Fluid delivery system PID auto-tuning
Through an online program estimating the transfer function of the fluid system and identifying the PID parameters, the problem of difficulty in adjusting the PID parameters online in the prior art is solved, and more accurate and robust PID tuning of the fluid system is achieved.
Patent Information
- Application Number
- CN202411877967.8
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Priority Date
- 2023-12-21
- Filing Date
- 2024-12-19
- Publication Date
- 2025-06-24
AI Technical Summary
Prior art It is difficult to effectively adjust PID parameters online when adjusting the pressure, flow rate or temperature of a pump, compressor or fan system driven by an electric motor, especially if the client system is away from the pump or compressor.
The transfer function of the fluid system is estimated through an online program, and the parameters of the process transfer function are identified using step injection, periodic relay and periodic relay methods with integrals, and the PID parameters used for system adjustment are calculated.
A more complete and accurate PID parameter detection of the fluid system is achieved, providing a more robust PID tuning than the prior art methods, suitable for various fluid delivery systems.
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Figure CN120195968A_ABST
Abstract
Description
Technical Field
[0001] The present disclosure relates to the field of regulation of systems, such as systems in which a pump, compressor or fan driven by an electric motor conveys a fluid, such as a gas or a liquid, to a client system, and includes regulating the pressure, flow rate or temperature of the fluid, and more precisely, to a process for PID regulation for tuning such a process. Background Art
[0002] It is known to provide speed regulation of a pump or a compressor by regulating the electric motor driving such a pump, compressor or fan. However, there are applications in which it is necessary to provide regulation of the flow rate or pressure of a fluid within a fluid system, such as a pipe for conveying such a fluid to a client system, especially when such a client system is remote from the pump or compressor.
[0003] There are also PID auto-tuning processes for characterizing a fluid system and refining a drive command for regulating the motor speed taking into account the fluid system characteristics. Known online PID auto-tuning methods are based on two principles, a step-based auto-tuning method and a relay-based auto-tuning method. Online auto-tuning means that the PID tuning must be carried out while the system is running. This requires implementing a dedicated algorithm.
[0004] Step-based auto-tuning is similar to offline auto-tuning based on process identification, but is carried out online. In open loop, command steps are applied around a stable operating point, and the response is recorded in order to achieve process identification, such as in Alberto Leva, Filippo Donida's “A remote laboratory on PID autotuning”, Proceedings of the 17th World Congress The International Federation of Automatic Control Seoul, Korea, July 6 - 11, 2008 IFAC Proceedings Volumes, Volume 41, Issue 2, 2008, Pages 8147 - 8152, available online on July 11, 2008, https: / / doi.org / 10.3182 / 20080706 - 5 - KR - 1001.01376.
[0005] Relay-based auto-tuning uses techniques such as the Ziegler Nichols closed-loop tuning model or methods developed by Astron and Hägglund based on such a model, see Dune K.J., & Hagglund, T. “PID Controllers: Theory, Design, and Tuning”. ISA - The Instrumentation, Systems and Automation Society - Research Triangle Park, North Carolina 1995, ISBN: 1 - 55617 - 516 - 7. These techniques basically enable the determination of stable oscillations by stepping the process variable up and down within a built - in dead - band.
[0006] The method consists of injecting a command by a relay around a stable operating point, the relay switching at each change of error sign, as Figure 3 shown. When the relay is active, the PID is bypassed. Since the loop remains closed, there is no risk of instability. This process will naturally cause the relay to switch at the process critical - point frequency, as proposed by Ziegler - Nichols, which is a useful point for PID tuning.
[0007] This procedure will naturally cause the relay to switch at the process critical - point frequency.
[0008] The critical point can thus be defined by the following:
[0009] Critical period: T cr = P
[0010] Critical gain:
[0011] It corresponds to the point where the phase is - 180°: at this phase, the gain of the controlled process must be lower than 1 to avoid instability: the critical gain corresponds to the maximum proportional gain that can be applied to the process to maintain stability.
[0012] Based on these data, Ziegler - Nichols proposed PID settings:
[0013]
[0014] For the industrial use of this method, some modifications must be considered:
[0015] - A relay with hysteresis should be considered instead of a pure relay. In the case of a pure relay, a small amount of noise can cause the relay to switch randomly. By introducing hysteresis, the noise must be greater than the hysteresis width for the relay to switch. In this case, the obtained point does not exactly correspond to the critical point, but to a point with a lower phase. For simplicity, this difference may not be considered in the proposed algorithm: the phase is assumed to be - 180°.
[0016] - Manage load disturbances. In fact, since frequent and large load changes are often encountered in industrial processes, any identification process should be able to at least more actively detect load changes to find the quality process model under load disturbances.
[0017] ο Under load disturbances, the relay feedback test will result in asymmetric oscillations.
[0018] ο To restore symmetry, relay bias must be considered: load disturbances can be regarded as command offsets.
[0019] The process described in Cheng-Ching Yu's "Autotuning of PID Controllers - A Relay Feedback Approach" (Springer, ISBN 978-1-4471-3636-1, published on April 17, 2013) is used to adjust the relay bias until the symmetry of the oscillation is restored.
[0020] The basic relay method leads to PID tuning using Ziegler-Nichols settings, but the problem is that these settings are not relevant to typical process characteristics: therefore, it is difficult to verify these settings with confidence. Summary of the Invention
[0021] In view of this situation, the present disclosure provides a method that is suitable for estimating the process transfer function through an online program without any prior process knowledge to provide complete PID tuning for a process with PID control.
[0022] The proposed method for calculating the PID parameters of a system that includes a motor driving a pump, compressor, or fan to deliver a fluid such as gas or liquid to a client system and includes regulating the pressure, flow rate, or temperature of the fluid, the method further includes a feedback sensor that provides a feedback signal on the system and a PID adjustment that controls the motor speed, the method includes:
[0023] Initial approximation of the first-order delay transfer function of the fluid system
[0024]
[0025] Where the three parameters of the transfer function of the process to be identified for calculating PID are:
[0026] - K static gain,
[0027] - θ delay,
[0028] - τ time constant,
[0029] And one or more of the following sequences:
[0030] a - Bypass PID regulation and implement the following processes:
[0031] - Periodic relay process, providing a first point (ω -180 ; G -180 ) at the -180° phase called the critical point,
[0032] - Periodic relay with an integral process, providing a second point (ω -90 ; G -90 ) at the -90° phase,
[0033] - Step injection, providing G0 of the third point at 0° phase and zero frequency,
[0034] b - Solve the relevant equations in the system of equations:
[0035]
[0036] cos(ω -90 ·θ) - ω -90 ·τ·sin(ω -90 ·θ) = 0
[0037]
[0038] sin(ω -180 ·θ) - ω -180 ·τ·cos(ω -180 ·θ) = 0
[0039] Calculate the following available transfer function parameters based on the points obtained through the above processes:
[0040] K = G0
[0041]
[0042] c - Apply the obtained transfer function parameters to calculate the PID parameters for system regulation:
[0043]
[0044] This method provides a more complete detection of PID parameters than the prior art methods.
[0045] Preferably, for the fluid application process with a large time constant, T d is approximated to zero because the derivative term is not necessary.
[0046] Starting from the estimated transfer function P estim (S) and considering the gain of the pulse, calculate the parameter ω. This is preferably done through the following formula:
[0047]
[0048] And the phase ω during the pulse is completed by the following formula:
[0049]
[0050] And according to the process implemented:
[0051] a - Through step injection, calculate the gain G0. The step injection gives the points at zero frequency and phase;
[0052] b - Through periodic relay, calculate the pulse: ω -180 And the gain: G -180 = |P estim (j·ω -180 )| Calculate the point at the phase = -180°;
[0053] c - Through periodic relay with integration, calculate the pulse: ω -90 And the gain: G -90 = |P estim (j·ω -90 )| Calculate the point at the phase = -90°.
[0054] The step injection command may include bypassing the system PID regulation, inputting a step with amplitude Δu into the current speed command of the motor, waiting for the process feedback to converge, measuring the feedback signal value Δv, calculating the static gain K as Δv / Δu, and then re - establishing the system PID regulation.
[0055] The step amplitude Δu can be limited so as not to exceed the upper limit sh of the motor speed.
[0056] The periodic relay process may include:
[0057] - Bypassing the system PID regulation,
[0058] - Providing a series of relay switches when the sign of the feedback signal changes,
[0059] - Waiting for the convergence of the feedback signal,
[0060] - Measuring the relay period T, the feedback amplitude A, and the relay amplitude d, so as to provide the critical period T u = T and the critical gain
[0061] - Re - establishing the system PID regulation.
[0062] The relay amplitude d can be limited so that the motor speed does not exceed the defined upper limit s h and the lower limit s l .
[0063] The periodic relay with an integration process includes:
[0064] - PID regulation of the bypass system,
[0065] - Applying a series of ramps or relay switches with integration around the final PID output, where the relay turns on for the sign change of the feedback signal,
[0066] - Analyzing the convergence of the feedback signal, and when convergence is achieved, recording the point at the 90° phase of the relay period T, and calculating:
[0067] Input amplitude:
[0068] - Process period at 90° phase: T -90 = T
[0069] - Process gain at 90° phase:
[0070] where A is the peak-to-peak amplitude of the feedback signal, D = 2·d is the peak-to-peak amplitude of the relay signal, and G is the slope of the relay triangular wave; - Re-establishing the system PID regulation.
[0071] If convergence is not achieved within the specified time limit or if the feedback signal exceeds the specified amplitude limit, the step injection, relay method, relay method with integration can be aborted and the PID regulation can be re-established.
[0072] Detecting convergence can include periodically providing measured values of the feedback signal samples and comparing them with the average value based on a dedicated number of samples, comparing the absolute difference between the measured value and the average value, and confirming the achievement of convergence when the absolute difference remains below the defined limit within the specified time period.
[0073] In the case where one of the methods does not reach convergence, the following calculations can be performed to recover the missing elements:
[0074] If (ω -90 ; G -90 and (ω -180 ; G -180 ) are known:
[0075] If G0 is known:
[0076] K = G0
[0077] Otherwise:
[0078]
[0079] Or In case Negative
[0080]
[0081] If (ω -90 ; G -90 ) is known:
[0082] If G0 is known:
[0083] K = G0
[0084] Otherwise:
[0085]
[0086] If (ω -180 ; G -180 ) is known:
[0087] If G0 is known:
[0088] K = G0
[0089] Otherwise:
[0090]
[0091] In the case where one of the three processes proposed does not reach convergence or is missing, these calculations provide a fallback position.
[0092] This sequence can be repeated from time to time during the operating life of the system to adapt the PID parameters to the aging of the system.
[0093] In a particular embodiment, the method may further include selecting a setting between a setting based on the above process and a setting based on the Ziegler - Nichols method, or selecting a setting based on a robust gain that is the minimum proportional gain, the maximum integral time constant, and the minimum derivative time constant.
[0094] T i = max(0.8·T cr ; τ); T d = 0 between the result of the method and the Ziegler Nichols setting.
[0095] This possibility of choosing between different settings providing positive tuning, moderate tuning, and conservative tuning offers the customer the possibility of adapting the PID to specific needs, such as adapting the PID regulation to facilitate rapid filling of a reservoir in the case of flooding, or conversely adapting the PID regulation to limit pressure variations in a water distribution system.
[0096] In this method, once the PID parameters are calculated, the PID regulation is re - established with the calculated parameters. Description of the Drawings
[0097] Other features, details, and advantages will be shown in the following detailed description and the drawings, where:
[0098] Figure 1 A basic closed-loop process with a PID is shown;
[0099] Figure 2 A simplified schematic diagram of the PID bypass implementation is shown;
[0100] Figure 3 are the known periodic relay command input signal and the output signal of the process;
[0101] Figure 4 An input signal with a series of commands of the present invention and the corresponding output signal are shown;
[0102] Figure 5 The input and output curves after a step injection are shown;
[0103] Figure 6 The Nyquist plot of the process is shown;
[0104] Figure 7 A relay with an example of an integrated command is shown;
[0105] Figure 8 An example of a possible simplified flowchart of the implementation of the process of the described method is shown. Detailed Description of the Invention
[0106] In the current design of the control system for a pump in a hydraulic system, the regulation includes a method based on a transfer function, which is a simple PI method. Using this method, based on the estimation of the process as a first-order transfer function, a simple PI tuning rule with a delay can be obtained.
[0107] In a fluid delivery system, according to Figure 1 Approximate PID 10 + process 20. The transfer function of such a process is given below, where U(s) and E(s) represent the Laplace transforms of the command and the error between the process P feedback and the target, respectively.
[0108]
[0109] In a fluid delivery application, the process transfer function can be assimilated to a first-order function with a delay. Therefore, the structure of the process transfer function P(s) becomes:
[0110]
[0111] Three parameters of the transfer function of the process must be identified: K is the static gain, τ is the time constant, and θ is the delay of the process.
[0112] Figure 2 The principle of the tuning method of the present disclosure is shown, where the PID regulation 10 is disconnected from the process 20 and replaced by a specific command module 40, and the specific command module 40 maintains the closed-loop structure between the setpoint and the output of the process;
[0113] As Figure 4 shown, the commands of the PID tuning method used in the present disclosure are a combination of a step injection 1, a periodic relay command 2 (also called the relay method), and a periodic relay integral command 3 (also called the relay method with integral), which will be discussed below. The combination of the step injection 1, the periodic relay command 2, and the periodic relay 3 with integral allows the identification of three points of the process transfer function on the Nyquist curve 34, as Figure 6 in reference to Figure 4 the process in:
[0114] The point 32 at the -180° phase (critical point) is obtained by the relay method 2,
[0115] The point 33 at the -90° phase is obtained by adding an integrator 3 in series after the relay, providing the relay method with integral or the periodic relay with integral,
[0116] The point 31 at the 0° phase corresponds to the process static gain: it is obtained by the step injection 1.
[0117] The need to identify the individual points in the Nyquist curve is that, in the case of only the critical point, only the -90° point, or only the 0° point, and without any process knowledge, infinity of the transfer function can correspond to these points. To approximate the correct transfer function, therefore, at least 2 points are required. However, the accuracy of the estimation may vary with the process and the identified points, and a more precise determination of such a transfer function is necessary. Using the step injection 1, the periodic relay command 2 (also called the relay method), and the periodic relay 3 with integral command, the present disclosure provides a more accurate determination of the transfer function.
[0118] Step injection procedure:
[0119] The role of the step injection 1 is to estimate the process static gain. The process starts with the bypass of the PID command, and a user-defined pump motor speed increase step Δu higher than the last PID output is applied to the input of the process, as Figure 5 shown. The user-defined speed increase step 1 can be reduced to prevent command limit overshoot or prevent exceeding the maximum pump motor speed.
[0120] Then, the process waits for convergence at the output sensor and when convergence is obtained after periodically providing samples of the feedback signal 4ΔY at sensor 30 of Figure 2 and comparing the absolute difference between the samples with the average value of the signal over a dedicated number of samples, convergence is confirmed when the absolute difference remains below a defined limit for a specified period of time.
[0121] When convergence is obtained, the process static gain K is estimated as ΔY / ΔU and the PID control is reconnected.
[0122] Basic relay method procedure:
[0123] Figure 3 The basic relay method shown provides a periodic relay command 2, i.e., a step increase and decrease in the motor speed. The method starts with bypassing the PID command, including applying a first step as a relay switch, and then the relay switch increases and decreases the pump motor speed near the last PID output when there is a sign change in the output signal 5 at sensor 30 of Figure 2 In this process with the input and output curves shown, hysteresis is considered to prevent inappropriate switching due to noise, and a bias is applied to ensure a symmetric shape of the relay (if not, it means the process is non - linear or there is a load disturbance intervention). Figure 3 The relay amplitude 2.d is user - defined but is corrected if it causes command limit overshoot.
[0124] The relay amplitude 2.d is user - defined but is corrected if it causes command limit overshoot.
[0125] The convergence of the relay period and the feedback change amplitude is analyzed and if convergence is obtained, the critical points can be recorded from the relay period T, the feedback amplitude A = 2.a, and the relay gain d:
[0126] Critical period:
[0127] T u = T
[0128] Critical gain:
[0129]
[0130] This procedure will naturally cause the relay to switch at the process critical - point frequency.
[0131] The critical point is then the point where the phase is - 180°: at this phase, the gain of the controlled process must be below 1 to avoid instability: the critical gain corresponds to the maximum proportional gain that can be applied to the process to keep it stable.
[0132] If convergence of the output is not achieved, or in the case of an abnormal non - relay switch, the process is aborted.
[0133] As described, the relay method gives a point at phase = -180° and provides
[0134] Pulses: ω -180
[0135] Gain: G -180 = |P estim (j·ω -180 )|
[0136] At the end of the program, the PID is then reconnected and the next step of the process is activated.
[0137] Relay method with integral program:
[0138] In this method, the PID is disconnected and the motor speed increases and decreases in a ramp as Figure 7 shown.
[0139] The function of this process is to use a relay with an integral method to estimate the process point at -90° phase. This method is based on the relay method but an integrator is added at the relay output.
[0140] This process also bypasses the PID command and applies a series of ramp signals 3 starting from the last PID output. Also in this case, the relay turns on the sign change of the feedback signal 6. Considering hysteresis to prevent inappropriate switching due to noise, the relay amplitude is user-defined but is corrected if it causes command limit overshoot.
[0141] The main difference from the relay method is the integration applied at the relay output. If the command limit of the motor is reached, the integration stops. Similarly Figure 7 the slope is the gain G of the relay method.
[0142] Analyze the convergence of the relay period and the amplitude of the feedback change, and if this convergence is reached, the point at phase -90° can be recorded considering the relay period T, the relay gain G, and the feedback amplitude A:
[0143] Input amplitude:
[0144] Process period at -90° phase: T -90 = T
[0145] Process gain at -90° phase:
[0146] Here, if the convergence is not achieved, the process is aborted.
[0147] At the end of this process, the PID is then reconnected and the next step of the process is activated.
[0148] Relay with integration method provides:
[0149] Pulse: ω -90
[0150] Gain: G -90 = |P estim (j·ω -90 )|
[0151] Return to Figure 1 , the global closed-loop transfer function is defined by the following formula:
[0152]
[0153] And the desired closed-loop global function specification is:
[0154]
[0155] where λ is the global time constant of the system in the closed loop.
[0156] This means:
[0157]
[0158] Then, based on the parameters (K, τ, θ) of the process transfer function, that is, its poles, zeros and transmission delays already identified by the above three-step process, we can identify the parameters of the PID controller as:
[0159]
[0160] In fluid applications (such as processes dealing with gases or liquids), the derivative term is set to 0 because the relevant process is slow and does not require a derivative correction term. Depending on the customer's requirements, tune the parameter for the global time constant λ:
[0161] λ = α·max(τ, θ)
[0162] where α can be configured between [0.1 to 2] according to customer requirements, for example, according to the known name:
[0163] α＝0.5 Positive tuning α＝1 Moderate tuning α＝2 Conservative tuning
[0164] As described above, based on the periodic relay command, Ziegler-Nichols proposed the PID setting:
[0165]
[0166] It is also possible to select the setting corresponding to the most robust setting between the settings based on the proposed process estimation with step injection, periodic relay commands, and periodic relay commands with integration and the setting based only on Ziegler Nichols: the minimum proportional gain, the maximum integral time constant, and the minimum derivative time constant. This allows for a process response that is always a first-order transfer function without any overshoot to avoid oscillations in the system.
[0167] Then, the customer selects between the different settings according to the process response he wants to have in his system according to the application:
[0168] A - Setting based on the Ziegler Nichols method:
[0169] K p = 0.4·K cr ; T i = 0.8·T cr ; T d = 0
[0170] where K cr and K cr are the critical gain and period determined in the relay-based method.
[0171] This method provides a fast process response with some oscillations such as overshoot and damping.
[0172] B - Setting based on the disclosed method, which provides transfer function identification with relay method, relay + integrator, and step injection:
[0173]
[0174] where (K, τ, θ) are the transfer function parameters identified from the process. This allows for different process responses: positive, moderate, and conservative, without oscillations except for a small overshoot with conservative tuning. The process will behave as a first-order transfer function with a delay, and the response time will depend on the tuning selection.
[0175] C - Setting based on the most robust gains (minimum proportional gain, maximum integral time constant, and minimum derivative time constant)
[0176] T i = max(0.8·T cr ; τ); T d = 0
[0177] The three - process cycle relay method, the integral - cycle relay method, the step - injection method, and the Ziegler - Nichols method are proposed. These last settings provide a robust process response without any oscillation and overshoot.
[0178] A possible software implementation of the method can be based on Figure 8 the flowchart. Such software can be integrated into a process - control device or a motor - control device that already contains PID - control software.
[0179] The method starts by bypassing the PID at 100, then completing a noise - detection process 110 with a first convergence - detection process 120, which may lead to the end of the process, and if convergence cannot be obtained, directly re - establishing the PID 240. After noise detection, the three methods disclosed above can be initiated. In the presented diagram, the method follows a static - gain estimation with a step - injection process 130, waits for convergence 140, and if convergence cannot be obtained, exits, then generates a flag 145.
[0180] The second process, i.e., the relay 150 to obtain the critical point, follows the step - injection and also includes a convergence - detection 160, which stops the relay and generates a flag 165 if convergence cannot be obtained.
[0181] The third process is a relay with an integrator 170 to obtain the point on the Nyquist curve with a 90° phase, which also has its convergence - detection step 180, which generates a third flag 185 if not obtained.
[0182] It should be noted that the tree - like process can be implemented in a different order, for example, the step - integration is in the last position and the relay with an integrator is in the first position.
[0183] When the process is completed, the calculation of the optimal tuning parameters 190 is completed to provide PID tuning 200 and the PID is re - established 240 with the updated parameters.
[0184] If a process does not converge at the gate 210, the missing - element recovery calculation is completed at 220, and if recovery is possible at 230, the recovered data is transmitted to the optimal - tuning - parameter step 190, otherwise the PID is re - established unchanged.
[0185] Industrial applicability
[0186] The technical solution proposed here can be used to tune hydraulic processes, such as water or gas distribution with regulated pressure or regulated flow.
[0187] The present disclosure is not limited to the above description and, in particular, as already said, the three process steps injection, periodic relay command and periodic relay command with integration can be implemented in any order.
Claims
1. A method for calculating PID parameters of a fluid system, the fluid system comprising a motor driving a pump, a compressor or a fan, the fluid system also comprising a feedback sensor providing a feedback signal on the system and a PID regulation controlling the speed of the motor, wherein the method comprises: -After an initial approximation of the fluid system by a first-order transfer function with a delayed form, Among them, the three parameters of the transfer function of the process to be identified are: -K static gain, -θ delay, -τ time constant, - One or more sequences of: a-Bypass PID regulation and implement the following process: - a periodic relay process that provides the first point (ω) at a phase of -180° called the critical point -180 ; G -180 ), - a periodic relay with an integration process, providing a second point at a phase of -90° (ω -90 ; G -90 ), - a step injection providing a third point G0 at ω = 0° phase and zero frequency, b- Solve the relevant equations in the system of equations: G0=K cos(ω -90 ·i)-ω -90 ·τ·sin(ω -90 ·θ)=0 sin(ω -180 ·i)-ω -180 ·τ·cos(ω -180 ·θ)=0 The following available transfer function parameters are calculated from the points obtained by the described procedure: K=G0 c- Apply the obtained transfer function parameters to calculate the PID parameters for system regulation:
2. The method of claim 1, wherein Td is approximately zero because the differential term is not necessary during fluid application.
3. The method according to claim 1 or 2, wherein the estimated transfer function P estim(S) Starting with the calculation of the parameters, and taking into account the gain of the pulse ω is done by the following formula: And the phase of the pulse ω is completed by the following formula: And according to the said process implemented: a-Through step injection, calculate the gain G0. The step injection gives the point at which the frequency and phase are zero; b-Through the periodic relay, calculate the pulse: ω -180 And gain: G -180 =|P estim (j·ω -180 )|Calculate the point at which phase = -180°; c- Calculate the pulse by periodic relay with integration: ω -90 And gain: G -90 =|P estim (j·ω -90 )|Calculate the point where phase = -90°.
4. The method of any one of the preceding claims, wherein step injection command comprises bypassing the system PID regulation, inputting a step with amplitude Δu to the current speed command of the motor, waiting for process feedback to converge, measuring the feedback signal value Δv, calculating a static gain K as Δv / Δu, and then re-establishing the system PID regulation.
5. The method according to claim 4, wherein the step amplitude Δu is limited so as not to exceed an upper limit s of the motor speed. h .
6. The method according to any one of the preceding claims, wherein the periodic relay process comprises: -Bypass system PID adjustment, - provide a series of relay switching when the sign of the feedback signal changes, - Wait for the feedback signal to converge, -Measure the relay period T, feedback amplitude A and relay amplitude d, thus providing the critical period T u =T and critical gain - Re-establish system PID regulation.
7. The method according to claim 6, wherein the relay amplitude d is limited so that the motor speed does not exceed a defined upper limit s h and the lower limit s l .
8. The method according to any one of the preceding claims, wherein the periodic relaying with an integration process comprises: -Bypass system PID adjustment, - Apply a series of ramps or relay switching with integration around the last PID output, where the relay switches on the sign change of the feedback signal, - Analyze the convergence of the feedback signal, and when convergence is achieved, record the point at the 90° phase of the relay period T, and calculate: ○ Input amplitude: ○Process period at -90° phase: T -90 =T ○Process gain at -90° phase: Where A is the peak-to-peak amplitude of the feedback signal, D = 2·d is the peak-to-peak amplitude of the relay signal, and G is the slope of the relay triangle wave; - re-establish the system PID regulation.
9. A method according to any one of claims 4 to 8, wherein detecting convergence comprises periodically providing a metric of feedback signal samples, and comparing the metric with an average value of the metric based on a dedicated number of samples, comparing the absolute difference between the metric and the average value, and confirming the achievement of convergence when the absolute difference remains below a defined limit for a specified time period.
10. The method of claim 9, wherein if convergence is not achieved within a specified time limit or if the feedback signal exceeds a specified amplitude limit, any one of the step injection method, the relay method, the relay method with integration is aborted and the PID regulation is reestablished.
11. The method of claim 10, wherein in the case where convergence of one of the relay process, the relay process with integration, or the step injection process is not achieved, recovery of the missing elements is accomplished by the following calculation: -If (ω -90 ; G -90 and (ω -180 ; G -180 ) is known: ○If G0 is known: K=G0 Otherwise: ■ ■Or In case Negative ○ ○ -If (ω -90 ; G -90 ) is known: ○If G0 is known: K=G0 Otherwise: ■ ○ ○ -If (τ -180 ; G -180 ) is known: ○If G0 is known: K=G0 Otherwise: ■ ○ ○ 12. A method according to any one of the preceding claims, wherein the sequence is repeated from time to time during the operational life of the system to calculate PID parameters adapted to the ageing of the system.
13. A method for calculating PID parameters for a fluid system, the fluid system comprising a motor driving a pump, compressor or fan, the fluid system further comprising a feedback sensor on the system to provide PID regulation to control the speed of the motor, the method comprising selecting a setting between a setting based on a method according to any one of the preceding claims and a setting based on a Ziegler Nichols method or selecting a setting based on robust gains, the robust gains being a minimum proportional gain, a maximum integral time constant and a minimum derivative time constant Between the method according to any of the preceding claims and the Ziegler Nichols method.
14. A method for tuning a PID regulation process, comprising calculating PID parameters using a method according to any one of the preceding claims and re-establishing the PID regulation using the calculated parameters.