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This article mainly explains "what is cascade PID". The content of the explanation is simple and clear, and it is easy to learn and understand. Please follow the editor's train of thought to study and learn "what is cascade PID".

What is cascade PID?

What is cascade PID? As the name implies, there are two PID connected in series. The following is an example of a double closed loop. The outer ring is the position ring, the inner ring is the speed ring, and the final actuator is the motor, which produces the speed and position. The specific block diagram is shown below.

Of course, the actuator can also be a quad, and the overall process is as follows:

Given the corresponding position height in the outer ring, the output of the outer ring PID is the expected value of the inner ring PID.

The output of the inner ring PID will produce the corresponding throttle size, and eventually the aircraft will produce a rising speed.

The feedback value of the inner ring is the speed, and the corresponding speed is controlled to reach the expected value of the speed required by the outer ring.

Finally, the outer ring reaches the desired position.

Maybe it's a little abstract here. All right, let's go on to refine the hardware details.

The algorithm control of PID is actually a kind of control without system model, and the system can be debugged according to the parameter experience.

But the model of the actual physical object has been determined a long time ago, and the physical meaning of the input and output of PID will change according to the actual controlled object.

In other words, the input of PID is basically related to the feedback amount of the system, and the actual amount of feedback is determined from the very beginning because of the system.

Inner ring and outer ring

If the outer ring is the cause, then the inner ring is the effect. Everything has cause and effect.

For example, the three rings of the servo controller:

Position ring

Speed ring

Current ring

The change of the outer ring will directly lead to the change of the inner ring, and the inner ring is the key to directly lead to the change of the actuator. If the aircraft is still used as an example here, for the entire four-axis flight system.

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We determine the output torque of the motor by controlling the current of the motor.

Torque and load together determine motor speed

The rapid rotation of the propeller produces the lift of the aircraft, which also determines the speed of the rise.

Finally, it also leads to the change of the position of the aircraft.

This is the whole control process.

If only a single-loop PID is used to control the system, can the desired position be achieved in a given system expectation?

The answer is yes.

So what's the point of cascading PID?

The answer is yes.

Let's imagine if we simply use single-loop PID to control the system.

Let's take a look at the PID system block diagram of the single ring.

We set a height and want the aircraft to reach the expected altitude, so the feedback value of the system is only the position.

So at what speed does the aircraft fly? With what kind of acceleration to start? We can not effectively control the speed of the aircraft, let it quickly reach the desired position, the specific position curve is shown in the following figure

In fact, it is not difficult to understand, because the initial height difference is very large, so the value of PID calculation output is very large, so the initial speed will be very large. As the aircraft gets closer and closer to the desired position, the deviation becomes smaller and smaller, the PID output decreases gradually, so the speed decreases gradually.

In fact, most of the time, PID is only the bottom layer, called inner loop PID, through which you can stabilize a system, optimize dynamic characteristics, and then nest other algorithms on the outer layer. Of course, it is also common for control systems with several layers of PID outside. That is, the cascade PID system we introduced, as follows

The essence of the controller is the functional mapping relationship between input and output.

In fact, from this point of view, PID is usually suitable for low-order linear time-invariant systems, on this basis, it is limited to three coefficients.

The whole system also needs to change according to the specific system, some systems actually only need two coefficients (such as PD or PI), and even some systems only need one (such as P). Therefore, in the above system, the outer ring only needs to use the P link, and the speed curve can be planned.

Suppose the speed curve planning is used here, because the speed of the aircraft can be controlled.

So we expect it to reach its maximum speed as soon as possible, so it accelerates uniformly from the beginning, begins to rise at a uniform speed after reaching the maximum speed, decelerates evenly when it is about to reach the desired position, and finally hovers to the target position.

Then the overall position change curve is as follows

In other words, the output of the outer ring PID is used as the input of the inner ring PID

The following is the pseudo algorithm of single-loop PID

Previous_error: = 0 / / Last deviation integral: = 0 / integral and / / cycle / / sampling period is dt loop: / / setpoint set value / / measured_value feedback value error: = setpoint − measured_value / / calculate the deviation integral: = integral + error × dt / / calculate the integral accumulation and derivative: = (error − previous_error) / dt / / calculate the differential Output: = Kp × error + Ki × integral + Kd × derivative / / calculate the PID output previous_error: = error / / save the historical deviation required for the next sampling wait (dt) / / wait for the next goto loop

So what do you need to do to change to cascade PID?

The specific pseudo algorithm is as follows

Previous_error: = 0 / / Last deviation integral: = 0 / / integral and previous_error_inner: = 0 / / Inner ring PID Last deviation integral_inner: = 0 / / Inner ring PID integral and / / cycle / / sampling period is dt loop: / / outer ring calculation / / setpoint outer ring set value / / measured_value outer ring feedback value error: = setpoint ring measured_value / / calculate the deviation integral: = integral + error × dt / / calculate the integral accumulation and derivative: = (error − previous_error) / (n*dt) / / calculate the differential output: = Kp × error + Ki × integral + Kd × derivative / / calculate the PID output previous_error: = error / / to save the historical deviation required for the next sampling = output / / the PID output of the outer ring is assigned to the PID input wait (n*dt) of the inner ring / / wait for the next sampling goto loop loop_inner: / / setpoint_inner inner ring set value / / measured_value_inner inner ring feedback value error_inner: = setpoint_inner ring measured_value_inner / / calculate the deviation integral_inner: = integral_inner + error_inner × dt / meter Calculate the integral cumulative sum derivative_inner: = (error_inner − previous_error_inner) / dt / / calculate the differential / / calculate the PID output output_inner: = Kp_inner × error + Ki_inner × integral_inner + Kd_inner × derivative_inner previous_error_inner: = error_inner / / save the historical deviation wait (dt) / required for the next sampling / wait for the next sample goto loop_inner

Here, the relevant variables of the inner ring PID are suffixed _ inner,loop is the outer ring PID for periodic control, and loop_inner is the inner ring PID for periodic control, the two are independent of each other, and the output of the outer ring PID can be assigned to the input of the inner ring PID.

In case of interference, the inner loop controller is first coarse tuned, and the outer loop controller is further fine tuned.

Therefore, the control effect must be better than the single-loop PID control system.

In structure, the cascade control system has only one more inner loop than the simple control system, but the practice has proved that for the same disturbance, the control quality of the cascade control system is incomparable to the simple control system.

PID parameter

The parameter tuning of cascade PID basically follows from the inside to the outside, first setting the parameters of the inner ring PID, and then setting the parameters of the outer ring PID.

According to the empirical method to debug the parameters, generally speaking, the proportional parameter P of the inner ring is set first, and then the integral parameter I is adjusted. The differential parameter D can be sorted out for the dynamic characteristics, and of course, the case of saturation needs to be dealt with.

In short, you can observe the input and output curves.

So what kind of response curve is good?

Generally speaking, there is no optimal, for example, some systems have restrictions on speed and acceleration, some systems must not have overshoot and so on, and some systems respond as quickly as possible. So again, I don't want you to think, I want me to think that fit is the best.

Thank you for your reading, the above is the content of "what is cascade PID", after the study of this article, I believe you have a deeper understanding of what is cascade PID, and the specific use needs to be verified in practice. Here is, the editor will push for you more related knowledge points of the article, welcome to follow!

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