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									                   A Two Degrees of Freedom PID Control System,
                           its Features and Applications
                                                                 ✝                                     ✝
                    Masanori Yukitomo*, Takashi Shigemasa , Yasushi Baba*, Fumio Kojima

                                                   * Toshiba Corporation
                                      1 Toshiba-Cho,Fuchu-shi,Tokyo 183-8511 JAPAN
                                          e-mail: masanori.yukitomo@toshiba.co.jp
                                         Toshiba IT & Control Systems Corporation
                                  2-24-1 Harumi-Cho,Fuchu-shi,Tokyo 183-8511 JAPAN

                           Abstract                              and processes with zero. In order to improve the issues,
                                                                 several advanced PID control technologies, such as, I-PD
PID control systems are widely used as a basic control           control systems by Kitamori [10][11] and two degrees of
technology for industrial control systems today, due to its      freedom PID control systems by Araki [1], Hiroi [7] and
well-known simple PID control structure. However, the            Shigemasa [14], have been proposed since early 1980s.
tuning of the PID control systems is not always easy,            However, these control systems have difficulties for long
because of its simple control structure for wide class of        dead-time processes. What is a widely applicable and
process characteristics. What is a widely applicable and         simple process controller with easy tuning and good control
simple process controller with an easy tuning and good           performance? This is a motivation of the paper.
control performance? This is a motivation of the paper. Prof.    Recently, ”From Model-based Control to Model-Driven
Hidenori Kimura of Univ. of Tokyo proposed “Morel-               Control” was proposed by Kimura [9]. He defined a
Driven Control (MDC) Concept” at CDC2000 Sydney. He              Model-Driven Control (MDC) concept as “ a control system
defined a model driven control as a control system               architecture which uses a model of the plant as a principal
architecture, which uses a model of the plant as a principal     component of controller”. Advantages of the MDC are
component of controller. PID d, PPI (Predictive PI), IMC         simple and easy to understand the control architecture, good
(Internal Model Control) and DMC (Dynamic Matrix                 tunability and its robustness. PID d control systems by
Control) belong to a class of MDC. Features of MDC are           Shinskey [17][18], PPI (Predictive PI) control systems by
simple structure, easy tuning approach and proven stability      Hagglund and Astrom [2] and Internal Model Control
and robustness. Based on the MDC concept, aiming for             (IMC) systems by Morari and Zafiriou [12] can be
wide applicability for even unstable processes, we               considered to belong to the same class of MDC. However, it
developed a model driven PID control system, named MD            is difficult to realize the Model Driven control system for
PID control system, combining with a PD local feedback,          unstable processes. In order to improve these issues, a
an IMC and a set-point filter. That was one degree of            Model-Driven PID control system, which is combined with
freedom type.                                                    PD feedback block, IMC block and set-point filter block
In this paper, we propose a new model driven two degrees         was proposed by Shigemasa et al. [15][16].
of freedom PID control scheme, named MD TDOF PID                 In this paper, we propose a new Model-Driven two degrees
control, in order to obtain better disturbance regulating        of freedom PID control system, named MD TDOF PID
property by extending conventional MD PID control system.        control, in order to obtain better disturbance regulating
Through some features and some practical field                   property by extending a MD-PID control system and a
experiments, the MD TDOF PID control system shows                tuning approach. The MD TDOF PID control system is
good control performances with easy tuning.                      capable of stabilizing for even unstable processes by using
                                                                 local PD (Proportional and Derivative) feedback, regulating
                                                                 quickly for disturbances and tracking quickly to changes of
                       1     Introduction
                                                                 set-point by using a TDOF IMC by Brosilow [4]. Main
As in Control Technology Survey Report by SICE [5], a            efforts for tuning phase are to identify a first order delay
report by Takatsu and Ito [21] and a paper by Desborough         system with dead time for the control process with local PD
and Miller [6], PID control systems are widely used as a         feedback. This paper shows properties of the MD TDOF
basic control technology in today’s industrial control           PID control system, a tuning approach, some results of
systems. However, the tuning of PID control systems is not       practical industrial field experiments.
always easy, because of its simple control structure for wide
class of practical process characteristics, such as long dead-
time processes, oscillatory processes, unstable processes
       2    A Model-Driven TDOF PID Control System                                 several approaches, such as model matching method by
                                                                                   Kitamori [10][11], frequency region methods, simulation
Block diagram of a Model-Driven TDOF PID control                                   and optimization.
system can be expressed as in Figure 1.
The control system consists of the following three block
diagrams.                                                                          Step2: Main Controller and set-point filter

(a) PD feedback compensator                                                        If the overall controlled process G(s) is identified as a first
                                                                                   order delay system with dead time as in Equation (1), the
(b) Main controller blocks consist of a gain block, a second                       tuning approach is as the same as PID d control systems
order Q filter with tuning parameter and a first order delay                       and PPI control systems as shown as;
model with dead time
                                                                                    1). Kc=1/K              : Gain
(c) Set-point filter
                                                                                    2). Tc=T                : Integral time constant
where r, v, u, y, d are set-point, internal input for local loop,
that is, an input for the process P(s), output and disturbance,                     3). Lc=L                :Dead time
By using well-designed PD feedback for practically wide                            Step3: Adjusting tuning parameters
class of controlled processes, the process with the local PD
feedback can be seen as a first order delay system with dead                       By using a second order Q filter,
time and set it to the model of the main controller.                                                                   (1 Tc s)(1            Tc s)
                                                                                                           Q(s)                                      (3)
                                                                                                                             (1      Tc s)
                      3      A Designing Approach
                                                                                   and the set-point filter
Step1: PD feedback compensator
                                                                                                            1         Tc s                           (4)
A role of the PD feedback compensator is to be able to                                                      1         Tc s
stabilize even unstable processes P(s) and to compensate
the transfer function from v to y, that is, the process with                       the output y can be expressed as equation. (5)
the local PD feedback, into a first order delay system with
dead time, as shown in equation (1). The total controlled                                  exp(-L c s)       exp(-L c s)     (1    Tc s)(1 Tc s) (5)
                                                                                    y                  r                  [1                    ]d
process including the controlled process with a local PD                                   1    Tc s         K c (1 Tc s)       (1     Tc s) 2
feedback F(s) can be designed or tuned to a first order
delay system with dead time as shown in equation (1).                              By introducing second order Q filter, there is a canceling
                                                                                   zero concerning for pole of the controlled process between
               G(s) [1 - P(s)F(s)]-1 P(s)                                          y and d, the MD TDOF PID control system has a strong
                                                                   (1)             capability to regulate quickly against disturbance and to
                                                                                   track quickly to the change of set-point without overshoot.
                       1 Ts
                                                                                   Tuning approach
                          K f (1 Tf s)                             (2)
               F(s)                                                                The key work in tuning phase is to identify the first order
                           1     Tf s
                                                                                   delay model with dead time as shown in equation (1) as the
If the transfer function of the controlled process P(s) is                         transfer function G(s) between v and y. A modeling tool
identified, the PD feedback F(s) can be designed by using                          composed of a minimum realization method from markov

                                                 Main Controller
                                                                                                                              G (s )
                  r          1     Tc s      +              +            (1 Tc s )(1 Tc s )        v       + u+                                  y
                                                    Kc                                                                        P(s )
                             1     Tc s      -              +               (1 Tc s ) 2                    -  +
                                                  Gain                                                                       Process
                          Set Point Filter                                   Q Filter

                                                                                                                      K f (1 T f s )
                                                                             1          Lc s
                                                                                  e                                    1      Tf s
                                                                           1 Tc s
                                                                                                                       PD Feedback

                                   Figure 1: Model Driven Two Degrees of Freedom PID Control System
parameters by Starr [19], a transfer function reduction
method based on the low frequency region by Iino and
Shigemasa [8] and a simple simulation method, is
introduced. The order of these models obtained by using
minimum realization method is relatively so high, it is not
suitable for process control. A reduction method in low
frequency region is used. That is, by matching a gain
frequency response of with a minimum phase part of a first
order delay system and by matching phase frequency
response with the first order delay system plus a dead time
system in low frequency region, a first order delay model
with dead time can be derived.
                            K exp(- Ls )
                P( s)                                  (6)
                              1 Ts
If the simple model is identified, the MD TDOF PID
control system can be designed easily according to the
previous section.
Practical robust stability of the MD TDOF PID control
system can be evaluated by using well-known stability
measures, such as gain margin, phase margin and the
Maximum sensitivity Ms through the Nyquist plot of the
control system. Astrom [2] recommended reasonable values
of Ms are 1.2 and 2.

                        4    Special Features

4.1 Widely applicable process controller
                                                                       Figure 2:Field comparative test results
As the MD TDOF PID control system has the following
                                                                       at Boiler test plant (Upper: Conventional
structures, such as a PD local feedback, a 2nd order Q filter,
                                                                       PID, Lower: Model Driven PID)
a first order delay model with dead time and set-point filter,
the control system can be applicable for not only long dead      5.1 Boiler test plant
time processes, but also integral processes, oscillatory         Figure 2 shows a result of comparative experiment at the
processes, small dead-time processes and even unstable           pressure control loop of a boiler test plant. The upper time
processes. The overall controlled process G(s) can be            responses show a result of conventional PID control system
approximated to a first order delay system with dead time        of which control parameters are determined by IMC tuning
as in equation (1), by well compensated with the PD              rule. The lower time responses show a result of a MD
feedback loop.                                                   TDOF PID control system. Both about thirty % of control
4.2 Two degrees of freedom characteristics                       performance measures, that is, the IAE(Integral Absolute
By using a second order Q filter with a canceling zero           Error) and the settling time of the loop, can be improved by
concerning parameter for slow pole of the controlled             using the MD TDOF PID Control at both a set-point
process, the MD TDOF PID Control system shows quick              tracking phase and a disturbance regulating phase.
disturbance regulating property. And by using the set-point
filter, transfer characteristics from the reference r to the
output y becomes a first order delay with dead time. So the      5.2 Paper manufacturing plant
MD TDOF PID Control system shows quick set-point                 Paper manufacturing company uses a great deal of water for
tracking property without overshooting.                          all of paper making processes, water treatment process and
                                                                 boilers. A reservoir is used for providing water to all of the
                                                                 paper making processes at this site. To keep water level of
         5    Practical industrial field experiments             the reservoir, river water is pumping up by using a variable
                                                                 speed inverter control pump and is sent to the reservoir at
As simulation results of MD PID control systems were             the 600 meters far from the pumping place. So the control
shown in the former papers, some results of field                process has integral mode, delay mode and dead time mode.
experiments of MD PID control systems are introduced in          So the water level was oscillating with long period by using
this section.                                                    a conventional PID control at a conventional PI control
                                                                 phase as in Figure 3. The amount of fluctuation of water
                                                                 level is reduced to about 1 of 3 by applying the MD TDOF
PID control. Finally the set-point (SV) was lowered, and
energy-saving and healthy operation has also been attained.

                         6    Conclusions

Based on the Model-Driven Control concept by H.Kimura,
we extended a new PID control system, named as Model-
Driven TDOF PID control system, which is combined with
a local PD feedback, second order Q filter, a first order
delay model with dead time and set-point filter. The MD
TDOF PID control system has strong capability to stabilize
by using the PD feedback and second order Q filter, to
regulate quickly against disturbance and to track quickly to
the change of set-point without overshoot. Various types of
PID control systems can be realized from the MD TDOF
                                                                     Figure 3: Comparison of water level control for a
PID control system smoothly by setting control parameters.
                                                                     reservoir using conventional PID control and MD
Since a key subject in tuning phase is modeling, the tuning          TDOF Control at a paper manufacturing plant
approaches are also discussed based on minimum
realization technology and reduction method in low                    Trans. of Society of Instrument and Control Engineers,15-4,
                                                                      549-555, 1979. (In Japanese)
Through practical industrial field experiments, practical
effectiveness for the MD TDOF PID Control system such            [11] Kitamori Toshiyuki, Partial Model Matching Method
                                                                      conformable        to    Physical   and    Engineering
as the quick responses for both set-point tracking and
                                                                      Actualities,Preprints of 1st IFAC Symposium on System
disturbance regulating response are shown.                            Structure and Control, 2001.
                                                                 [12] Morari    M. and E. Zafiriou, Robust Process Control.,
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