WO2000028389A1

WO2000028389A1 - System for controlling the temperature of a technical process

Info

Publication number: WO2000028389A1
Application number: PCT/DE1999/003441
Authority: WO
Inventors: Bernd-Markus Pfeiffer
Original assignee: Siemens Aktiengesellschaft
Priority date: 1998-11-10
Filing date: 1999-10-28
Publication date: 2000-05-18
Also published as: DE19851827A1

Abstract

The invention relates to a system for controlling temperature, especially of a plastic extruder. Said system has a controller which is subdivided into an I-controller (1) which produces an integral-action component (y1) from a system deviation (xd), and a PD controller (2) which produces a proportional and a differential component (ypd) from a controlled variable (x). By superimposing said components in a summing element (3) a manipulated variable is produced. The novel controlling system is characterized by a good response to setpoint changes and simultaneously by a good interference behavior. The invention is used for adaptive controllers.

Description

description

Device for regulating the temperature of a technical process

The invention relates to a device for regulating the temperature of a technical process according to the preamble of claim 1.

So-called plastic extruders are used in plastics processing, especially in the manufacture of plastic profiles. For example, PVC profiles for window frames can be produced with a plastic extruder. With regard to temperature control, such plastic extruders are divided into several zones. Plastic granulate is fed into the extruder in a first zone and is conveyed through further heating and cooling zones via extruder screws. In a nozzle, the plastic is given its product-specific shape by being pressed through the nozzle with the appropriate contour at high pressure. Individual zones of the extruder, for example the first zone, can only be heated, while other zones are provided with both heating and cooling. Temperatures are measured in the zones using thermocouples. Pulse-controlled electrical are used as actuators for a heater

Resistors on heating coils or heating plates, for example an adjustable blower can be used as cooling. Depending on the operating state, temperature zones must either be heated or cooled, since the plastic has to be melted at the beginning, but later, high frictional energies are released by operating the system with the extrusion screw. The effects of the heat of friction on the temperature can be modeled by a fault at the process input. A PI or PID controller, which can be used to regulate the temperature of a zone, should be set for good storage behavior with a constant setpoint, so that faults that affect the process can occur as quickly as possible be settled. Because of this "sharp" setting, overshoots occur when the setpoint changes, which in many cases cannot be tolerated in temperature control. When designing the PI or PID controller, there is a conflict of objectives between a design for good storage behavior or a design for good control behavior of the control loop. It has been found that good control behavior in temperature control systems with PI or PID controllers can hardly be achieved together with good storage behavior.

As a way out of this conflict of objectives, the German patent application with the official file number 19722431.8 proposes a change in structure. With large, positive jumps in leadership size, e.g. B. when heating up a cold extruder to the operating point, the I component of the controller is switched off. In other words, instead of a PI or PID controller, a P or a PD controller is used in these situations. In the vicinity of the setpoint, the I component is again connected to the controller without bumps. In practice, however, such a structure changeover is complicated and expensive to implement, since different controller structures have to be set for different operating cases. It also requires a lot of storage space for the various controller structures and for the switching mechanisms that have to be implemented in software. In zones that are provided with both heating and cooling, a structural change would not only be necessary for positive, but also for negative setpoint jumps. In the case of a controller that only has to control a heating system, there is no need to change the structure in the event of negative setpoint jumps because the manipulated variable is limited by switching off the heating and because the control loop behavior is dominated by the actuator limitation in the event of larger negative setpoint jumps. Measures to limit the I component from running away when the actuator has reached the limit can thus already reduce overshoot of the controlled variable. The model However, a process which is equipped with heating and cooling has different reinforcements for heating and cooling, so that the case distinctions to be carried out during a structural changeover become considerably more problematic. In addition, the structure switchover is only effective in the event of setpoint jumps, but not in the event of sudden major interferences.

The mode of operation of the control device proposed in the German patent application with the file number 19722431.8 in the case of a process identification is to be explained below with reference to FIG. 12. In phase 1, which extends to time t ₀ , a manipulated variable y = 0 is applied to a process. In a temperature control, this phase corresponds to the situation that when the heating is switched off, the constant manipulated variable y = 0 is output to the process. The controlled variable x is in a first stationary state x = x ₀ = c _g . The value c _g is recorded as an equivalent value and stored.

As soon as an operator specifies a sufficiently large setpoint jump, step 2 is entered and the maximum manipulated variable y = y ₂ = y _max is applied to the process by a control unit in a controlled mode. In a temperature control, this corresponds to the full heating output. This manipulated variable is maintained until a turning point WP can be determined in the course of the controlled variable x. A turning point is considered to be recognized when the slope of the step response SA has decreased for the first time in two successive sampling steps. So that the slope information is not falsified by measurement noise, the measured values of the controlled variable x are subjected to low-pass filtering. If the control deviation xd has decreased by a predetermined value between 50 and 80% of the step height, which is preferably 60%, a turning point WP is assumed even without a decreasing slope in the step response. Using a tangent WT at the turning point WP, which is also referred to as a turning tangent, a delay time t _u can be derived from the Intersection point of the WT tangent with the straight line x = x ₀ results, are calculated as:

with t _w - time of the turning point WP, t ₀ - time of the setpoint jump, t _n ι - an auxiliary variable, x _w - value of the controlled variable x at the turning point WP, x ₀ - value of the controlled variable x in the first steady state and dx

- slope of the WT tangent. German

With this information, an IT process model is identified with the transfer function

G (s) = s (T, s + 1)

their reinforcement

and time constant

= 2t _u

be set.

In phase 3, which is initiated by the occurrence of the turning point WP, a PI structure of the linear controller R is now set, and the parameters of the PI controller are determined using the ITI model. The gain factor K _{pi of} the PI controller is set in the same way as a P controller for the Regulation of an ITI route in the asymptotic borderline had to be designed:

* P! = T _Ύ K ₁

In an initially careful setting in which overshoots are largely avoided and a sufficiently fast control behavior is achieved, the reset time T _n ι of the PI controller is two to ten times, preferably six times, the time constant Ti.

Switching from controlled to regulated operation is bumpless by initializing the I component of a PI or PID controller when switching over.

Since the ITI model does not run into a new steady state after a setpoint jump, ie models a process without compensation, the process amplification cannot be identified directly at first. However, so that large amplification factors of the process controlled with the PI controller with compensation do not lead to problems, the PI controller is only designed very carefully because of the still incomplete information about the process P. As soon as a steady state is reached with this rough regulation, the gain K _{p2 of} a process model can be determined with compensation to:

With

Xi - value of the controlled variable x in the second steady state,

Xo - value of controlled variable x in the first steady state, yi - value of manipulated variable y in the second steady state and yo - value of manipulated variable y in the first steady state. As a criterion for reaching the second steady state, it can be checked, for example, whether the control deviation lies below a predetermined limit value and / or the gradient of the controlled variable is less than a fraction of the gradient of the turning tangent WT.

With the knowledge of the process amplification K _p2 , the information from the turn tangent WT can now be further evaluated to determine a more precise model, for example a PT2 or a PTlTt model. The transfer function of a PT2 model in the Laplace area is:

G (s) = ^Kp2

(T _? S + 1) (T ^ s + 1)

the transfer function of a PTlTt model

K

G (s) p2 -I _t s

(Zs + 1)

The compensation time t _{a of} the step response, which results from the intersection of the turning tangent WT with the straight line at x = xrj, which marks the first stationary state, and the straight line at x = c _g + K _p2 ^• y ₂ , which marks a stationary state , which was approached by the controlled variable x, if the manipulated variable y ₂ created in the controlled operation during phase _{2 was} also maintained in the controlled operation at the process P, is calculated to:

t = t + tt = $ * - ^{+ C} - * ?. dx ", I dt

t _h2 - a second auxiliary variable, y ₂ - value of the manipulated variable y and c _g - equivalence, which is established as a steady state when the manipulated variable y = 0 is applied to process P.

If the compensation time t _a is greater than or equal to ten times the delay time t _u , a PT2 model is preferably used for process identification. A method known from the book "Regelstechnik I" by Heinz Unbehauen, 7th edition, Vieweg Verlag, Braunschweig / Wiesbaden, 1992, pages 363 to 367, is used and further developed to calculate the time constants T ₂ and T _{3 of} the PT2 model. The step response of the PT2 model is considered with the ratio

f

of the two time constants T ₂ and T ₃ . The step response reaches its turning point WP at the time

lnf f f - 1

The compensation time t _a CLOSES from the course of the step response

and the delay time t _u too

t, = - ^ - In (- ² - - t + r, + T ₂ T ₃ - T, X, certainly. After inserting f

So that this nonlinear system of equations can be solved analytically according to T ₂ and f, the exponential functions have to be approximated by linear approximations, which provide good results at least for the practically relevant range 2 <f <20. The following two equations with constants pi to p ₄ provide a suitable approximation:

p ₃ = 1.0722 P ₄ = 2.0982

P ₃ ^f + ₄

The time constants T ₂ and T _{3 of} the PT2 model are calculated using these equations:

A PI or PID controller is designed with this PT2 model.

The object of the invention is to create a device for regulating the temperature of a technical process, in particular in the case of a plastic extruder, which is distinguished both by good disturbance behavior and good management behavior. This object is achieved by the new device for regulating the temperature of a technical process according to the features of claim 1. Advantageous further developments of the control device are described in the subclaims.

The invention has the advantage that components of a standard controller can be used for implementation. A complicated case distinction, as was necessary with the familiar structure switchover, is no longer necessary. The new control device can be interpreted as cascade control. In a lower-level control loop, an inert temperature range is made faster with a P controller or, advantageously, a PD controller. This subordinate control loop is controlled by an overlaid I controller in a stationary manner precisely to the setpoint. In practice, this structural decomposition shows a bumpless increase in the manipulated variable after a jump in the setpoint, with a slightly longer rise time compared to the known structure switchover, but finally reaches the steady state at the setpoint more quickly.

In general, the behavior of temperature control systems can be described at least approximately by a VZ2 model. If a PD controller is used for the subordinate control loop, the mathematical methods of optimization in the state space for controller design can be used in an advantageous manner, which provide good control behavior as a mathematically exact method. The results of this optimization for different VZ2 processes can be approximated by a polynomial, so that simple setting rules for online use can be derived. The controller design can thus be carried out with a simple computing unit after the route identification. A control device can be implemented with little effort, which automatically adapts to an existing temperature control system during the initial start-up and during later operation. Based on the drawings, in which an exemplary embodiment of the invention is shown, the invention as well as embodiments and advantages are explained in more detail below.

Show it:

1 shows a control loop model which is used to explain a draft of an I controller and a subordinate PD controller, FIG. 2 shows a structure of a simulation model of the system with an upstream split range unit,

3 shows a circuit diagram of a control circuit with a control device for split-range operation, FIG. 4 shows a profile of the guide variable w (t) and the controlled variable x (t) in the circuit diagram according to FIG

FIG. 5 shows the associated course of the manipulated variable y (t), FIGS. 6, 7 and 8 step responses of a process, a subordinate PD control loop and a closed control loop with a complete control device, FIG. 9 shows a response to a step-like cooling Fault at the process input, FIG. 10 shows a response to an abrupt fault at the process output and FIG. 11 shows a fictitious step response of a PID controller without a structural breakdown.

FIG. 1 shows the structural diagram of a control loop in which a PID controller is broken down into an I controller 1 and a PD controller 2. A control difference x _d formed from a reference variable w and a control variable x is fed to the I controller 1. From this, the I controller 1 generates an integral component γ _± . Only the controlled variable x is connected to an input of the PD controller 2. The PD controller 2 supplies a proportional and a differential _component y _pd . Be in a summing element 3 the two parts y and y _pd overlaid to a manipulated variable y. Before a process 4 arrives, a fault z _{e is applied} . In response to such a manipulated variable y _pr , process 4 supplies a controlled variable x _pr , which in turn is superimposed on a disturbance variable z _a at the output of the process. The controlled variable x finally represents a temperature which is detected, for example, with thermocouples and fed back to the control device. The actual temperature is therefore:

x (s) = G (s) (y (s) + z _e (s)) + z _a (s)

With

G (s) - Laplace-transformed transfer function of process 4.

The total manipulated variable y of the disassembled controller is:

y (s) = K _t (s) (w (s) - x (s)) - K _pd (s) x (s)

With

_K. (s) - transfer function of the I controller 1 and

K _Pd (s) - transfer function of the PD controller 2.

The behavior of the control loop in different situations is characterized by the following transfer functions:

Transmission behavior of the subordinate PD control loop:

) = G _pd (s) y (s),

z _e (s) = z _a (s) ≡ 0

With

G _pd - transfer function of the subordinate control loop. Leadership behavior of the closed control loop:

x (s) = G _d (s) w (s),

G _pd (s) K, (s)

G _r , (s) =,

\ + G _pd (s) K, (s) z _e (s) = z _a (s) ≡ 0

With

G _cl - transfer function of the closed control loop.

Reaction to a fault at the process input:

x (s) = G _ze (s) z _e (s), ^G " ^S) = 'l + G (s) K (s) w (s) = 0, K (s) = K, (s) + K _pd (s)

With

G _ze - transfer function of the behavior to a disturbance at the process entrance.

Response to a fault at the process output:

x (s) = G _2a (s) z _a (s), 1 ^z T + G (s) K (s) w (s) = 0

With

G _za - transfer function of the behavior to a fault at the process output.

It can be seen from the transfer functions G _2e and G _za that it does not matter whether the controller is disassembled or not. Since processes in temperature control show behavior with delays, a VZ2 model is used to model process 4 with the transfer function:

G (s)

(t, 5 + l) (t ₂ 5 -f- l)

with k - process amplification, ti - first time constant of the process and t ₂ - second time constant of the process 4.

In a status display, VZ2 processes have two statuses: the actual value x and its change over time x ^* = dx / dt. The transfer function G (s) of process 4 can thus be converted into an equivalent state space representation:

£ [l 0], d = 0

with x - state vector,

A - system matrix, b - input vector, c '- transposed output vector and d - pass factor. A state controller for this process has the form:

y = -kx = ~ (k, x + k ₂ x ')

and can therefore be with

realize as a PD controller with a gain k _pd and a derivative time t _pd , which is described in the Laplace area by a transfer function k _pd with

K _pd {s) = k _pd (l + t _pd s).

This representation opens up the possibility of designing the PD controller for a VZ2 process using the strict mathematical methods of optimization in the state space. A quadratic quality criterion can be advantageous for this

With

J - quality index,

Q - unit matrix and r - a weighting factor

can be minimized, which takes into account both deviations of the states and deflections of the manipulated variable in a dynamic compensation process. Since all states are considered to be of equal importance, the unit matrix is used for Q. The characteristic of the state controller can advantageously be varied with the weighting r of the actuating deflections: the greater the weighting factor r, the greater the changes in the manipulated variables deteriorate the value of the quality criterion and the more cautiously the operator reacts Regulator. In order to accelerate the wear process 4 with the PD controller 2 as much as possible, a weighting factor r between 0.0002 and 0.02, preferably equal to 0.002, is selected. A standardization of the sizes w, y, x and x ^{* is} assumed to a value range up to 100%.

The solution to the described optimization task is possible with a software tool available under the name MATLAB with a single command line. However, the software tool executes a complex mathematical algorithm that solves the associated continuous matrix-Riccati equation and is generally not suitable for use on controller assemblies in automation devices. Therefore, the optimization for a number of different VZ2 processes can advantageously be carried out offline and then attempts can be made to derive simple setting rules for online use from the results. This has the advantage that the controller can be easily adapted to different processes.

The optimization shows that a loop gain of 21.4 must be set for the lower-level control loop for different processes. The gain k _{pd of} the PD controller therefore becomes too

21.4

given. The smaller time constant of the VZ2 model is chosen as the second time constant t ₂ . The lead time

t pd ~ ^a d2 * 2

depends on the smaller time constant t ₂ , whereby the auxiliary quantity α _d2 depends non-linearly on the ratio f = tχ / t _{2 of} the two time constants ti and t ₂ . Based on the results of the optimization of the controller in the state space, the rele- vanten range 1 <f <40 a fifth order polynomial is determined, which approximates the results numerically:

a _d2 = 4.89 • 10 ^{~ 8} ■ - 5.9290 • 10 ^{~ 6} • f ⁴ + 2.7814 • 10 ^"4 • f ³ - 0.00648 • f ² + 0.08486 • / + 0.162.

If the PD controller is set according to these formulas, the lower-level control loop advantageously has a complex, well-damped pole pair for all lines. The damping amounts to about 0.9 and is therefore close to the asymptotic limit case with the damping 1. A major advantage of the shown dismantling of a PID controller is that the lower-level control loop with the transfer function G _pd for a typical temperature range is about 20 times faster when the unregulated process G reacts to changes.

For the design of the superimposed I controller 1 with a transfer function

('.. ^{• s} ) it should be taken into account that in practice not an ideal, but a real PD controller 2 with a delayed D component is used, which adds another time constant to the lower-level control loop. The reset time t ^ of the I controller 1 can be made dependent on the already optimized derivative action time t _{pd of} the PD controller 2:

In a series of simulations, values are sought for the auxiliary variable α _ld that ensure overshoot-free guiding behavior of the closed control loop with the transfer function G _c ι. This results in a linear relationship for the auxiliary variable α _ld :

α _ld = 0.179. f + 3.35 For safety reasons, the auxiliary variable _ld should be limited to a minimum value of 3.5.

Instead of the PD controller 2, a simple P controller can also be used, which then generates a manipulated variable y _p from the controlled variable x. To explain the design of a control device with an I controller 1 and a P controller 2, the structure shown in FIG. 1 is again used, with only the output variable y _{pd of} the previous PD controller being replaced by the new output variable y _p is. The design of a PI controller disassembled in the manner shown is carried out in an analogous manner according to the scheme already described, so that it is sufficient to state the resulting setting formulas. The P controller with a transfer function K _p = k _p for the lower-level control loop cannot be regarded as a state controller, but is designed directly for an attenuation of 0.9 by increasing the controller gain

0.437f -0.133 k „=

"k

is chosen. The _{reset time} t _{l2 of} the _higher-level I controller with the transfer function

\ 2

(t, ι - ή

will depend on the time constant

t ", = 1L

of the closed subordinate circle. The _reset time t _l2 is determined to

a ψ = -5.10414 10 ^"6 f ⁴ + 0.000487705 f ³ - 0.0168150 f ² + 0.263083 f + 1.13409

The structure breakdown of a PI or PID controller shown has the advantage over the known structure switchover that faster readjustment tents can be implemented, in particular in the case of sudden disturbances and in the case of behavior that is exactly free from overshoot.

In the event of a setpoint jump, the known structure switchover causes a jump in the manipulated variable and a very fast start-up behavior. However, with the known structure switchover, the control loop needs some time for the final settling to the setpoint. A PI or PID controller with

Structural decomposition, on the other hand, shows a bumpless increase in the manipulated variable with a slightly longer rise time, but ultimately reaches the steady state at the setpoint more quickly. A major advantage of the structure decomposition is, however, that there is no need to change the structure by intervening in the controller during operation. This means that the new controller with structure decomposition can also be used with advantage in processes with two actuators, especially in a temperature control system with heating and cooling. The control device is also advantageously suitable for automatic commissioning, for example with a PC-supported controller commissioning method, since the structural breakdown can be defined when designing a software controller and loaded onto a controller as permanent parameterization.

FIG. 2 shows the model of a temperature control system with two actuators and an upstream split-range unit 5. The model of the temperature control system is subdivided into a model 6 for heating, a model 7 for Kuhlen and a model 8, which serves to output the temperature of the steady state, which is heating and cooling. Models 6 and 7 can, for example, be VZ2 elements with the same time constants, but differ in their amplification. Output variables x _h , x _k and x _b of models 6, 7 and 8 are superimposed in a summing element 9, which generates a resulting control variable x _pr '. The split-range unit 5 consists of two characteristic elements 10 and 11. With positive values of a manipulated variable y _pr 'applied to the split-range unit 5, the characteristic element 10 outputs the manipulated variable unchanged to the model 6 for heating , while the characteristic element 11 supplies the value "0" to the model 7 for Kuhlen and thus switches off the cooling. On the other hand, in the case of negative values of the manipulated variable y _pr ', the heating is switched off by the characteristic element 10 and the value of the manipulated variable y _pr ', weighted by a factor p, is transferred from the characteristic element 11 to the model 7 for cooling.

The simplest parameter, which characterizes the different behavior when heating and cooling, is the ratio of the maximum slope of the controlled variable x _pr 'with the heating switched on to the maximum slope with the cooling switched on. A steady-state amplification of the cooling cannot be determined without further ado, since for this purpose heating and cooling had to be operated simultaneously with known parameters of the model for heating. However, since an upstream controller, due to the split range unit 5, outputs a non-zero manipulated variable y _h to the model 6 for heating if the manipulated variable y _pr 'is positive, and a non-zero manipulated variable y _k to the model 7 for heating Cooling, if this is negative, there is no value for the manipulated variable y _pr '

Heating and cooling can be activated at the same time. In normal operation of a temperature control, this would also be a pure waste of energy.

In order to identify the amplification of model 7 for Kuhlen, the following model presentation is helpful. The heat losses of the process to the environment are neglected relaxes. The behavior of the process during the initial phase of heating can then be described at least approximately as a function of a manipulated variable y _h for heating by an IT1 model, ie by a delayed integrator:

^G A * ⁾ = s (t _2h s + l)

with Gi _h (s) - transfer function in the initial phase of the heating process, ki _h - amplification for heating and t _2h ^_ second time constant of model 6 for heating.

The behavior in the initial phase of cooling is described in a corresponding manner by the following delayed integrator:

x _k (s) = G, _k (s) y _k (s),

s (t _2k s + \)

With

Gi _k (s) - transfer function of model 7 in the initial phase for cooling, ik - amplification and t _2k - second time constant of model 7 for cooling.

FIG. 3 shows a control circuit with a control device which also contains the parts which are necessary for automatic identification of the process on the basis of the model concept described above. The mode of operation and the design of a controller 30 after the process has been identified have already been illustrated in FIG. 1, the mode of operation of a Split range unit 5 described with reference to Figure 2. The same reference numerals are used for the same parts.

A process 32 is provided in FIG. 3 with a heater 33 and a cooler 34. The temperature of the process is fed back to controller 30 as controlled variable x.

Before an identification process, a factor p is first set to the value "1" by a control unit 35, so that even negative values of the manipulated variable y are output by the characteristic element 11 without an additional weighting to the cooling 34 of the process 32. An automatic identification process is initiated by a request signal 36 which the control unit 35 receives from an operating unit (not shown in FIG. 3). The control unit 35 uses a signal 37 to flip a switch 38 so that the manipulated variable y is not specified by the controller 30 but by the control unit 35 with a signal 39. A request signal 36 can be generated, for example, at the same time as the control device is started up for the first time that the command variable w jumps.

FIGS. 4 and 5 show the courses of the guide variable w, the controlled variable x and the manipulated variable y during the automatic identification of the process 32 and a subsequent fault compensation. The time t in seconds is plotted on the abscissa of the diagrams in FIGS. 4 and 5, the temperature in ° C. on the ordinate in FIG. 4 and the manipulated variable in% on the ordinate in FIG. At a time t = 0 s, the process 32 is in a first steady state, in which the value of the controlled variable is x 0 ° C. At the point in time t = 0 s, the command variable w is set abruptly from previously 0 ° C. to the value 170 ° C. The control unit 35 then sets the manipulated variable y to a constant value +80% with the signal 39, at which 80% of the heating power is transferred to the process 32 and the cooling 34 is switched off. At about time t = 1100 s, a The turning point in the course of the controlled variable x was determined by the control unit 35 and, as already known from the German patent application mentioned at the beginning with the official file number 19722431.8, a first ITI model was identified which describes the behavior of the process during the heating process at least approximately. With a m Depending ^¬ ness of the first ITL model specific controller behavior controls the control unit 35 is between about the points in time t = 1100 s and t = 6800 s the process 32 in the vicinity of a second static tionaren state in which the controlled variable x is The guide size w reached 170 ° C. In a manner already known, a VZ2 model can be determined from a turning tangent wh and the second stationary state, which describes the gain of the heater 33 and the dynamics of the process 32.

From the second stationary state at 170 ° C., the control unit 35 sets the signal 39 to the value -20%, which is given to the control signal y via the switch 38 at the time t = 6800 s. At this value of the control signal y, the split-range unit 5 switches off the heating 33 and sets the cooling 34 to 20% of the maximum cooling capacity. The value of the control signal is kept constant at this value V _{LLM TUN} until an inflection point m curve of the controlled variable x (see FIG. 4) can be seen.

A simple and effective identification of the gain during the cooling process is achieved by adopting the IT1 models described above, deviating from the actual VZ2 model describing the process behavior, during the initial phase of the cooling process and during the initial phase of the heating process. In accordance with the structure shown in FIG. 2, the actual value of the controlled variable x is then obtained using the formula:

x Xh ~ k < since the effects of heating and cooling are superimposed in the summing element 9.

In the initial phase of cooling at time t = 6800 s, in which the process is suddenly cooled from the working point, two effects overlap: a jump in the cooling capacity from 0 to y _{LLM TUN} and a jump in the heating capacity from the stationary value y _∞ at the working point back to the value 0 with a jump height -y _∞ . The measured slope

dx wk = k _Λ (-y _∞ ) + k _Λ y _. LLM DO

at the cooling turning point, which is marked in FIG. 4 by the turning tangent wk, is composed of two parts, of which one part, namely k _lh (-y _∞ ), already consists of the

Turn tangent wh could be determined during the heating process and the stationary end value. This equation can be solved for the desired gain k _lk during cooling:

The determined ratio of the gains k _lh and k _lk is given by the control unit 35 to the characteristic element 11 of the split-range unit 5 (see FIG. 3) for an adjustment of the gain of negative signals with the factor p:

_, /,

Thereafter, the control unit 35 parameterizes the I controller 1 and the PD controller 2 of the controller 30 and flips the switch 38, so that the manipulated variable y 'generated in the controller 30 is given to the split range unit 5 as the manipulated variable y. This happens approximately at time t = 7800 s (see FIG. 5). The controller 32 heats the process 32 back up to the operating point at the temperature 170 ° C. After successful initial 4 and 5, the reaction to a sudden disturbance z _{e of} the high 40% at the process entrance is shown, as it arises in a plastic extruder at the start of production due to the start-up of the Ford screw. The fault occurs approximately at time t = 12500 s. In response to this disturbance, the control device m advantageously switches from heating mode to cooling mode in a bumpless manner, as can be clearly seen in the course of manipulated variable y after time t = 12500 s. According to the course of the controlled variable xm FIG. 4, the disturbance z _e only causes a brief deflection to approximately 180 ° C. and the controlled variable x already returns to the setpoint 170 ° C. after a short time.

A process model, as shown in FIG. 2, was used in the simulations of the control loop. Model 6 for heating and model 7 for Kuhlen are each VZ2 models with the same dynamics. The time constant t _x was set to 3700 s, the time constant t ₂ to 350 s. A gain k = 12 was assumed for cooling and a gain k = 6 for heating. These values are derived from the behavior of a real plastic extruder.

As a result of the initial setting, a gain k = 5.8788 during heating, a first time constant ti = 3613 s and a second time constant t ₂ = 370 s were determined for the process. The ratio of the gains k _lh : k _lk was found to be 0.43, which is sufficiently close to the theoretical ideal value of 0.5. In accordance with this result of the process identification, the reset time t _x χ of the I controller 1 is set to 1098 s, the gain k _pd and the lead time t _{pd of} the PD controller 2 to 3.6402 and 215 s, respectively.

A binary signal 40, which is fed to the control unit 35, can be used in the control device to set whether identification should be carried out during a cooling process. With this measure, the regular device can be adapted to the particular circumstances of the zones of a plastic extruder, so that it can also be used for pure heating zones. This is advantageous since both forms, ie zones with heating and cooling and zones with pure heating, usually occur in a mixture on a plastic extruder.

In the case of blower cooling in particular, it is advantageous to initiate the cooling process to identify the gain of the model for cooling from the working point. The cooling capacity is strongly influenced by the ratio of the process temperature to the ambient temperature. If different working points have to be set for different plastics in a plastic extruder, this dependency can be compensated for by a characteristic element in the signal path of the factor p in FIG. 3. In extreme cases, when the process temperature is equal to the ambient temperature, the fan cooling becomes ineffective.

To illustrate the mode of action of the cascade control, step responses of the transfer functions G, G _pd and G _c ι shown above are shown in FIGS. 6, 7 and 8. In other words, a jump of height 1 at time t = 0 s was applied to the simulation models of the respective transmission elements. The time scale on the abscissa is the same in each case. The time t = 0 s is marked on the left end of the abscissa, and the time t = 25000 s is marked on the right end. According to FIG. 6, the step response of the route with the transfer function G only reaches 90% of the stationary final value 6 at about 10,000 s, which corresponds to the gain k of the process. As shown in FIG. 7, the lower-level control loop reacts with a PD controller 2 to a unit step in the integral component y much faster and already reaches 90% of the stationary end value after about 1000 s. The route 6 is thus significantly accelerated by the PD controller 2. If the leadership variable w jumps at time t = 0 s, the control variable reaches x, as in FIG. 8 shows the value 1 of the target size w exactly and without overshoot. Already after approx. 2000 s, it exceeded 90% of the stationary end value.

FIGS. 9, 10 and 11 show step responses of transmission elements with the transmission functions G _ze , G _za or with a transmission function which was determined for comparison with a control circuit using an undismantled PID controller. The time t is plotted linearly in seconds on the abscissa of FIGS. 9, 10 and 11. At the left end of the scale is the time t = 0 s, at the right end the time t = 3000 s. According to FIG. 9, the control loop with a disassembled PID controller reacts to a unit step of the disturbance variable z _e with a deflection of the control variable x that hardly exceeds the value 0.2. Already after 2500 s the fault is almost completely corrected. From the course of the controlled variable x in FIGS. 10 and 11 it can be seen that the simulated response to a fault z _a at the process output principally affects the management behavior with an undismantled PID controller, ie a PID controller in which the control difference is based on the I - and the PD controller is guided, corresponds and has an overshoot of about 15%. The different polarity that results from the signs on the summation elements in FIG. 1 leads to mirror-image courses. However, a sudden disturbance at the process output does not occur in practice, since the controlled variable x, namely the temperature of a real inert system, cannot change suddenly in a temperature control. A comparison of the courses of the controlled variable x in FIGS. 8 and 11 clearly shows that the controller 30 with structure breakdown reaches the new setpoint without any overshoot and with a faster rise.

A control device for carrying out the method can advantageously be implemented with an internal sequence control with several different phases, which differ in the operating modes of the control device and in the models. that are used as the basis for the process identification. The control device can equally be implemented as a hardware circuit or as a computing unit with a program memory into which a suitable operating program has been loaded.

Claims

claims

1. Device for controlling the temperature of a technical process (4), in particular in a plastic extruder, characterized by an I controller (1), which consists of a control difference (x _d ), which consists of a guide variable (w) and a control variable (x) is formed, an integral component (y _x ) is generated by a P controller or a PD controller (2), which in a subordinate control loop from the controlled variable (x) has a proportional component (y _p ) or a proportional component. and generates a differential component (y _pd ), and by means of a summing element (3) for superimposing the components (y _x , y _p , y _pd ) generated by the controllers (1, 2) into a manipulated variable (y) for the process (4 ).

2. Device according to claim 1, characterized in that in the case of a PD controller (2) in the lower-level control loop, the gain k _pd and derivative time t _pd are calculated by a method in which em VZ2 model is determined, which the process behavior at least describes approximately, and a controller design is carried out according to the mathematical methods of optimization in the state space.

3. Device according to claim 2, characterized in that for the optimization in the state space em good criterion

with x_ = (x, x ^* ) - transposed state vector, x - state vector,

Q - unit matrix, y - manipulated variable and r - em weighting factor between 0.0002 and 0.02

is minimized.

4. Device according to claim 1, characterized in that in the case of a PD controller (2) in the lower-level control loop, a VZ2 model is determined, which at least approximately describes the process behavior, that the gain k _pd and the derivative time t _{pd of} the controller ( 2) are determined at least approximately according to the formulas

t _pd = a _d2 -t ₂ and

_d2 = 4.89 ^■ 10 ^{"" 8} - / ⁵ - 5.9290 -10 ^{~ 6} - / ⁴ + 2.7814- 10 ^{"4 ■} -0.00648 ^■ f ² +0.08486 ^■ / + 0.162

with k - segment gain, ti, t ₂ - time constants of the segment, α _d2 - an auxiliary variable and f = tι / t ₂ - ratio of the segment time constants.

5. Device according to one of claims 2 to 4, characterized in that the reset time tu of the I controller (1) is at least approximately determined according to the formula

t _Λ = (0.179- +3.35) -t pd

with f = tι / t ₂ - ratio of the path time constants ti and t ₂ and t _pd - derivative action time of the PD controller (2).

6. Device according to claim 1, characterized in that in the case of a P controller in the lower-level control circuit, a VZ2 model is determined, which at least approximately describes the process behavior, that the gain k _{p of} the P controller is at least approximately determined according to of the formula 0.437f-0.133

* "=

with f = tι / t ₂ - ratio of the path time constants t _x and t ₂ as well as k - path gain.

7. Device according to claim 6, characterized in that the reset time t _{i2 of} the I controller is at least approximately determined according to the formulas

/ = - - - t "'1 + ² '

«^ = -5.10414 - 10 ^{" 6} • f ⁴ +0.000487705 • f ³ - 0.0168150 ^■ f ² + 0.263083 ^• f + 1.13409

With

Gi _P - an auxiliary variable and t _P i - time constant of the closed subordinate control loop.

8. Device according to one of the preceding claims, characterized in that at least a first actuator (33), in particular for heating the process (32), and a second actuator (34), in particular for cooling the process (32), are provided, that a control unit (35) is present to identify the process,

which sets the manipulated variable (y) of the first actuator (33) to a first constant value (80%) during an identification process and switches off the manipulated variable of the second actuator (34),

which, after a first turning point in the course of the controlled variable (x) has been determined, identifies a first ITI model of the process (32), - Which regulates the process depending on the first IT1 model at least in the vicinity of a second stationary state (170 ° C) deviating from the first steady state, - Which on the basis of the turning tangent (wh) at the first turning point and on the basis of the values of the manipulated variable (y) and the controlled variable (x) in the first and in the second steady state identify a VZ2 model which describes the dynamics of the process (32) and the gain for the first actuator (33),

- Which switches the first actuator (33) out of the second steady state and sets the manipulated variable of the second actuator (34) to a second constant value (20%) - Which, after a second turning point in the course of

Control variable (x) was determined, a process gain ki _k for the second actuator (34) determined according to the formula

_fr _ ^dχ _Wk / ^dt + k _lh -y _∞

^K ιk - y TO DO

with dx _wk / dt - slope of the tangent (wk) at the second turning point, k _ih - process amplification of the identified first ITl model, y _∞ - value of the manipulated variable (y) output in the second steady state and yLMruN ~ second constant value of the manipulated variable.

9. Device according to claim 8, characterized in that the first actuator (33) is a heater and the second

Actuator (34) cooling is that the second steady state (170 ° C) is a typical

Working point of the process (32) corresponds.

10. Device according to one of the preceding claims, characterized in that the summing member (3) is followed by a split range unit (5), such that the range of values of the manipulated variable (y) generated by the summing member (3) in two sub-areas It is subdivided that at a value of the manipulated variable (y) in a first sub-range (0 to 100%) a manipulated variable for heating (33) is output and cooling (34) is switched off and that at a value of the manipulated variable (y) in a control variable for the cooling (34) is output and the heating (33) is switched off in a second partial range (-100% to 0).

11. Device according to claim 10, characterized in that the range of values generated by the summing element (3)

The manipulated variable includes a positive and a negative partial range, that if the manipulated variable in the positive partial range is used, the manipulated variable is output unchanged to the heater (33) and that if the manipulated variable is in the negative partial range, the manipulated variable (y) with a factor (p) weighted output to the cooling (34), which corresponds to the ratio of the reinforcement k _{ih of} the heater (33) to the reinforcement k _{ik of} the cooling (34).