PID is a proportional, integral, differential short, PID control difficulty is not programmed, but the parameters of the controller tuning. Tuning is the key to correctly understand the physical meaning of the parameters, PID control principle can be manually controlled furnace temperature for employers to understand. Read the article does not require advanced mathematical knowledge.
1. Proportional control
Experienced operator to manually control the electric furnace oven temperature can get very good quality control, PID control and manual control of the control strategy has a lot of similarities.
Here's how the idea of the operator with proportional control to manually control the electric furnace furnace temperature. Suppose detection furnace thermocouple, digital temperature display instrument. In the control process, the operator reading the eyes furnace, and the furnace temperature is compared with a given value, the error value of the temperature obtained. Then hand operating potential, current regulation of the heating, furnace temperature maintained around a given value.
Stable furnace operator knows the value of a given rough position potentiometer (We will call this position L), and controls the rotational angle of the potentiometer of the heating current was adjusted according to the temperature error value. When the furnace temperature less than a given value, the error is positive, the position L on the basis of increased angle potentiometer clockwise to increase the heating current. When the furnace temperature is greater than a given value, the error is negative, in the position L on the basis of the counterclockwise rotational angle of the potentiometer decreases, and to make a difference L is proportional to the position error angle. The control strategy is proportional control, i.e., proportional to error proportional part of the PID controller output.
There are various closed loop delay effect. For example, a larger time delay after the angle adjustment potentiometer, the temperature was increased to a new steady state value corresponding to the rotational angle. Because of the delay factor, the adjusted angle of the potentiometer can not immediately see the effect of the adjustment, and therefore closed-loop control system adjusts the difficulty is mainly due to delayed action of the system.
If the scale factor of the proportional control is too small, i.e., after the rotation angle adjustment potentiometer position L of the difference is too small, inadequate regulation of the slowly varying output of the system, adjusting the total time required is too long. If the scale factor is too large, i.e., the rotation angle position of the adjustment potentiometer L differ too large, adjustable intensity is too strong, the resulting adjusted too far, and even the temperature fluctuated, it oscillates back and forth.
Increasing the scale factor of the system responsive, faster adjustment, and may reduce the steady state error. Excessive scaling factor but that the overshoot amount is increased to increase the oscillation frequency adjustment time becomes longer, the dynamic performance deterioration, the closed-loop scale factor is too large even make the system unstable.
Simple proportional control is difficult to ensure regulation just right, completely eliminate errors.
2. Integral control
PID controller integrals correspond to the area (the gray portion in the figure) of the coordinate axes surrounding the error curve of FIG. PID control routine is performed periodically, the cycle period is called the sampling performed. The computer program of FIG. 1 with the area of each rectangle is approximated and accurate integration, the figure is the sampling period TS.
1 a schematic view of FIG integration operation
PID operation every time, on the basis of the original on the integrated value, increasing the value of a minute portion ev (n) proportional to the current error. When the error is negative, the incremental integration is negative.
Manual adjustment temperature, corresponding to the control angle in accordance with the time integral of the error value, periodically trimming potentiometer, each adjustment angle increment is proportional to the time error. When the temperature is lower than the set error value is positive, the integral term is increased, the heating current is gradually increased, the integral term decreases and vice versa. So long as the error is not zero, because the output of the controller integral action will be constantly changing. Integral adjustment of "general direction" is correct, the integral term has the effect of reducing the error. Not until the system is stable, then the error is always zero, and the ratio of the differential portion part are zero, the integral part of it does not change, and exactly equal to the output value of the controller of the desired steady state corresponding to the temperature control position angle potentiometer system L. Thus the role of the integral part is to eliminate the steady state error and improve the accuracy of the control, the integral action is generally required.
Error proportional to the integral of the integral portion of the PID controller output. Because the integration time TI in the denominator of the integral term, TI is smaller, faster integration term changes, the stronger the integral action.
3. PI control
The integral term in the controller output is proportional to the value of the current accumulated error values and the error value of the previous past, integral action itself so severe a hysteresis characteristic, unfavorable stability of the system. If the coefficient of the integral term is set too bad, difficult to correct its negative effects by integral action itself quickly. The proportional term without delay, as long as an error occurs, the proportional part takes effect immediately. Thus integral action rarely used alone, it is generally used in combination with proportional and derivative composition PI or PID controller.
PI and PID controllers overcomes the disadvantages of both simple proportional control with a steady-state error, avoiding the slow response simple integral adjustment, dynamic and had bad, it is widely used.
If the controller has integral action (e.g. a PI or PID control), can eliminate the steady state error integrating step input, then the scaling factor may be adjusted to be smaller.
If the points too strong (i.e., the integration time is too small), each corresponding to the angle trim potentiometer value is too large, the dynamic performance of the cumulative effect of system output will deteriorate, overshoot is increased, so that the system does not even stable. Integral action is too weak (ie, the integration time is too large), then eliminate the static error is too slow, the value of the integration time should be made moderate.
4. Derivative action
The rate of change of error is differential error, the quicker the error changes, the greater the absolute value of the differential. The error increases, the differential is positive; when the error is reduced, which is a negative differential. Differential Differential error proportional part of the controller output, reflecting the trend in controlled variables change.
Experienced operator when the temperature rises too fast, but has not yet reached the set value, depending on the temperature change of trend, a premonition that the temperature will exceed the set value, overshoot. Thus regulator angle potentiometer, heated in advance to reduce the current. This is equivalent to a moving target when soldiers shooting from afar, taking into account the time the motion of bullets, you need a certain amount as advance.
2 step response curve of FIG.
FIG 2 c (∞) is the controlled quantity c (t) or steady state value controlled amount of a desired value, the error e (t) = c (∞) - c (t). Start rising phase of the process in Figure 2, when the amount has not been accused of exceeding its steady-state value. However, since the error e (t) decreasing, and the differential portion differential controller output error is negative, the controller output is reduced, corresponding to a given braking effect in advance, the amount charged to impede rise, so overshoot can be reduced. Therefore, differential control and forecasting has advanced features, has not yet appeared before the overshoot can be given control action in advance.
Oscillation closed loop control system and even the root cause of instability is greater lag factor. Because the error differential term can predict trends change, this "leading" role can counteract the effects of lag factors. Suitable derivative control action may cause overshoot decreases, the stability of the system.
For large hysteresis characteristic of the controlled object, if the effect is not satisfactory PI control, differential control can be considered to increase, in order to improve the dynamic characteristics of the system in the adjustment process. If the differential time is set to 0, the derivative part will not work.
Differential time and derivative action is proportional to the strength, the larger the derivative time, the stronger the derivative action. If the derivation time is too large, rapid changes in the error, response curve may be a "glitch."
Differential control is to reduce the disadvantage of interference noise-sensitive, allowing the system to suppress interference. This could be part of the filter increasing the inertia differential portion.
5. The sampling period
PID control routine is performed periodically, the cycle period is called the sampling performed. The smaller the sampling period, the sampled values can reflect changes in the analog. But the operation is too small will increase the workload of the CPU, the difference between two adjacent samples of little change, will make the derivative part of the PID controller output close to zero, so it should not be made too small sampling period.
Shall ensure that the amount charged at the time of rapid change (such as rising phase of the startup process), to have a sufficient number of sampling points, sampling points will not because too little loss of important information is collected analog in.
6. PID parameter adjustment method
When tuning PID controller parameters, it can be based on qualitative relationship between the parameters and steady-state performance and the dynamic performance of the system controller, a method of adjusting the experimental parameters of the controller. Experienced commissioning generally can quickly get satisfactory results debugging. The most important in debugging problems when the system performance is unsatisfactory, know which parameter adjustment, this parameter should be increased or decreased.
To reduce the required tuning parameters, may be employed first PI controller. To ensure the safety of the system, more conservative set of parameters should start commissioning, such as scaling factor not too big, not too small integration time, in order to avoid system instability or abnormal conditions of excessive overshoot occurs. Gives a signal given step, the amount charged in accordance with the output waveform of the system performance information can be obtained, for example, overshoot and settling time. PID parameters should be based on the relationship between the system performance, iteratively adjusting the PID parameters.
If the amount is too large overshoot step response, after several oscillation to stabilize or simply unstable, the scale factor should be reduced, increasing the integration time. If you do not overshoot step response, but the amount charged rises too slowly, the transition process is too long, it should be in the opposite direction to adjust the parameters.
If slower to eliminate the error, the integration time can be suitably reduced, to enhance the integral action.
Iteratively adjusting proportional coefficient and integration time, if the overshoot is still large, may be added to the differential control, differential time is gradually increased from 0, the controller repeatedly adjusting proportional, integral and derivative parameters portions.
In summary, the commissioning of PID parameters is an integrated, process the parameters influence each other, several attempts actual debugging process is very important and necessary.
7. Experimental verification
S7-300 PLC experiments using PID control function block FB 41, the controlled object by the two inertia series, whose time constants are 2s and 5s, a scale factor of 3.0. Trend display man-machine interface for a given curve and the output of the closed loop response curve.
The author of this excerpt from the log in the "sense of the PID parameters tuning method" (see Annex) "automation" magazine in 2010 published the first five, the paper gives the experimental results demonstrate the PID controller parameters of the proposed tuning method.
http://blog.gkong.com/liaochangchu_117560.ashx
first term in parentheses is a proportional term, the second term is an integral term, the third term is a derivative term, just in front of a coefficient. In many cases, only need to use the discrete time, the control can be turned into
the front of each item has coefficients that are needed to experiment to try and determine, for convenience, these coefficients unified look:
this to see a lot clearer, and each item in front of proportion, differentiation, integration has a coefficient and discrete formula, it is suitable programming.
Talking about this, the principles and methods of PID say finished, and the rest is practice. In true engineering practice, the most difficult is to determine if the coefficient of three items, which requires a lot of experiments and experience to decide. Through trial and correct way of thinking, you can select the appropriate coefficient to achieve good control.
https://blog.csdn.net/qq_25352981/article/details/81007075
