PID controller calibration link - Solutions - Huaqiang Electronic Network

RF cable can be customized for other specifications

Photocoupler

The primary task of any closed-loop control system is to stabilize (stable), fast (fast), and quasi (accurate) response commands. The main task of PID tuning is how to achieve this task.

Increasing the proportionality factor P will speed up the response of the system. It acts on the output value faster, but it is not stable at an ideal value. The bad result is that it can effectively overcome the influence of the disturbance, but there is a residual error. Excessive proportional factors will cause the system to have a large overshoot and cause oscillations, which will deteriorate the stability. The integral can eliminate the residual on the basis of the ratio, and it can correct the error and reduce the steady-state error for the system with accumulated error after stabilization. The differential has a leading role. For the control channel with capacity lag, the differential participation control is introduced. When the differential term is set properly, it has a significant effect on improving the dynamic performance index of the system, which can reduce the system overshoot and stabilize. Increased in sex and reduced dynamic error.

In summary, the response speed of the P-proportional control system is fast acting on the output, just like "now" (now working, fast), the accuracy of the I-integral control system, eliminating the cumulative error in the past, like " In the past "(clearing past grievances, returning to accurate orbits), the stability of the D-differential control system has an advanced control effect, like "future" (looking forward in the future, taking precautions and stabilizing to develop). Of course, this conclusion cannot be generalized. It just wants beginners to understand the role of PID more quickly.

In the adjustment, the task you have to do is to balance the adjustment between these three parameters in the case of the system structure, to achieve the best control effect, to achieve a stable and accurate control characteristics.

The proportional control can adjust the deviation quickly, timely and proportionally, and improve the control sensitivity, but there is static difference and the control precision is low. The integral control can eliminate the deviation, improve the control precision and improve the steady-state performance, but it is easy to cause shock and overshoot. Differential control is a kind of advanced control, which can adjust the system speed, reduce the overshoot and improve the stability. However, the time constant is too large to introduce interference, and the system impact is large. If it is too small, the adjustment period is long and the effect is not significant. The proportional, integral and differential control cooperate with each other, and the parameters of the PID regulator, namely the proportional coefficient KP, the integral time constant Ï„i and the differential time constant Ï„D, can be reasonably eliminated, and the deviation can be quickly, accurately and smoothly eliminated, and a good control effect can be achieved.

Proportional link

The deviation signal e(t) of the control system is proportionally reflected, and once the deviation occurs, the controller immediately produces a control action to reduce the deviation. The system output has a Steady-state error when there is only proportional control.

The smaller the P parameter, the stronger the proportional action, and the faster the dynamic response, the stronger the ability to eliminate errors. However, the actual system has inertia. After the control output changes, the actual y(t) value changes need to wait for a while to change slowly. Since the actual system has inertia, the proportional action should not be too strong, and the proportional action is too strong, which will cause the system oscillation to be unstable. The size of the P parameter should be determined on the basis of the above quantitative calculation based on the system response, on-site commissioning, and the P parameter is usually adjusted from large to small, so as to achieve the fastest response without overshoot (or no overshoot). Good parameters.

Advantages: Adjust the open-loop proportional coefficient of the system, improve the steady-state accuracy of the system, reduce the inertia of the system, and speed up the response.

Disadvantages: With only the P controller, the excessive open-loop proportional coefficient will not only increase the overshoot of the system, but also make the system stability margin smaller or even unstable.

2. The link

The output of the controller is proportional to the integral of the input error signal. Mainly used to eliminate static differences and improve the system's no difference. The strength of the integral action depends on the integral time constant T, the larger the T, the weaker the integral action, and vice versa.

Why should we introduce the role of points?

The output of the proportional action is proportional to the magnitude of the error. The larger the error, the larger the output, the smaller the error, the smaller the output, the zero error, and the output is zero. Since the output is zero when there is no error, the proportional adjustment cannot completely eliminate the error, and it is impossible to bring the controlled PV value to a given value. There must be a stable error to maintain a stable output to keep the PV value of the system stable. This is the so-called proportional effect is the difference adjustment, there is a static difference, the strengthening of the proportional effect can only reduce the static difference, can not eliminate the static difference (static error: static error, also known as steady-state error).

In order to eliminate the static difference, an integral action must be introduced, and the integral action can eliminate the static difference so that the controlled y(t) value finally coincides with the given value. The purpose of introducing the integral action is to eliminate the static difference and make the y(t) value reach the given value and keep it consistent.

The principle of the integral action to eliminate the static difference is that as long as there is an error, the error is integrated, so that the output continues to increase or decrease until the error is zero, the integration stops, the output does not change, and the PV value of the system remains stable. The value of y(t) is equal to the value of u(t) to achieve the effect of no difference adjustment.

However, since the actual system has inertia, the y(t) value does not change immediately after the output changes, and it has to wait for a while to change slowly. Therefore, the speed of the integral must match the inertia of the actual system. The inertia is large and the integral action is Should be weak, the integration time I should be larger, and vice versa. If the integral action is too strong, the integral output changes too fast, which will cause over-integration, resulting in integral overshoot and oscillation. Usually, the I parameter is also changed from large to small, that is, the integral action is from small to large, and the system response is observed to achieve rapid elimination of errors, reaching a given value without causing oscillation.

For an automatic control system, if there is a steady state error after entering the steady state, the control system is said to have a steady state error or a system with Steady-state Error. In order to eliminate the steady-state error, an "integral term" must be introduced in the controller. The integral term versus the error is integrated over time, and as time increases, the integral term increases. Thus, even if the error is small, the integral term increases with time, which pushes the controller's output up so that the steady-state error is further reduced until it equals zero. Therefore, the proportional + integral (PI) controller can make the system have no steady-state error after entering the steady state. The PI controller not only maintains the "memory function" of the integral controller to eliminate the steady-state error, but also overcomes the shortcomings of the reaction insensitivity when the integral control is used alone to eliminate the error.

Advantages: Eliminate steady-state errors.
Disadvantages: The addition of the integral controller will affect the stability of the system and reduce the stability margin of the system.

3. Differential links

It reflects the trend of the deviation signal and can introduce an effective early correction signal into the system before the deviation signal becomes too large, thus speeding up the system's motion speed and reducing the adjustment time. In differential control, the output of the controller is proportional to the differential of the input error signal (ie, the rate of change of the error).

Why introduce a differential effect?

As I have analyzed before, whether the proportional adjustment function or the integral adjustment function is based on the adjustment of the error to eliminate the error, it is post-adjustment, so this adjustment is not bad for the steady state. It must be said that there is a difference, because the disturbance caused by the load change or the change of the given value must wait for the error to occur, and then slowly adjust to eliminate it.

However, the general control system not only has requirements for stability control, but also has dynamic requirements. It usually requires load changes or given adjustments to cause disturbances, and the speed to return to steady state is fast, so the light has proportional and integral adjustment. The effect is not fully satisfactory and a differential action must be introduced. Proportional action and integral action are post-adjustment (that is, adjustment occurs after an error occurs), while differential action is pre-preventional control, that is, when y(t) is found to be larger or smaller, a change is immediately prevented. Control signals to prevent overshoot or overshoot.
The larger D is, the stronger the differential action is, and the smaller D is, the weaker the differential action is. When debugging the system, D is usually adjusted from small to large, and the specific parameters are determined by experiments.

For example, due to the change of y(t) caused by the set value adjustment or load disturbance, the proportional action and the differential action must wait until the y(t) value changes, and the error is small, and the proportional and integral adjustment effects are also small, correcting The ability to make errors is also small, and when the error is large, the proportional and integral effects are increased. Because it is not ideal to adjust the dynamic indicators afterwards. The differential action can start to adjust before the error is generated, and it is controlled in advance, so the timeliness is better, the dynamic error can be minimized, and the overall effect is better. However, the differential action can only be used as a supplement to the proportional and integral control. It can't play a leading role. The differential action can't be too strong. Too strong will also cause the system to be unstable and generate oscillation. The differential action can only be adjusted after P and I are adjusted. From small to big, try to add it a little bit.

The automatic control system may experience oscillation or even instability during the adjustment of the overcoming error. The reason is that there is a large inertia component (link) or a delay component, which has the effect of suppressing the error, and the change always lags behind the error. The solution is to make the change of the effect of the suppression error "advance", that is, when the error is close to zero, the effect of suppressing the error should be zero. That is to say, it is often not enough to introduce only the "proportional" term in the controller. The proportional term is only the amplitude of the amplification error, and the current need to increase is the "differential term", which can predict the trend of error variation. In this way, the controller with proportional + differential can make the control effect of the suppression error equal to zero or even a negative value in advance, thereby avoiding the serious overshoot of the controlled amount. Therefore, for controlled objects with large inertia or hysteresis, the proportional + derivative (PD) controller can improve the dynamic characteristics of the system during the adjustment process. PD control only works during dynamic processes, blocking the constant steady state condition. Therefore, the differential control cannot be used alone under any circumstances.

Advantages: The response speed of the system is faster, the overshoot is reduced, the oscillation is reduced, and the dynamic process has a "predictive" effect.

In the low frequency band, the PI control law is mainly used to improve the system type, eliminating or reducing the steady-state error; in the middle and high frequency bands, the PD law is mainly active, increasing the cutoff frequency and the phase angle margin, and improving the response speed. Therefore, the controller can comprehensively improve the control performance of the system.