Method and a process control system using the method for minimizing hunting

A method for process control to minimize hunting using a controller wherein a PID arithmetic operation is performed with respect to a deviation of a setting parameter and a processed variable fed back from a process, and a resultant manipulation variable is applied to the process including the steps of monitoring the waveforms of the setting parameter and the processed variable from the process to obtain an oscillation period of the deviation, identifying process characteristics of the process, obtaining a phase angle of a frequency response of an open-loop transfer function of a system from the oscillation period and the process characteristics, and detecting a hunting of the process by the magnitude of the phase angle. A process control system includes a self-tuning controller having a control means for performing a PID arithmetic operation with respect to a deviation between a setting parameter and a processed variable fed back from a process, process identification means for identifying process characteristics and determining optimal PID parameters, monitoring means for monitoring the waveforms of the setting parameter and the processed variable from the process to obtain an oscillation period of the deviation, means for obtaining a phase angle of a frequency response of an open-loop transfer function of the process obtained from the oscillation period and process characteristics, means for detecting a hunting of the process by the magnitude of the phase angle, and means for performing a tuning operation of the controller in accordance with the detecting result by the means for detecting.

BACKGROUND OF THE INVENTION 
1. Field of the Invention 
The present invention relates to process control systems. More 
specifically, the present invention is directed to a method and a process 
control system utilizing the method in a process controller for minimizing 
hunting of the process. 
2. Description of the Prior Art 
In order to perform satisfactory process control using a feedback control 
system, hunting of a process must be detected at an early stage, and an 
appropriate countermeasure taken to minimize the hunting. In one 
conventional system for detecting hunting, when a deviation (e=sp-pv) of a 
process variable (pv) with respect to a setting parameter (sp) has 
exceeded a predetermined threshold value e.sub.th, it is thereby 
determined that hunting has occurred. If the deviation temporarily 
increases for any reason, this must be prevented from being interpreted as 
hunting. For this purpose, an oscillation period of a manipulation 
variable (mv) and a process variable (pv) with respect to a process is 
calculated, and an interpretation is made based on a change in oscillation 
period. 
In the conventional hunting discriminating system, however, hunting can be 
detected only after the deviation (or the amplitude of an oscillation 
waveform) is considerably increased. When the beginning of PID parameter 
tuning depends only on an operator's request and if process 
characteristics naturally change, an old PID parameter is left untuned, 
and optimal control is disabled. In addition, detection timing of hunting 
is undesirably delayed. In any case, hunting must be detected at an early 
stage. 
SUMMARY OF THE INVENTION 
An object of the present invention is to provide an improved method and a 
process control system using the method for minimizing hunting of the 
process. 
In accomplishing this and other objects, there has been provided, in 
accordance with the present invention, a method for minimizing hunting of 
a controlled process using a controller wherein a PID arithmetic operation 
is performed with respect to a deviation of a setting parameter and a 
processed variable fed back from a process, and a resultant manipulation 
variable is applied to the process including the steps of monitoring the 
waveforms of the setting parameter and the processed variable from the 
process to obtain an oscillation period of the deviation, identifying 
process characteristics of the process, obtaining a phase angle of a 
frequency response of an open-loop transfer function of a system from the 
oscillation period and process characteristics, and detecting the hunting 
of the process by the magnitude of the phase angle. A process control 
system utilizing this method comprises a controller having a control means 
for performing a PID arithmetic operation with respect to a deviation 
between a setting parameter and a processed variable fed back from a 
process, process identification means for identifying process 
characteristics, monitoring means for monitoring the waveforms of the 
setting parameter and the processed variable from the process to obtain an 
oscillation period of the deviation, means for obtaining a phase angle of 
a frequency response of an open-loop transfer function of the process 
obtained from the oscillation period and process characteristics, means 
for detecting a hunting of the process by the magnitude of the phase 
angle, and means for subsequently performing a tuning operation of the 
controller in accordance with the detecting result by the means for 
detecting.

DESCRIPTION OF THE PREFERRED EMBODIMENT 
In the hunting discriminating or detecting system of the present invention, 
the waveforms of a setting parameter and a process variable are 
continuously monitored, and a phase angle of a frequency response of an 
open-loop transfer function of a process and controller system is obtained 
from an oscillation period of a deviation and process characteristics, and 
hunting of the process is detected from the magnitude of the phase angle. 
In a process tuning system utilizing the present invention, PID parameter 
tuning is performed in accordance with the hunting discrimination result. 
It is known that the process system is rendered unstable due to process 
variations or the like when the phase angle is close to "-.pi.". 
Therefore, hunting can be detected in accordance with whether or not the 
phase angle falls within a predetermined range having "-.pi." as the 
center point. When the hunting discrimination result is obtained, tuning 
is started, and new, optimal PID parameters are obtained. 
FIG. 2 is a block diagram of a process control system according to an 
embodiment of the present invention. Referring to FIG. 2, reference 
numeral 1 denotes a self-tuning controller; and reference number 2 denotes 
a controlled object, e.g., a process. The controller 1 comprises an adder 
(subtractor) 11 for calculating a deviation e=sp-pv between a setting 
parameter "sp" and a processed variable "pv" which is fed back from the 
process 2, a controller 12 for outputting, to the process 2, a 
manipulation variable "mv" which is obtained through PID arithmetic 
operation with respect to the deviation "e", a process identifier 13 for 
identifying process characteristics, and determining and outputting 
optimal PID parameters to the controller 12, and a waveform monitor 14 for 
discriminating hunting of the process and sending a signal for starting 
tuning of the PID parameters (in other words, identification of the 
process characteristics) to the identifier 13. 
In the above arrangement, the process is already identified as a system of 
an idle time "L" and a primary delay "Tp" by the identifier 13 of the 
self-tuning controller 1. At this time, a PID parameter can be calculated 
by the Nichols' equation in accordance with process types of a controller 
(i.e., PI, DPI, PID and the like). Optimal parameters are given as 
follows: 
Proportional Gain: Kc 
Integration Time: Ti 
Differentiation Time: Td 
In order to obtain a transfer function Gc(S) (where S is the Laplace 
operator) in PID control, the transfer function is approximated using the 
above parameters as: 
EQU Gc(S)=Kc{1+(1/Tis)+Tds} (1) 
If the process 2 is identified as the system of the idle time L and the 
primary delay Tp, the transfer function Gp(S) of the process is expressed 
by: 
EQU Gp(S)=(Kp.multidot.e.sup.-LS)/(1+Tps) (2) 
Therefore, a frequency response .DELTA.(j.omega.) of an open-loop transfer 
function .DELTA.(S) of the system consisting of the controller 1 and the 
process 2 can be expressed by: 
EQU (S)=Gc(S).multidot.Gp(S) (3) 
This yields: 
EQU .DELTA.(j.omega.)=Ge(j.omega.) (4) 
EQU Gain of .DELTA.(j.omega.):g=g1+g2 (5) 
Phase angle of 
EQU .DELTA.(j.omega.):.theta.=.theta.1+.theta.2 (6) 
g1, g2, .theta.1 and .theta.2 in equations (5) and (6) are then calculated. 
From equation (1), the frequency response Gc(j) of the transfer function of 
the controller 1 can be rewritten as: 
EQU Gc(j.omega.)=Kc{1+(1/jTi)+J.omega.Td)}=Kc[1-j.multidot.{(1-.omega..sup.2 
TiTd)/Ti}] (7) 
EQU Therefore, 
EQU Gain g1=20 log Kc.sqroot.1+{(1-.omega..sup.2 TiTd)/.omega.Ti .sup.2 (8) 
EQU Phase angle .theta.1=/{1-j.multidot.{(1-.omega..sup.2 
TiTd)/.omega.Ti=tan.sup.-1 {-(1-.omega..sup.2 TiTd)/.omega.Ti (9) 
Meanwhile, from equation (2), the frequency response Gp(j.omega.) of the 
transfer function of the process can be expressed by: 
EQU Gp(j.omega.)=(Kp.multidot.e.sup.- j.omega.L)/(1+j.omega.Tp) (10) 
EQU Therefore, 
EQU Gain g2=20 log Kp-20 log .vertline.e.sup.j.omega.L (1+j.omega.Tp)=20 log 
Kp-20 log .sqroot.1+(.omega.Tp).sup.2 (11) 
EQU Phase angle .theta.2=-/e.sup.j.omega.L 
-/(1+j.omega.Tp)=-{.omega.L+tan.sup.-1 (.omega.Tp) (12) 
From equations (5), (8), and (11), therefore, the gain "g" of the frequency 
response .DELTA.(j.omega.) of the open-loop transfer function is expressed 
by: 
EQU g=20 log Kc.sqroot.1+{(1-.sup..omega.2 TiTd)/.omega.Ti}.sup.2 +20 log Kp-20 
log 1+(.omega.Tp).sup.2 (13) 
From equations (6), (9), and (12), the phase angle .theta. of the frequency 
response (j) of the open-loop transfer function is expressed by: 
EQU .theta.=tan.sup.-1 {-(1-.omega..sup.2 TiTd)/Ti}-.omega.L-tan.sup.-1 
(.omega.Tp) (14) 
The Nyquist diagram of the frequency response .DELTA.(j.omega.) of the 
open-loop transfer function represented by equations (13) and (14) is as 
shown in FIG. 3. Referring to FIG. 3, point A (.omega.=.omega..sub.hA) and 
point B (.omega.=.omega..sub.hB) are plotted on the curve of 
.DELTA.(j.omega.). If only a process gain is increased for any cause, and 
other parameters are not changed, the gain g is increased and the phase 
angle .theta. is not changed from equations (13) and (14). Therefore, the 
curve of .DELTA.(j.omega.) is moved to .DELTA.'(j.omega.), as indicated by 
the arrow, and the points A and B are moved respectively to points A' and 
B'. A unit circle which has the origin O as the center and a radius 1 is 
drawn. The points B and B' are located outside the circle, and no 
self-oscillation occurs although the gain is larger than one. This is 
because the points B and B' do not satisfy a condition .theta.=-.pi. for 
oscillation, where the phase angle .theta.=-.pi.. In contract to this, 
both the points A and A' have the phase angle .theta.=-.pi.. The system of 
point A is stable because it is located inside the circle. However, the 
point A is easily moved to the point A' due to an increase in process 
gain, and self-oscillation is started. 
In order to discriminate whether a process tends to be unstable, the 
oscillation waveform of a deviation e=sp-pv of a process system as shown 
in FIG. 4 is continuously monitored, first and second oscillation periods 
T1 and T2 are obtained at times delayed by half the period, and an 
oscillation period T.sub.h is determined from the average value of the 
periods T1 and T2. 
EQU T.sub.h =(T1+T2)/2 (15) 
An angular frequency .omega..sub.h can be calculted as: 
EQU .sub..omega.h =2.pi./T.sub.h (16) 
The formula for calculating the phase angle .theta. of the open-loop 
transfer function .DELTA.(j.omega.) is given as equation (14). As 
described above, the process parameters (i.e., the idle time L, the 
primary delay Tp and process gain Kp) obtained by the identification 
mechanism 13 and PID parameters (i.e., the controller gain Kc, the 
integration time Ti, and the differentiation time Td) are substituted in 
this equation, and the angular frequency .omega..sub.h given by equation 
(16) from the oscillation period T.sub.h is also substituted, thereby 
calculating the phase angle .theta.. 
If the phase angle .theta. is close to -.pi., as described above, it is 
assumed that the system can be easily rendered unstable by causes such as 
process variations. Therefore, in this embodiment, this range is 
determined as: 
EQU -0.9.pi..ltoreq.0.ltoreq.-1.1.pi. (17) 
When .theta. calculated by equation (14) falls within this range, the 
waveform monitor 14 sends a process identification signal St to the 
identifier 13 irrespective of the gain "g" of the frequency response 
.DELTA.(j.omega.) of the open-loop transfer function, thereby producing 
re-identification. 
In response to the identification signal St, the identifier 13 identifies 
the varied process, sets new PID parameters accordingly, and supplies then 
to the controller 12. Since the controller 12 starts its control using the 
new PID parameters, the Nyquist diagram of the open-loop transfer function 
is derived from .DELTA.'(j.omega.) to .DELTA.(j.omega.) as shown in FIG. 
3, and stable control can be continued. 
The self-tuning controller 1 can be constituted by combining independent 
circuit components. Alternatively, a microcomputer can be used, and the 
function equivalent to the controller 1 can be executed by a program 
pre-stored in a compouter memory. In this case, the adder 11, the 
controller 12, the identifier 13, and the waveform monitor 14 can be 
realized by corresponding programs. FIG. 1 shows an example of a flow 
chart of a program corresponding to the operation of the waveform monitor 
circuit 14. 
Referring to FIG. 1, when execution of the program enters the waveform 
monitor operation program, the controller 1 checks the presence/absence of 
a change in setting parameter sp (step 101). In this embodiment, hunting 
discrimination is made when the setting parameter "sp" is constant. If the 
parameter "sp" is constant, the oscillation periods T1 and T2 of the 
deviation "e" are calculated (step 102). In this case, the deviation "e" 
is monitored in an appropriate sampling period, and waveform monitoring 
for 1.5 periods is performed upon inversion of the sign of the deviation 
"e". When the two oscillation periods T1 and T2 which are delayed by half 
the period are not the same, these periods are ignored as errors. In this 
embodiment, only when the resultant periods satisfy the following relation 
(step 103) 0.9.ltoreq.T1/T2.ltoreq.1.1, are they adopted as normal 
parameters. 
An average value T.sub.h of these oscillation periods is then calculated 
(step 104), the angular frequency .omega..sub.h is calculated from the 
oscillation period T.sub.h (step 105), and the phase angle .theta. is also 
calculated therefrom (step 106). It is next checked if the calculated 
phase angle falls within the predetermined range, thereby discriminating 
hunting (step 107). If hunting is discriminated, the identification signal 
St is supplied to the identifier 13, thereby initiating a tuning start of 
the PID parameters (step 108). As described above, since the operation of 
the identifier 13 is also realized by the program corresponding thereto, 
the sending operation of the identification signal St is realized thereby, 
e.g., setting a predetermined flag in a predetermined area of the memory. 
When an error occurs, that is, T1/T2 falls outside the predetermined range 
(step 103), the following check operations are not performed. If the phase 
angle falls outside the predetermined range and the stability is kept 
(step 107), the value of T2 is used as the value of T1 without initiating 
a tuning start. After the oscillation period T2 which is delayed from the 
new value of T1 by half the period is calculated (step 109), step 101 is 
executed. 
When the identification signal St is sent (step 108) and the setting 
parameter "sp" varies (step 101), the waveform monitor program is ended. 
In this manner, the phase angle .theta. is calculated in real time and 
hunting is discriminated. If the hunting is detected, tuning is 
immediately performed. Optimal control can be performed for a process 
requiring a high-speed response, resulting in convenience. 
In equation (2), since the process identification mechanism functions near 
an equilibrium point of a limit cycle, in practice, the first term "1" of 
the denominator of the right side can be omitted. If such approximation is 
made, equation (14) can be rewritten as: 
EQU =tan.sup.-1 {-(1-.omega..sup.2 TiTd)/.omega.Ti}-.omega.L-(.pi./2) (14') 
Hunting discrimination can be similarly performed using the phase angle 
.theta. obtained by equation (14'). 
The preceding discussion is directed to an example wherein the present 
invention is applied to the self-tuning controller 1 comprising the 
controller 12 and the identification mechanism 13. This system is suitable 
for a case wherein a phase angle is continuously calculated using process 
characteristics identified by the identifier 13, hunting discrimination is 
made in real time, and control for keeping stability is performed. The 
hunting discrimination system of the present invention is not limited to 
this case. If the process characteristics can be obtained, the present 
invention can be applied to a normal controller. As a result of hunting 
discrimination, tuning can be performed immediately or later whereby the 
present invention is not limited to real-time control. 
According to the present invention as described above, a phase angle of a 
frequency response of an open-loop transfer function of a feedback loop is 
obtained from process characteristics and an oscillation period of a 
deviation obtained through waveform monitor of a setting parameter and a 
processed variable, and it is used to determine whether or not a system 
may become unstable. Therefore, hunting of a process can be detected by a 
smaller oscillation than in a conventional system. More specifically, an 
increase in gain in an unstable direction can be detected earlier. Process 
tuning is performed based on the hunting discrimination result. Therefore, 
the process can be reliably and optimally controlled, resulting in high 
efficiency and low cost. Since hunting discrimination is made using the 
phase angle, detection can be free from the influence of noise unlike the 
conventional case of using the absolute value of a deviation. 
Accordingly, it may be seen that there has been provided, in accordance 
with the present invention, a method and an apparatus using the method for 
process control to minimize hunting.