zhejiang Province as an example, the PID controller parameter degradation tracing method is adopted, which includes the following implementation steps:

[0188] Step 1: Collect the operating data of the liquid level control loop, including the liquid level set value, the actual liquid level value, and the PID controller output value. After preprocessing the operating data such as removing the mean, the one-step prediction error method is combined with the final prediction error rule to obtain the time series AR model of the PID control loop.

[0189] AR Model:

[0190] y(k)+a1y(k-1)+…+a n y(kn)=e(k)

[0191] Optimization goal:

[0192]

[0193] Equivalently converted to MA model, extracting the first d items to obtain the expected closed-loop model

[0194] After the AR model is calculated, it is converted into an MA model, and the first d terms are extracted to obtain the expected closed-loop model.

[0195] MA Model:

[0196] y t =(f0+f1q -1 +…+f d-1 q -d+1 +f d q -d +…+f n q -n +…)e t

[0197] Expected closed loop model:

[0198]

[0199] α=exp(-t s / τ C ), t s is the sampling time, τ C is the expected response time, d = 1 + integer (t θ / t s ), t θ is the system delay, where t s =1, d=23.

[0200] Enter the calculation adjustment performance index RPI

[0201]

[0202] Here, it is calculated that RPI=0.43<0.8, that is, the controller performance is deteriorated.

[0203] Step 2: For the system with degraded performance, use the following second-order closed-loop transfer function model with time lag (SOPTD) to fit the closed-loop step response sequence obtained in step 1.

[0204] SOPTD model:

[0205]

[0206] Based on the image or the time constant τ and the damping ratio ζ, it can be determined that the system controller is over-tuned.

[0207] Step 3: For loops where the controller is tuned too fast, use the improved oscillation detection indicator based on ACF to monitor whether the loop has oscillation.

[0208] Improved oscillation detection indicator based on ACF:

[0209]

[0210] In the above formula

[0211]

[0212] Here, it is calculated that OsctIndex=0.65, that is, when 0.25≤OsctIndex<1, it is determined that oscillation exists in the loop.

[0213] Step 4: Calculate the cross-correlation function of the controller output (OP) and the system output (PV), and use the in-phase and out-of-phase degree index based on the cross-correlation function to trace the cause of PID controller degradation to see whether it is dominated by excessive proportional action or excessive integral action.

[0214] Cross-correlation function:

[0215] R op,pv (τ)=E{op(t)pv * (t-τ)}

[0216] like Figure 2 As shown, after obtaining the cross-correlation function, calculate the in-phase time index Δτ and the in-phase degree index Δρ

[0217] In-Phase Time Index:

[0218]

[0219] In-phase index:

[0220]

[0221] According to the criteria, it can be determined that the degradation of the loop control performance is dominated by the excessive proportional action.

[0222] Example 2

[0223] Taking the pressure control loop of an air separation plant in Zhejiang Province as an example, the PID controller parameter degradation tracing method is adopted, which includes the following implementation steps:

[0224] Step 1: Collect the operating data of the pressure control loop, including the pressure setting value, the actual pressure value, and the PID controller output value. After preprocessing the operating data such as removing the mean, the one-step prediction error method is combined with the final prediction error rule to obtain the time series AR model of the PID control loop.

[0225] AR Model:

[0226] y(k)+a1y(k-1)+…+a n y(kn)=e(k)

[0227] Optimization goal:

[0228]

[0229] Equivalently converted to the MA model, the first d terms are extracted to obtain the expected closed-loop model.

[0230] After the AR model is calculated, it is converted into an MA model, and the first d terms are extracted to obtain the expected closed-loop model.

[0231] MA Model:

[0232] y t =(f0+f1q -1 +…+f d-1 q -d+1 +f d q -d +…+f n q -n +…)e t

[0233] Expected closed loop model:

[0234]

[0235] α=exp(-t s / τ C ), t s is the sampling time, τ C is the expected response time, d = 1 + integer (t θ / t s ), t θ is the system delay, where t s =1, d=9.

[0236] Enter the calculation adjustment performance index RPI

[0237]

[0238] Here, it is calculated that RPI=0.62<0.8, that is, the controller performance is deteriorated.

[0239] Step 2: For the system with degraded performance, use the following second-order closed-loop transfer function model with time lag (SOPTD) to fit the closed-loop step response sequence obtained in step 1.

[0240] SOPTD model:

[0241]

[0242] Based on the image or time constant τ and damping ratio ζ, it can be determined that the system controller is too weakly tuned.

[0243] Step 3: For the loop where the controller is too weak, the closed-loop impulse response sequence is fitted using a piecewise curve fitting method based on the particle swarm optimization algorithm, as follows:

[0244] Segmented Curve

[0245]

[0246] Optimization goals

[0247]

[0248] Written in matrix form

[0249] Φθ=Y

[0250] in

[0251]

[0252] The residual sum of squares is

[0253]

[0254] The parameter estimates based on least squares are

[0255]

[0256] The best turning point t P It can be calculated using the particle swarm optimization algorithm. The update formula for the speed and position of each particle in the population is as follows:

[0257]

[0258] in It represents the speed of the individual at the kth iteration, that is, the direction and size of parameter update. represents the individual optimal solution. represents the group optimal solution. represents the individual position, the objective function corresponding to the position is fitness, w is the inertia weight, c1 and c2 are learning factors.

[0259] Here, the population size is 5, the maximum number of iterations is 20, and the position function is the residual sum of squares f = ε 2 , take the inertia weight w = 0.8, take the learning factor c1 = c2 = 1.49445. Due to the integer programming problem, rounding is required during initialization and speed and position update.

[0260] Step 6: Calculate the decline index m in the proportional dominant region of the fitting curve, compare it with 50%, and calculate the pulse half-value time t taken for the pulse response value to drop to 50% of the initial moment k ,and By comparison, the fall time of the fitting curve is calculated and compared with the expected recovery time, so as to trace back the cause of the PID controller degradation, whether it is dominated by the weak proportional action or the weak integral action.

[0261] The ratio-dominant region is [t θ ,t P ], where t θ is the system delay, t P To calculate the best turning point, the decline index m can be calculated by the following formula:

[0262] Decline index:

[0263]

[0264] Pulse half-value time:

[0265]

[0266] in represents the closed-loop impulse response value at time t, It means that the closed-loop impulse response value is known, and the function of the corresponding time is obtained. Here the calculation result is m=64%>50%.

[0267] Then calculate the fall time, which refers to the fall time from t θ Starting from time t, the closed-loop pulse response value drops to t θ Moment The time consumed can be calculated by the following formula

[0268] Fall time:

[0269]

[0270] Here we calculate t fall =52.5>2τ C =36

[0271] According to the judgment criteria, the degradation of the system is dominated by the fact that the integral action is too weak.

[0272] In a chemical circuit, the method of the present invention can timely discover and identify defects in the control system and the circuit, optimize the control system parameters, and thus improve the reliability and operating performance of the system.

[0273] The above-described embodiment is only a preferred solution of the present invention, but it is not intended to limit the present invention. A person skilled in the relevant technical field may make various changes and modifications without departing from the spirit and scope of the present invention. Therefore, any technical solution obtained by equivalent replacement or equivalent transformation falls within the protection scope of the present invention.

Claims

1. A PID controller parameter degradation tracing method, characterized in that: The details are as follows: S1: Collect loop operation data, calculate the time series AR model of the PID control loop, calculate the closed-loop pulse response sequence and the closed-loop step response sequence, and use a method based on the regulation performance index to determine whether the system control performance is deteriorated; if the system control performance is not deteriorated, end the determination; if the system control performance is deteriorated, proceed to step S2; S2: For the system with performance degradation, use the second-order closed-loop transfer function model SOPTD with time lag to fit the closed-loop step response sequence, and judge whether the system is adjusted too fast or too slow by the time constant τ and the damping ratio ζ; if the system is adjusted too fast, proceed to step S3; if the system is adjusted too slowly, proceed to steps S5 and S6; S3: For the loop whose controller is adjusted too fast, use the improved oscillation detection index based on ACF to monitor whether the loop has oscillation; if the loop does not have oscillation, end the judgment; if the loop has oscillation, proceed to step S4; S4: If there is oscillation in the loop that is tuned too fast, use the in-phase and out-of-phase degree index based on the cross-correlation function to trace the cause of PID controller degradation to whether it is dominated by excessive proportional action or excessive integral action; S5: For the loop where the controller is tuned too slowly, the closed-loop impulse response sequence is fitted using a piecewise curve fitting method based on a particle swarm optimization algorithm to obtain a fitting curve; S6: Calculate the decline index in the proportion-dominated area of ​​the fitting curve, compare it with 50%, and calculate the decline time of the fitting curve, compare it with the expected recovery time, and trace back the cause of the PID controller degradation to whether the proportional action is too weak or the integral action is too weak; The step S1 is specifically as follows: Collect the operating data of the PID control loop, the operating data includes system input data, system output data and controller output data; use the prediction error algorithm to calculate the time series AR model of the PID control loop; the prediction error algorithm is a one-step prediction error method combined with a final prediction error criterion, and the prediction error algorithm adopts the following model structure, AR Model: y(k)+a1y(k-1)+…+a n y(kn)=e(k) Optimization goal: Where y represents the output value of the loop; y(k), y(k-1), …, y(kn) represent the output values ​​of the loop at time k, time (k-1), …, time (kn) respectively; e(k) represents the white noise value at time k; a1, …, a n They represent the model parameters corresponding to different output values ​​at different times before time k; n is the number of preset time selections; θ represents the model parameter matrix, θ=[a1 a2…a n ] T ; N represents the number of model parameters; is the one-step forecast value, which means the prediction of the system output value at time k at time (k-1). The specific form is shown in the following formula: One-step forecast value: The output dataset [·] T represents transposition; the optimization objective is further transformed into the least squares proposition expressed by the following formula: After the AR model is calculated, it is converted into an MA model, and the first d terms are extracted to obtain the expected closed-loop model; MA Model: y t =(f0+f1q -1 +…+f d-1 q -d+1 +f d q -d +…+f n q -n +…)e t Expected closed loop model: Where d is the system delay; q is the forward propagation operator, q -1 f(k)=f(k-1); α=exp(-t s / τ C ), t s is the sampling time, τ C is the expected response time; i is the parameter of MA model; e t is white noise; The MA model is then used to calculate the closed-loop impulse response sequence and the closed-loop step response sequence; Then, a method based on the adjustment performance index is used to determine whether the system performance is degraded, as follows: Adjustment performance index: in represents the output variance of the expected closed-loop system, represents the output variance of the actual system, Represents the output variance of white noise, and the RPI value range is (0,1); if the RPI is less than 0.8, it is considered that the system control performance has deteriorated; The step S2 is specifically as follows: For the system with degraded control performance, the following second-order closed-loop transfer function model with time lag SOPTD is used to fit the closed-loop step response sequence obtained in step S1; SOPTD model: Among them, θ represents the time lag, s represents the complex variable; Then, the time constant τ and the damping ratio ζ are used to determine whether the system is set too fast or too slow; The improved oscillation detection index based on ACF in step S3 In the above formula Among them, h1 is defined as the distance between the autocorrelation coefficient value and the zero coordinate axis when the time lag is 0, and h i Defined as the continuous extreme value points of the curve in the autocorrelation diagram, n is the number of extreme value points; when OsctIndex<0.25, it is considered that there is no oscillation in the loop; when 0.25≤OsctIndex<1, it is considered that there is oscillation in the loop; The step S4 is specifically as follows: If the loop that is set too fast has oscillation, calculate the cross-correlation function between the controller output OP and the system output PV. Cross-correlation function: R op,pv (τ)=E{op(t)pv * (t-τ)} Where E{·} means to find the expectation; τ is the time difference between the two signal values, called lag; * means complex conjugate; t means time; After the cross-correlation function is obtained, the in-phase and out-of-phase degree index is calculated; the in-phase and out-of-phase degree index includes the in-phase time index Δτ and the in-phase degree index Δρ; In-Phase Time Index: In-phase index: where τ left and τ right are the first zero crossing points on the left and right sides of the cross-correlation function curve when the time lag τ = 0, R0 represents the cross-correlation function value corresponding to the time lag τ = 0, and R max represents the extreme point of the cross-correlation function closest to the τ = 0 axis; like and The reason for the degradation of the PID controller is that the proportional action is too dominant; if and The reason for the degradation of the PID controller is that the proportional and integral effects are both too strong and dominate together; if and Then the reason for the deterioration of the PID controller is that the integral action is too dominant; The step S5 is specifically as follows: The segmented curve is The optimization goal is Among them, k and q are the parameters of the first straight line, a and b are the parameters of the second curve, and t θ is the system delay, t P is the turning time, f(t P ) indicates that t P is the residual sum of squares at the turning point; Write the piecewise curve in matrix form Φθ=Y, in The residual sum of squares is The parameter estimates based on least squares are Best turning point The particle swarm optimization algorithm is used to calculate the update formula of the speed and position of each particle in the population as follows: in Represents the speed of the individual at the kth iteration, that is, the direction and size of parameter update; represents the individual optimal solution; represents the optimal solution of the group; represents the individual position, and the objective function corresponding to the position is fitness; w is the inertia weight, c1 and c2 are both learning factors, and r1 and r2 are random numbers in the interval [0,1]; According to the best turning point t P * Get the fitting curve The step S6 is specifically as follows: The proportional dominant region of the obtained fitting curve is where t θ is the system delay, To calculate the best turning point, the decline index m is calculated by the following formula: Decline index: Compare the obtained m value with 50%, and calculate the pulse half-value time t taken for the pulse response value to drop to 50% of the initial moment k , Pulse half-value time: in represents the closed-loop impulse response value at time t, It represents the function of finding the corresponding time when the closed-loop impulse response value is known; The obtained t k Value and Compare and then calculate the falling time of the fitting curve; the falling time refers to the time from t θ Starting from time t, the closed-loop pulse response value drops to t θ Moment The time taken; the fall time is calculated by the following formula, Fall time: Compare the resulting fall time with the expected recovery time; If m≤50% or Then the reason for the deterioration of the PID controller is that the proportion is too weak to dominate; If m ≥ 50% and At the same time fall >2τ C , then the reason for the degradation of the PID controller is that the integral is too weakly dominated.

Images