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PID regulator understanding and application

Abstract: PID is a proportional, integral and differential for short, PID control difficulty is not programmed, but the parameter controller tuning. Tuning is key to correctly understand the physical meaning of the parameters, PID control principle can manually control the furnace temperature for employer to understand. Read this article does not require advanced mathematical knowledge.

PID is a proportional, integral and differential short, the difficulty is not programmed PID control, but the parameters of the controller tuning. Tuning is key to correctly understand the physical meaning of the parameters, PID control principle can manually control the furnace temperature for employer to understand. Read this article does not require advanced mathematical knowledge.

1. Proportional control

Experienced operator manually control the electrical heating furnace furnace, you can get a very good quality control, PID control and manual control of the control strategy has a lot of similarities.

The following describes how to use the proportion thinking the operator to manually control the furnace temperature control electric furnace. Suppose that the furnace temperature thermocouple detection with digital instrument display temperature. In the control process, the operator reads the oven with your eyes, and given value compared with the furnace temperature to obtain the error value of the temperature. Then hand operation potentiometer, adjust the heating current furnace temperature stayed in the neighborhood for a given value.

The operator know the approximate location of the furnace temperature stabilized at a given value of the potentiometer (we called it the position L), and then the temperature error value adjusted according to the angle control potentiometer heating current. Furnace temperature is less than a given value, the error is positive, based on the L position potentiometer clockwise increases the corner to increase the heating current. When the oven temperature is greater than a given value, the error is negative, based on the L position potentiometer counterclockwise to reduce the angle and make the difference between angular position of the error is proportional to L. The control strategy is proportional control, that portion of the error is proportional to the ratio of the output of the PID controller.

There are various closed loop delay effect. For example there is a greater time delay adjustment potentiometer after corner, to a temperature rise to a new steady state value corresponding corner. Because there is a delay factor can not be seen immediately after the adjustment potentiometer adjust the effect of the corner, so the closed-loop control system adjusts the difficulty is mainly due to the delayed effect of the system.

If the scale factor proportional control is too small, i.e., adjusted potentiometer L angular position difference is too small, inadequate regulation, the system output changes slowly, to adjust the total time required is too long. If the scaling factor is too large, that is, after adjusting the angle and position potentiometer L of difference is too big, too strong adjustment efforts, will result in adjusted too far, even the temperature fluctuated back and forth shocks.

Increasing the scale factor to make the system responsive, adjust the speed, and can reduce steady-state error. But the scale factor over the General Assembly so that overshoot increases, increase the oscillation frequency regulation time extends the dynamic performance deteriorates, the scale factor is too large even make the closed-loop system unstable.

A simple proportional control is difficult to ensure regulate consist entirely eliminate errors.

2. Integral control

Integral PID controller corresponds to the area (shown in gray section) and axes surrounded error curve in Figure 1. PID control program is performed periodically, the cycle execution is called the sampling period. A computer program used in Figure 1 of each rectangular area and to approximate the exact integral figure TS is the sampling period. Figure 1 schematic integration operation

Each time PID operation, based on the integral value of the original, adding a value to the current error ev (n) is proportional to the small parts. When the error is negative, incremental integration is negative.

When manually adjust the temperature, the equivalent of integral control error value based on the then periodically trimming potentiometer angle, angle increment with each adjustment value is proportional to the time error. When the temperature is lower than the set error value is positive, the integral term is increased, so that the heating current increases, the integral term decreases and vice versa. So as long as the error is not zero, the output will be because of the integral role of the controller and constantly changing. Integral regulation "direction" is correct, the integral role of reducing the error term. Not until the system is stable, then the error is always zero, the proportion of part and derivative parts are zero, the integral part of it does not change, and exactly equal to the steady-state output value of the controller is required, corresponding to the temperature control system angular position potentiometer L. Therefore the role of the integral part is to eliminate the steady-state error and improve control precision, integral action is usually necessary.

Integral proportional integral part of the error in the output of the PID controller. Because the integration time TI in the denominator of the integral term, TI is set smaller, the integral term, the faster, the stronger the integral action.

3. PI control

Controller output and the accumulated value of the integral term is proportional to the current error value and the last previous error value, and therefore the integral role itself has serious hysteresis characteristics, unfavorable stability of the system. If the coefficient of the integral term is set to be good, its negative effect is difficult to itself quickly corrected by the integral action. The proportional term without delay, as long as the error appeared, the proportional part will immediately work. So integral action rarely used alone, it is generally used in combination with the proportional and derivative composition PI or PID controllers.

PI and PID controller only overcome the simple ratio adjustment steady-state error shortcomings, and avoid the simple integral control response is slow, dynamic and had bad, so it is widely used.

If the controller has integral action (such as using PI or PID control), integration can eliminate the steady-state error to a step input, then you can adjust the scale factor to be smaller.

If the points too strong (ie integration time is too small), the equivalent of every trimmer angle is too large, the dynamic performance of their cumulative effect causes the system to deteriorate output overshoot increases, and even the system does not stable. Integral action is too weak (ie the integration time is too large), then eliminate the steady state error is too slow, the value of the integration time should be made affordable.

4. Derivative action

Differential rate of change of the error is an error, quicker the error changes, the greater the absolute value of its derivative. When the error increases, the differential is positive; when the error is reduced, the differential is negative. Differential proportional to the derivative component of the controller output of the error, reflecting the controlled volume trends.

Experienced operator when the temperature rises too fast, but has not yet reached the set value, depending on the temperature trends, premonition temperature will exceed the set value, overshoot. Then adjust the potentiometer corner, reduce advance current heating. This corresponds to a moving target when soldiers firing from afar, taking into account the time the motion of bullets, requires a certain amount as advance.

Figure 2 c (∞) is the amount charged c (t) of the steady-state value or expected value of the amount charged, the error e (t) = c (∞) - c (t). Raising stage of the process in FIG. 2, when the amount has not been charged with exceeding its steady state value. But because the error e (t) decreasing, the derivative part of the differential and the controller output error is negative, reducing the output of the controller, the equivalent of a braking action given in advance, in order to hinder the amount charged rise, it is possible to reduce the overshoot. Therefore, the differential control features with an advanced forecasting, has not yet appeared before the overshoot can be given in advance to control action.

Oscillation closed loop control system that the root cause of instability even greater lag factor. Because the differential term trends can be forecast error, this "ahead of" the effect may offset the lagging factors. Appropriate derivative control action can reduce overshoot, increase the stability of the system.

For larger hysteresis characteristics of the controlled object, if the PI control is not satisfactory, you can consider increasing the differential control in order to improve the dynamic characteristics of the adjustment process. If the derivation time is set to 0, the derivative part will not work.

Derivative time is proportional to the strength of the derivative action, 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."

Shortcoming differential control is to reduce interference noise sensitive, the system's ability to suppress interference. This could be an increase in the derivative part of the inertial filter link.

5. The sampling period

PID control program is performed periodically, the cycle execution is called the sampling period. The smaller the sampling period, the more samples can reflect changes in analog. But the operation is too small will increase the workload of the CPU, the difference between two adjacent samples is almost no change, will the derivative part of the PID controller output is close to zero, so it should not be made too small sampling period.

Should ensure the rapid changes in the amount charged (for example during startup of the rising phase), to have a sufficient number of sampling points, sampling points will not because too little amount of lost simulations were collected important information.

6. PID parameter adjustment method

When tuning PID controller parameters, based on the qualitative relationship between the parameters and the system dynamic performance and steady-state performance of the controller between the experimental method to adjust the parameters of the controller. Experienced commissioning staff can quickly get general satisfactory debugging results. In commissioning the most important issue is when the system performance is not satisfactory, adjust know which one argument, which should be increased or decreased.

In order to reduce the need for tuning parameters, you can first use PI controller. To ensure the safety of the system, set more conservative parameters should start in debugger, such as scale factor not too big, not too small integration time in order to avoid system instability or excessive overshoot of unusual circumstances. Give a step for a given signal, the output waveform of the controlled amount of available system performance information, such as overshoot and settling time. Relations should be based on PID parameters and system performance, repeated PID parameter adjustment.

If the step response overshoot too, after several oscillation to stabilize or simply unstable, the scale factor should be reduced, increasing the integration time. If the step response does not overshoot, but increased the amount charged is too slow, too long transition period, should be in the opposite direction to adjust the parameters.

If you eliminate the error rate low, it can reduce the integration time, enhance the integral action.

Iteratively adjusting the proportional coefficient and integration time, if the overshoot is still larger, you can add differential control, differential time increases from 0, repeatedly adjust the controller proportional, integral and differential parameters section.

In short, debugging PID parameter is a comprehensive process of mutual influence of each parameter, the actual process of debugging multiple attempts are very important and necessary.