GB2353608A  Tuning a process control loop  Google Patents
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 GB2353608A GB2353608A GB0020529A GB0020529A GB2353608A GB 2353608 A GB2353608 A GB 2353608A GB 0020529 A GB0020529 A GB 0020529A GB 0020529 A GB0020529 A GB 0020529A GB 2353608 A GB2353608 A GB 2353608A
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 G05—CONTROLLING; REGULATING
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 G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
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 G05B13/0265—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric the criterion being a learning criterion
 G05B13/0285—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric the criterion being a learning criterion using neural networks and fuzzy logic
Abstract
Description
2353608 CONTROL LOOP AUTOTUNER WITIf NONLINEAR TUNING RULES ESTEVIATORS
The present invention relates to a system and method for tuning a process controller using nonlinear tunina rules estimators including neural networks and fuzzy 10 logic.
A Proportional, Integral, Derivative (PID) controller is a common controller used in industrial processes, including computercontrolled industrial processes. Such C PID controllers and their variations and combinations, such as P, P1, PD, have enjoyed widespread application in the control of industrial processes. Typical industrial processes are controlled by one or more feedback loops incorporatina PID controllers.
A fuzzy logic controller (FLQ is also a known process controller used to control process parameters by maintaining process variables within parameters related to desired set point values. FLCs are nonlinear controllers and are becoming more widely used in industrial environments.
One type of known method for parameter tuning of a PID controller is the ZieglerNichols method. Relayoscillation autotuning is also a wellknown and recognized tuning technique. Relayoscillation tuning identifies the Ultimate Gain and g Ultimate Period of a process. PID controller settings can be determined from these parameters using ZieglerNichols rules and modifications. An extension of the relayoscillation tuning technique that goes beyond identifying the Ultimate Gain and Ultimate Period is provided in "System and Method for Automatically Tuning a Process Controller", U.S. Pat. No. 5,453,925, September 1995, to Wilhelm K.
Wojsznis and Terrance L. Blevins, (hereinafter Wojsznis), which is incorporated herein in its entirety.
In recent years, significant progress has been made with model based tuning, in particular with Internal Model Control (IMQ and Lambda tuning. Both approaches result in a first order closed loop response to setpoint changes. A tuning parameter relating to the speed of response is used to vary the tradeoff between perfonnance and robustness. Both methods adjust the PID controller reset (or reset and rate) to cancel the process pole(s) and adjust the controller Gain to achieve the desired closed loop response. IMC and Lambda tuning have become popular because oscillation and overshoot are avoided and control performance can be specified in an intuitive way through the closed loop time constant.
One of the limitations of model based tuning is the need for process model identification. An equivalent firstorder plus Dead Time process model with parameters of Static Gain, Apparent Dead Time, and Apparent Time Constant is usually identified for selfregulating processes. For integrating processes, model parameters of Process Integral Gain and Dead Time are determined. Model identification is typically made by an open loop step test. Compared to the relayoscillation method, open loop methods are not easy to automate. With open loop methods, human intervention is often required to assure an accurate model due to nonlinearities in the process, valve hysteresis, and load disturbances. A different technique is required for selfregulating and integrating processes.
What is needed is a system and method for tuning in a relay oscillation environment that provides necessary PID tuning parameters over all ranges of model parameters and identifies model parameters of a process.
According to the present invention, we provide a system for tuning a process control loop, the system comprising a tuner module for receiving an error si nal t> 9 representative of a difference between a set point and a process variable to generate a first process control signal for controlling the process, a nonlinear module for applying a nonlinear procedure to generate at least one parameter signal, a controller module for receiving the error signal and the at least one parameter signal from the nonlinear module, the controller module generating a second process control signal for controlling the process, and switching means coupled to the process for coupling one of the tuner module and the controller module to the process to select the appropriate process control signal for controlling the process.
1 The system provided uses nonlinear approaches in the nonlinear module to approximate the desired controller tuning parameters. The nonlinear approaches include neural retww! tuning, fuzzy logic tuning and nonlinear functions, including sigmoid tuning.
A system al ' so provides that the nonlinear module use nonlinear approaches to approximate the desired process model parameters. According to an embodiment of the resent invention, process model identification is obtained using neural networks, p ZP fuzzy logic and nonlinear functions, including signioid tuning which beneficially give better model parameters than prior known analytical formulas for relayoscillation identification.
The present invention may be better understood, and its numerous objects, features, and advantages made apparent to those skilled in the art by referencing e g th accompanying drawings.
0 FIG. I A is a block diagram schematic of a relayosc illation tuning system in accordance with the present invention.
FIG. IB is tuning plot according to an embodiment of the present invention.
FIG. I C is a graph showing Nonlinear Coefficient Functions for Computing Controller Integral Time and Gain.
FIG. 2 is a graph showing tuning and step responses for the process with LIT 0 17 0.2 and Loop Scan = I sec.
FIG. 3 is a graph showing tuning and step responses for the pocess with UT 0 C7 0.5, Loop Scan = A sec.
FIG. 4 is a graph showing tuning and step responses for the process with LIT 0.7, Loop Scan = A sec.
FIG. 5 is a graph showina tuning and step responses for the process with 1JT 0 0.7, Loop Scan =.1 sec, with a fast response.
I FIG. 6 is a diagram showing a neural network assisted tuner.
FIG. 7 is a flow diagram showing the steps necessary for developing the neural network in accordance with an embodiment of the present invention.
FIG. 8 is a graph showing the results predicted by Neural Network vs.
Actual/Required Integral Time using the method according to an embodiment of the 4=1 17 present invention.
FIG. 9 is a gfaph showing the results predicted by Neural Network Model 4.7 Integral Time  Actual/Required Integral Time using the method according to an embodiment of the present invention.
FIG. 10 is a graph of the results predicted by Neural Network Model for the Subrange of Tj Values 15 to 33 according to an embodiment of the present invention.
FIG. 11 is a graph of input membership functions within an embodiment of the present invention.
The use of the same reference symbols in different drawings indicates similar or identical items.
Referring to Figure I A, a schematic block diagram of a relayoscillation tuner system 100 is presented that maybe controlled in accordance with new nonlinear approaches. Process 190 may include any controllable process. An output signal, shown as process variable (PV) 130 is provided by process 190 and added to summer where PV is compared to a set point (SP) I 10. The difference between PV and SP is used to determine to relayoscillation tuner system 100 provides the Ultimate Gain K,, and Ultimate Period T,, for a process. As shown, relay oscillation tuner system 100 includes a summer 120, a relay 150, and tuning rules 160. The set point 0 (SP) I 10 is provided to summer 120, together with process variable (PV) 130.
Summer 120 subtracts PV from SP, providing the result to relay 150, tuning rules 160 0 I= and controller 170. Tuning of the process takes place either automatically or under user control. Tuning of the process 190 optionally may include an automatic 0 controlled selfoscillation tuning procedure such as the procedure described in 0 Wojsznis. The selfoscillation procedure includes controlling switch 180 to either couple the output of controller 170 to process 190 or couple the output of the relay to the process 190. In one embodiment, relay 150 performs the self oscillation procedure with tuning rules 160 controlling switch 180. Switch 180 either couples controller 140 to process 190 or couples tuning rules 160 and relay 150 to process 190. The procedure is an oscillating procedure that determines a time delay, Ultimate Gain and Ultimate Period.
An Apparent Dead Time Td is determined at tuning initialization. The Apparent Dead Time Td is determined by applying a tangent from the slope of the process output PV 130 during tuning initialization. The tangent is extrapolated to intercept the set point SP or mean value line of the process output before tuning. The time between the initial relay step and this intercept is the apparent Dead Time. Other methods for determining Td are also within the scope of the present invention. Such other methods include those provided in Wojsznis.
Figure I B represents a graph of the process input and process output signals during parts of the oscillation procedure. The time duration between time tl (10) switching of the relay 150 and the time 2 (20) at which the process output reaches the maximum approximates the Dead Time. The Dead Time is otherwise computed as a difference between the time of ISPPV1 increment and the time of iSPPV1 decrement.
The evaluation time with this approach takes one or more Ultimate Periods (Tu). The apparent Dead Time may be calculated as the average of the two or three results.
The Dead Time, Ultimate Gain, and Ultimate Period are sufficient to calculate a firstorder plus Dead Time process model. The equations (1) and (2) for calculating first order plus Dead Time are:
T, tan(;r 2 , T, 2 ir T.
K 1 1 41r 2T,2 (2 K cl+ where Tc = process time constant T, = ultimate period Td = process apparent Dead Time K, = process static gain K,, = ultimate gain The process time constant in equation (1) is expressed by a tangent function which gives a good approximation for the arguments less than 1r13 when the Dead Time is relatively large in relation to the time constant. For processes with 1 1 insignificant Dead Time a large error results in the time constant computation, even. fora small error in Dead Time identification (Tangent argument is close to X12,and small error in argument gives a large error in tangent value). Some improvement is achieved by using a linear function shown in equation (3) for the arguments greater 5 than z 13:
T, = T' (tan Ir + 2 ( ir 2 xT, Ir (3) 2 x 3 T 3 ZieglerNichols (ZN) Rules for PID Controller Tuning Relayoscillation tuning naturally matches ZN rules and provides the Ultimate Gain K,, and Ultimate Period n. The original ZN formulas for P1 controller are 10 provided by the following formulas:
K= 0.4K,, and Ti = 0. 8 T,, These formulas give a Phase margin that varies greatly from about 20 degrees to 90 15 degrees, depending on the ratio r of the Process Dead Time L to the Process Time 1 Constant T. Consequently, performance varies greatly from an extremely oscillatory response for a process with a ratio close to 0. 1 to an extremely sluggish response for a CO process with a ratio close to 1.0.
A PID controller tuned with the original ZN rules, K = 0.6K,,, Ti = 0.5 n, and Td = 0. 125 n experiences similar behavior. Various modifications of the original formula have been proposed to address the problem. One tendency is to make Gain smaller and Integral 25 Time shorter, according to the formulas:
2 K = 0.4K,,, Ti = Y3 T,,, and Td Y1 ' The above modification improves performance for loops withr close to 3, but loops with small values of T become even more oscillatory.
Other more flexible formulas (4), (5) and (6) provide for the Phase/Gain 30 margin design:
T T = ' (tan 0 + %F4a + tan (4) 9 4jra T.f =a ri (5) K = K.cosO/ (6) IG.
where:
a is the design selection of the ratio Td:Ti with the default value 0. 15.
Q, is the desired Gain margin with the default value 2.0.
0 is the Phase margin.
K, Td, and Ti are the controller parameters.
With a specified Phase and Gain margin, the formula (7) provides constant coefficients to compute Ti, Td and K from T,, and K, A typical design of 0 = 45 0 gives 10 the following coefficients:
K = 0.38K,, Ti = 1.2n, and Td = 0. 18 T,, (7) This design is suitable for small c, but gives an extremely sluggish response for.r higher than.2.
Assuming the Phase margin 0 = 330 and Gain marin = 3.0 results in the following C1 coefficients for formula (8):
K = 0.27K, Ti = 0.87T,,, and Td = 0. 13 T,,; (8) These coefficients are suitable to design for a narrow range c in the neighborhood of.25.
A further known modification includes defining controller parameters as 0 functions of normalized Dead Time L or normalized GainK = where K.
L+T 1K p K, is Process Static Gain. However, the above approach uses both Dead Time and Time Constant, or the Static Gain of the process. Therefore, it cannot be used directly with relayoscillation tuning 1.
Nonlinear Tuning Rules Estimators In developing tuning rules estimators, certain assumptions and considerationsare be taken into account. First, all input parameters are obtained during the relayoscillation test (that is, the Ultimate Gain, Ultimate Period and Dead Time). Second, the major deficiency of Ziegler Nichols rule is an inadequate controller Integral Time for processes with small Dead Time and excessive Integral Time for processes with a significant Dead Time. Third, tuning rules should give controller tuning parameters and responses close to model based tuning (IMC or Lambda).
The relayoscillation tuning test illustrated in Figures I A and IB and described in the corresponding discussion, provides for the Ultimate Gain K,, and Ultimate Period T,,. To overcome the deficiencies of ZN rules, nonlinear estimators have been found to be an improvement in defining, tuning parameters.
A sigmoid expression provides a smooth transition between two different values, and is used for developing nonlinear estimator. The following formulas satisfy the above requirements:
Ti =fl(T,,,L)T,,;K =f2(T,,)K,,; Td = dl Ti; (9) fl(T, L) = al + bl (10) 1 + exp  T1. cl / d 2 L L f2 (7, L) = a2 + (b2  f I(T., L))k2 where al, a2, bl, b2, cl, c2 are heuristic coefficients and al is in the ranae 0.3 to 0.4 0 a2 is in the range 0.25 to 0.4 bl =0.6, b2 =1.0, cl =7.0, c2 _=4.0, dl =0.125, d2 =1.0 Formula (10) gives the value of the coefficient used for the Ti computation, which varies from a minimal value of a 1 to a maximum value of a 1 + bl. as shown in Figure 1 C. Formula (11) provides an adjustment of the coefficient for K computation 25 in the rancre 1 a2+(b2  a 1  b 1), a2+(b2  a 1)].
This approach results in significantly improved tuning responses, which are 1 close to the IMC or Lambda tuning (rather than to the ZN quarter amplitude decay). Some typical step responses for various UT are shown in Figures 2 through 6. An example of loop tuning and loop step response for a secondorder process with Gain 1, T 1 = 10 sec, T2 = 3 sec, L = 2 sec is shown in Figure 2.
Relayoscillation tuner system 100 produced the following controller settings: K= 1.65, Ti = 12.36, and Td = 1.97, as compared with the IMC calculations: K= 1.0, Tj = 12.5, and Td = 1.97. Figure 3 shows a graph L increased up to 5 sec. and Figure 4 shows an L increased up to or 8 sec.. In both Figure 3 and in Figure 4, step 5responses are similar to model based tuning, although integral action is somewhat weaker than needed for IMC response (tuner gave Te = 15.7 and 18.3 7 as compz.ed with 14.0 and 15.5, according to IN4C calculations).
P A tuner design according to the new nonlinear approaches according to the present invention allows the user to make adjustments to tuning performance by selecting Slow, Normal, and Fast response selections. For example, Figure 5 shows the loop step response for process LJT = 0.7 with Fast selection. Using the speed selection increases the general flexibility of the design by better fitting the tuning response to specific conditions and requirements. One of ordinary skill in the art would appreciate that a DeltaV TIM system manufactured by FisherRosemount Systems, Inc. implemented in a Windows NT application program or other appropriate program is capable of implementing the new adjustable response selections.
Referring now to Figure 6, a relayoscillation tuner block schematic is shown that optionally uses the new nonlinear approaches in accordance with an embodiment of the invention. The shown control loop system can include both nonlinear tuning z and nonlinear process modeling techniques. Optionally, the system can include linear tunin and nonlinear process modeling techniques or nonlinear tuning and linear I process modeling techniques.
As shown in the embodiment of Figure 6.. process 630 is coupled via a switch 670 to either a relayoscillation tuner 600 or controller 610. The controller 610 is further coupled via a second switch 690 to receive either a first parameter sig a 651 gn I from the controller design 650, or a second parameter signal 641 output from analytical controller desio gn 620 and process model 640. The controller 6 10 provides an output when switchably coupled to process 6')0. Each of relay oscillation tuner 600, process model 640, controller design 650, controller 6 10, process 630 and the analytical controller design 620 may be implemented as software modules, hardware, or a combination of both.
As will be described later, the switch 670 is set to the appropriate process control signal for controlling process 630. Relayoscillation tuner 600 is also coupled to provide signals to nonlinear module 660, which includes process model 640 and controller design 650. Both the controller design 650 and process model 640 use neural networks, fuzzy logic, nonlinear function or other nonlinear or linear techniques further described below. Relayoscillation tuner 600 and controller 610 receive an error signal 680 representative of the difference between a set point and a process variable and generates a first process control signal for controlling the process 630. Relayoscillation tuner 600 also provides signals to nonlinear module 660.
The first parameter signal and the second parameter signal are coupled to controller 610 via switch 690. The output from the process model 640 is shown coupled to analytical controller design 620. Parameter signal 641 includes process model parameters included in parameter signal 642 calculated using nonlinear techniques in process model module 640. In a preferred embodiment, parameter signal 641 further includes controller parameters calculated in analytical controller design 620 using the process model parameters determined in process model module 640 and output in signal 642. One of ordinary skill in the art will appreciate that controller parameters may be generated from process model parameters. Accordingly, analytical controller design 620 optionally applies linear techniques to determine the controller parameters.
Parameter signal 651 output from controller design 650 includes controller parameters calculated using nonlinear techniques. Switch 690 coupled to controller 610 provides an option to choose (1) the controller parameters calculated in analytical controller design 620 along with the process model parameters generated using nonlinear techniques in process model 640; or (2) the controller parameters calculated usincy nonlinear techniques in controller design 650.
Alternatively, in one embodiment, analytical controller design 620 is removed from the system implementation. With analytical controller design 620 removed, switch 690 may be coupled to both parameter signal 651 and to parameter signal 642.
Accordingly, in this embodiment, switch 690 is unnecessary. Thus, controller 610 receives both the controller parameters in parameter signal 651 and the process model parameters in parameter signal 642. Both parameter signal 651 and parameter signal 642 are generated in nonlinear module 660 using nonlinear techniques, such as neural networks, fuzzy logic, nonlinear function or other nonlinear or linear techniques described below.
Neural Network Assisted Tunin Referring to Figure 6, controller design 650, controller parameters are determined optionally using a neural network modeling approach. Such a neural network modeling approach improves fitting of three PD) controller parameters over a wide range of model parameter changes. Neural network control schemes are generally divided into two broad categories. One approach is to replace a controller using a neural network. The neural network is trained by mimicking, a controller oi: a human expert. The approach uses a separate training for every loop, and thus is not a good candidate for tuner design, which calls for tuning results in a simple and standard tuning, pr6cedure. An alternative approach uses neural network as an aid for modeling, control law implementation, or supervisory action. A specific tuner design is shown in Figure 6. The tuner optionally uses neural networks or other nonlinear techniques described below to compute the process model and PID controller parameters.
Similar to the selfosc illation procedure described relative to Figure 1, the tuner design of Figure 6 also employs a selfoscillation procedure. The self oscillation procedure includes controlling switch 670 to either couple the output of controller 6 10 to process 630 or couple the output of the relay oscillation tuner 600 to theprocess630. According to one embodiment. controller 610 receives controller parameters from either controller design 650 or analytical controller design 620 via switch 690. In this embodiments analytical controller design 620 receives process model identification parameters from process model 640. In another embodiment, analytical controller design 620 is removed from the process control loop.
Accordingly, controller 6 10 receives process model identification parameters from process model 640 and controller parameters ftom analytical controller design 620.
Switch 670 either couples controller 6 10 to process 6_3 30 or couples relayoscillation tuner 600 to process 630. Controller design 650 employs nonlinear techniques to determine controller parameters. One technique described below includes using neural networks.
The procedure of developing neural networks techniques involves several basic steps, shown in Figure 7. Figure 7 is a flow diagram demonstrating the neural network steps. Step 700 shows the first step, developing simulated control loop configurations anticipating future tuner use. Normally, either a second order or third order plus Dead Time process model is used. Step 7 10 specifies an assumed ranc ge of 0 model parameter changes. Step 720 specifies that a developer compute the PID 35 controller settings for every set of model parameters using LMC rules, Lambda tuning D CI or any other preferred controller design. Step 730 provides that a developer run the autotuner for the same sets of model parameters and record tuning results  T,,, K,  and L. Step 740 provides that a developer verify the performance of the control loop with computed parameters, adjusting parameters as needed. Step 750 provides that a developer train the neural network usina simulation tuning results as neural network 0 inputs and model parameters and controller parameters as neural network outputs. Step 760 provides that the developer implzment the trained neural network into the tuner.
The neural network described above relative to Figure 6 and described in Figure 7 can be any type (Sigmoid or Radial Basis functions). In one embodiment of the present invention, neural network is used with the neuron's transfer function given by:
0U.  1 + as the neuron input. In is a weighted sum of external inputs.
In vIn, The neural network is selectively applied with multiple outputs (outputs K and Ti for the controller neural network and Kp and T for the model neural network) or several single output neural networks. The advantage of using a single output neural P network is faster training. Therefore, one embodiment implements a single output 1  neural network. In an illustrative tuner design, the following neural network inputs and outputs are defined:
Inputs: n, K,,, L, Noise Level, Relay Hysteresis, and Scan Rate.
K,, L, and Noise Level are defined during tuning test.
Z> 0 Relay Hysteresis and Scan Rate are tuner parameters.
Outputs: K, Ti, Td, 4 and T.
K, Ti, and Td constitute PID controller parameters.
K. and Tjointly with L are firstorder plus Dead Time process model parameters.
Implementation Issues and Test Results 12 In one example of the new nonlinear methods, neural network models are 'implemented to enhance the relayoscillation Autotuner in a scalable industrial control system. The Autotuner includes two parts: the tuner function block, which is implemented in the controller, and the tuner application. The tuner application is implemented in a Windows NT console or other appropriate console. Neural network models are added to the tuner application. In one embodiment, the neural network models are transparent to the tuner user with the Autotuner having no selections or Z settings associated with neural networks.
According to the method described herein, the neural network is trained for the secondorder plus Dead Time process model. The specification below defines available input and output datt for training neural network models:
Process Neural Network model:
Inputs: Ultimate Gain K., Ultimate Period T,,, and Dead Time L defined during the relay tuning experiment.
Outputs: Process Gain 0.5, 1.0, 1.5; Process Time Constant I in sec., 1.0, 2.0, 5.0, 10.0, 20.0, 50.0, 100.0, 200.0; Process Time Constant 2 in sec., 1.0, 2.0, 5.0, 10.0; Dead Time in sec., 1.0, 2.0, 5.0, 10.0, 20.0, 50.0, 100. 0, 200. 0.
Controller Neural Network model:
Inputs: Same as for Process Neural Network model.
Outputs: PID Controller Gain K, Integral Time Ti, and Derivative Time Td computed from process model parameters for thle outputs, criven above, i. e., Process 117 Gain 0.5, 1.0, 1.5; Process Time Constant I in s.c., 1.0, 2.0, 5.0, 10.0, 20.0, 50.0, 100.0, 200.0; Process Time Constant 2 in sec., 1.0, 2.0, 5.0, 1 0.0;'Dead Time in sec., 1.0, 2.0, 5.0, 10.0, 20.0, 50.0, 100.0, 200.0.
Experimental Testin:
An experimental simulation tuning test was run 142 times, which is approximately the minimum number of samples suitable for training a simple neural network according, to those skilled in the art. The samples gave a good correlation coefficient and, in general, close values of the predicted output to the required output.
The graphs of the results for T, are given in Figures 8 and 9.
In some intervals of the predicted parameters range, the prediction error was unacceptable. There are two specific cases of this effect. One case involves small values of predicted controller parameters (relative to prediction error). In this case, predicted parameter error even as small as 1% of the maximurn value gives unacceptable parameters. In particular, referring ur to Fig e 8, when the actual value is close to the prediction error, Tj can be zero or c,,cn negative.
Another error situation occurs when few samples are included in the subrange. For example, whena user wants to extend the range of neural network modeling by making only a few simulations for an extended subrange, such as Tj > 50.0 in Figure "P :1 Z Z 8, an error could occur.
Neural Network Tuning Rules:
To prevent anomalies, according to the illustrative nonlinear techniques, the I neural network tuning, models uses the following steps/rules. First, collect as many samples as possible. Collect at least the minimum number of samples required for a simple model. Second, select the range for the predicted parameter so that a parameter value within range changes not more than a few times, (about five). If predicted values change more thana few times (about 15), split the range of parameter chanc,es on several subranaes and develop several neural network models. Third, give I= special attention to small predicted values. If predicted values are comparable in size 20 to prediction error, make a separate neural network model for the small values.
For example, a model was developed with a narrowed subrange of Tj values I from 15 to 33 (instead of I to 320 in the fall range). Despite fewer than the minimum number of samples, the prediction was much better than attained by the original model for the whole range. A gaph of the neural network model prediction for the subrange of Tj is given in Figure 10. The prediction error relative to LMC parameters is below 5%, while an error of the nonlinear function estimator for the test cases L/T >.5 exceeds 12.0%.
Linear and Nonlinear Corrective Functions for Process Model Identification Referring back to Figure 6 in combination vvith formulas (1) and (3) (reproduced below), the use of linear and nonlinear corrective functions for process model identification is described. As described above, process model 640 provides process model parameters optionally using linear or linear corrective functions. The techniques described below apply linear, nonlinear function, neural networks and 14 fuzzy logic as corrective functions for process model identification performed in process model 640.
The process time constant (Tc ) produced by formulas (1) and (3) are significantly shorter for smaller process apparent Dead Time to ultimate gain ratios (Id) and an excessive process time constant (Tj for process apparent Dead Time to T.
ultimate period ratios ( Td) bigger than.25 as shown in Table' I and 2. T.
T = 7. tan( Jr _ 2 jr T, 2;r T.
T, = T. (tan 'T + 2 (z 2 ir T, jr (3) 2 x 3 T. 3 A corrective function f(T.lTd) applied to the identified process time constant, Tc (corrected) = T, (identified)f (T,, / T,,) should have f (T,, / Td) values above I for small Td and less than 1 for T.
Td bigger than.25. T.
A simple linear function with coefficients developed from simulated tests corrects for the process time constant according to equation (12):
T,(correcled) = T, 0.4 4.8 +1.05 (12) T, For a nonlinear function, a sigpoid expression provides a smooth transition between two different values. Sim , oid corrective function is reasonably well defined by knowing minimum and maximum values. The following formulae (13) for process time constant estimate was developed based on a small set of simulated data:
Is T,(corrected) = T, 0.8 + 0.4 1.0 (13) I+ exp (TIL  4.6)/ 0.2 1 + exp (T L  6 0) 10.3 Formula 12 gives the value of the coefficient ,,17)ed for T , computation, which varies from a minimal value of.8 to a maximum value of 2.2. After correcting, time 5 constant, process static gain is recomputed using formula (2), reproduced below:
I V, + 4 z 2 T' K, T. 2 (2) Tuning and calculation results for the process with static gain 1.0 are compiled in Table 1, and with static gain 0.5 in the Table 2. In both cases, the process is modeled as a second order with T1=10sec, T2=2sec plus dead time shown in column Td.
Identifier approximated the model by a first order plus dead time model (Td identified). Model parameters shown are initially identified (Td, Kp, and Tc) and corrected by using linear and nonlinear estimating formulas (Kp and Tc) 4D timare Ultirnate Td Td Tc Kp Tc Kp Tc Kp Gain Period In identif identif identif Corr Corr Corr Corr model linear linear sicrmoid sigmoid funct funct funct Rinct 7.812 9.55 1 1.24 4.921.434 9.374.799 10.42.887 5.65 13.4 2 2.2 6.77.589 9.728.826 10.57.895 3.7 19.85 4 4.2 9.7.879 10.65.949 8.92.809 2.85 25.5 6 6.2 12.28 1.11 10.35.960 10.38 12J 963 2.08 35.5[ 10 10.0 14.4 1 1.319 972.956 11.9 1.1 1 Table 1. Process model identification results for the model with Kú7 Ultimate Ultimate Td Td T Kp Tc Kp Tc Kp Gain Period In identif identif identif Corr Corr Corr Corr model linear linear siggrnoid sigmoid funct funct funct funct 12.84 9.75 1 1.142 5.064.266 10.99.5 5 10.95.55 8.78 13.4 2 1.838 6.879.384 12.36.66 14.34.77 6.43 19.9 4 3.53 10.0.514 12.99.65 11.69.59 5.24 25.45 6 5.748 12.388.614 11.59.57 10.68.53 3.96 10 9.73515.315.725 10.8 12.70.61 Table 2. Process model identi Lication results for the model with Kp = 0.
Application of both corrective functions significantly improved process model identification.
Fuzzy Logic Assisted Identification A typical Fuzzy Logic Controller is a type of nonlinear controller. Unique features of the Fuzzy Logic controller are the controller operation and the controller development. Fuzzy control algorithm is defined by linguistic rules. Controller input parameters are represented by Fuzzy Sets. Controller operation is well illustrated by usin,.c, control surface, particularly for controllers using input parameters.
The procedure for developing FL corrective function is similar to the procedure for developing a fuzzy logic controller. The following method is for determining a FL corrective function.
First, assume the corrective function for process model time constant has the form:
Tc(correctec = Tc[ I + AF (14) where AF is fuzzy logic corrective function. Function value corresponds to the incremental fuzzy logic controller output. The potential advantage of using a fuzzy logic function over an ordinary nonlinear function is that the fuzzy logic function is a more flexible function design and an easy way to include two or more arguments.
Second, apply the function with two arguments and use Tu/Td ratio as a first argument and Ultimate Gain as a second araument.
Z 6F= jT" 1 (15) d It is possible to use various number and types of membership flanctions. For the sake of ease of implementation, use simple triangle membership functions on the input Z parameters and singleton functions on the output signals. FigUre I I and Table 3 show 0 0 details of the fuzzy lo&ic corrective function design. Referring to Table 3, P represents positive and N represents negative.
UG OR Up/L N p N N p p NS PL 1 Negative: N = A, Negative Small: NS =.2, Positive: P=.5, Positive Large: Pl_=1.2 Table 3. Corrective function inference rules.
Defuzzification on the output signal applies to singleton membership 5 functions.
Tc Kp Tc Tc Tc Kp Kp Kp in in Corr Corr Corr Corr Corr Corr model model linear Sigmoid FL linear Sigmoid FL hinction function function function 11 1 9.374 10.42 10.13.799.887.86 11 1 9.728 10.57 9.55.826.895.81 11 1 10.65 8.92 10.00.949.809.89 11 1 10.35 10.38 10.29.960.963.95 11 1 9.72 11.9 10.30.956 1.12.99 11.5 10.99 10.95 11.14.55.55.56 11.5 12.36 14.34 13.54.66.77.73 11.5 12.99 11.69 13.53.65.59.68 11.5 11.59 10.68 12.38.57.53.61 11.5 10.84 12.70 12.16.54.61.59 Table 4. Comparison of identified time constant and process gain obtained by various corrective functions.
Experimental Results of Fuzzy Logic Simulation:
The Fuzzy Logic corrective function gave time constant and gain estimate I  I comparable to the estimates obtained with linear and nonlinear corrective functions.
According to Table 4, a relay oscillation identifier with added correctiVe I functions provides first order plus dead time model, which can be used for PD) controller model based tuning calculations.
Both nonlinear functions and neural network models sign i., ificantly improve relayoscillation based tuning rules. Adhering to the specified principles of developing neural network tuning models, neural network modeling provides a number of advantages. A user can implement any preferred tuning rules (not necessarily Lambda I or DvIC) and use the same methodology to develop neural network tuning models.
Z 0 Developed in simulation, an neural network model can accommodate specific features of the tuner design. Scan rate and noise level affecting controller design are easily added as input parameters for prediction.
Other embodiments 18 Although the systems and methods described herein use a tuner that calculates the Ultimate Period and the Ultimate gain of a process in order to develop information, any other types of tuners that measure any process characteristics are usable, including openloop tunes and other closedloop tuners. Furthermore, the factors determined and control parameters using the system and methods disclosed may be entered either by a user or automatically.
Further, the elements shown in any schematic block diagrams referred to herein 1 may be embodied in hardware or implemented in an appropriately programmed digital computer or processor that is programmed with software, either as separate programs or as modules of a common program.
1 Although the present invention has been described with reference to specific examples, which are intended to be illustrative and not delimiting of the invention, it will be apparent to those of ordinary skill in the art that changes, additions and/or deletions may be made to the disclosed embodiments without departing from the spirit and scope of the invention.
In the present specification "comprise" means "includes or consists of' and "comprising" means %ncluding or consisting of'.
The features disclosed in the foregoing description, or the following claims, or the accompanying drawings, expressed in their specific forms or in terms of a means for performing the disclosed function, or a method or process for attaining the disclosed result, as appropriate, may, separately, or in any combination of such features, be utilised for realising the invention in diverse forms thereof.
Claims (19)
 I A system for tuning a process control loop, the system comprising: a tuner module 600 for receiving an error signal representative of a difference between a set point and a process variable to gont,rate a first process control signal for controlling the process; a nonlinear module 660 for applying a nonlinear procedure to generate at least one parameter signal; a controller module 6 10 for receiving the error signal and the at least one parameter signal from the nonlinear module, the controller module generating a second process control signal for controlling the process; and switching means 670 coupled to the process for coupling one of the tuner module and the controller module to the process to select the appropriate process control signal for controlling the process.
 2 The system of claim I wherein the nonlinear module 660 includes: a nonlinear process identification module 640 for applying a nonlinear procedure to generate process model identification parameters.
 The system of claim I or claim 2 wherein the nonlinear module includes: a nonlinear controller design module 650 for providing a nonlinear estimation of a plurality of controller tuning parameters.
 4 The system of claim 3 wherein the controller is further coupled to receive the estimation of controller tuning parameters from the nonlinear controller design module.
 The system of claim 3 or claim 4 wherein the nonlinear controller design module allows adjustments to the controller module, the adjustments altering a response speed of the controller.
 6 The system of any one of the preceding claims further comprising:an analytical controller design module 620 coupled to the nonlinear module, the analytical controller design module capable of providing a plurality of controller parameters to the controller based on a plurality of model identification parameters received from the nonlinear module.
 7 The system of any one of the preceding claims wherein the controller is a proportional, integral, and derivative feedback controller.
 8 The system of any one of the preceding claims wherein the nonlinear module 660 includes at least one neural network module.
 9 The system of any one of the preceding claims wherein the nonlinear module 660 includes a nonlinear process identification module 640 and a nonlinear controller design module 650, wherein an output from the nonlinear process identification module 640 and an output from the nonlinear controller design module 650 are coupled to the controller module.
 The system of claim 8 wherein the neural network module uses one of a sigrnoid function and a radial basis function.
 11 The system of claim 8 wherein the neural network module uses a sigmoid function wherein a transfer function is given by Out = I+e' wherein In is a weighted sum of a plurality of external inputs of the form In wi Ini.
 12 The system of any one of the preceding claims wherein the nonlinear module includes a fuzzy logic module.
 13 The system of any one of the preceding claims wherein the parameter signal includes a plurality of control parameters using nonlinear estimators of a plurality of tuning parameters for tuning the process control loop.
 14 The system of claim 13 wherein the nonlinear module calculates the plurality of control parameters using nonlinear estimators using nonlinear functions to create nonlinear estimators of the plurality of tuning parameters.
 The system of claim 13 wherein the nonlinear module calculates the plurality of control parameters using nonlinear estimators using neural networks to estimate the relay oscillation tuning parameters.
 16 The system of claim 13 wherein the nonlinear module calculates the plurality of control parameters using nonlinear estimators using fuzzy logic to estimate the relay oscillation tuning parameters.
 17 The system of claim 14 wherein the nonlinear function is a sigrnoid function.
 18 The system of claim 17 wherein heuristic coefficients are used with the sigrnoid function to provide parameters including an integral time, a gain and a derivative time.
 19 A system substantially as hereinbefore described with reference to the accompanying drawings.Any novel feature or novel combination of features described herein and/or in the accompanying drawings.
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US5453925A (en) *  19930528  19950926  Fisher Controls International, Inc.  System and method for automatically tuning a process controller 
US5742503A (en) *  19960325  19980421  National Science Council  Use of saturation relay feedback in PID controller tuning 
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US4754391A (en) *  19850918  19880628  YamatakeHoneywell Co. Ltd.  Method of determining PID parameters and an automatic tuning controller using the method 
US5453925A (en) *  19930528  19950926  Fisher Controls International, Inc.  System and method for automatically tuning a process controller 
US5742503A (en) *  19960325  19980421  National Science Council  Use of saturation relay feedback in PID controller tuning 
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