"I. history of PID
Before talking about ADRC algorithm, we first review its predecessor: PID algorithm.
H. Nyquist, who was born in Sweden in 1932 and later immigrated to the United States, published a paper and used the graphical method to judge the stability of the system. On this basis, H • w • bode et al. Established a method to design feedback amplifier in frequency domain. This method was also used in the analysis and design of automatic control system.
At the same time, the principle of feedback control began to be applied to industrial processes. In 1936, A. Callender and A. Stevenson in Britain gave the method of PID controller, and since then, the PID algorithm has been formally formed. PID control is a very important control method in automatic control technology. The PID controller decades ago was still mechanical, such as the air pressure controller in Figure 1.
Fig. 1 Mechanical PID air pressure controller
Today, almost all products with "automatic control" capability adopt PID algorithm, ranging from weapons, aircraft and ships to household appliances, IOT equipment, toys and so on. For example, our daily air conditioner uses PID algorithm to control the temperature at our expected value; Mobile navigation accurately analyzes the motion state by PID algorithm; UAV flight attitude is stabilized by PID algorithm. PID is everywhere around us, trying our best to help human beings realize "automatic control". But different from decades ago, with the development of computer technology, today's PID is mostly "soft control", that is, running software control in the processor, and the structure is greatly simplified.
2、 Principle and deficiency of PID
Figure 2 shows the PID speed regulation system of DC motor. No (T) is the desired target speed of the motor, n (T) is the actual speed of the motor, and U (T) is the output voltage of the PID controller. Comparing no (T) with n (T), the deviation value E (T) = no (T) - n (T), which is calculated by the PID controller, outputs the control voltage U (T) to drive the motor to change the speed. When the actual speed is small, i.e. no (T) > n (T), e (T) > 0, the PID controller increases the U (T) output, and the actual speed of the motor will increase; When the actual speed is too high, i.e. no (T)
Fig. 2 DC motor PID speed regulation system
The PID controller is calculated using formula 1. There are three terms on the right of the formula: proportion, integration and differential.
Formula 1
The function of the proportional link is to respond quickly to the deviation. The larger the KP, the stronger the control ability. However, too large KP will increase the overshoot (the amount exceeding the given value). In addition, the proportional link can reduce the static error (the deviation compared with the given value when it is stable), but it can not be completely eliminated. Fig. 3 uses the proportional link to increase the speed of the motor from zero to 2500 R / min. the lifting process is relatively fast, but there is overshoot and static error.
Figure 3 function of scale link
The function of the integration link is to eliminate the accumulated deviation (static error). In the control process, as long as there is a deviation, the output of the integration link will continue to increase until the deviation e (T) = 0, and the output can be stable at a certain value. However, the integration link will reduce the response speed and increase the overshoot. The greater the Ti, the weaker the integral effect. Figure 4 shows that the previous static error is eliminated by adding the integral link on the basis of the proportional link, and the motor tends to 2500 R / min, but another section of overshoot is added.
Figure 4 function of proportional link + integral link
Figure 5 uses the PID link to control the motor. Each link does its duty, the proportional link P quickly increases the speed, the integral link I eliminates the static error, and the differential link D suppresses the overshoot.
Fig. 5 functions of proportional link + integral link + differential link
Although PID is widely used, it has obvious shortcomings. PID response is slow. It needs to wait until the error occurs before compensating the control. If the control force is too large (proportional coefficient Kp), there will be overshoot. If it is too small, the response will be slow. PID is sensitive to environmental changes. For example, when the propeller of UAV rotates at high speed, it is subject to strong compressed air resistance, and the PID force needs to be large to maintain a stable speed. However, at low speed, the air resistance is very small, and the propeller will vibrate and unstable under the strong PID force, so another set of weak PID is required.
3、 The birth of ADRC
Interference, or disturbance, refers to the change of the external environment of the system or the change of the internal characteristics of the system, which ultimately affects the performance of the system. For example, for the propeller of the UAV mentioned above, the air resistance changes with the speed, which affects the stability of the motor speed. This is an external disturbance; When the motor runs for a long time, the temperature rises obviously, and the resistance value of the copper coil increases. The relationship between the original estimated voltage of V and the current of a does not exist, which is an internal disturbance.
Let's assume that if the world is beautiful and there is no internal and external disturbance, the ideal effect can be achieved in any case as long as the PID parameters are adjusted once for any system. But things backfire, disturbance is everywhere, how to achieve "he is strong, he is strong, and the breeze blows the hills; The anti disturbance effect of "the moon shines on the river" has always been the core research work in automatic control engineering.
The auto disturbance rejection control (ADRC) technology was formally and systematically proposed by the late researcher Han Jingqing in 1999 based on the classical PID control theory. His inspiration comes from the guide car (also known as Sinan car), which is a device used to indicate the direction in ancient China. It is different from the compass in using geomagnetic effect. It does not use magnetism. It is a mechanical device that uses the mechanical transmission system to indicate the direction.
The principle is: the guide car with two wheels is driven by manpower, and the differential between the two wheels during steering is transmitted by the mechanical transmission system in the car to bring the wooden man on the motor car to the opposite angle of the steering direction of the car, so that the wooden man on the car indicates the direction. No matter where the car turns, the wooden man's hand always points to the direction set when the guide car starts“ Although the vehicle is transported back, the idea of "manual guide" has been sublimated in ADRC algorithm.
Figure 6 guide car
4、 Principle of ADRC
Fig. 7 is a block diagram of ADRC speed regulation control of DC brushless motor. The core of ADRC has three modules: tracking differentiator, extended state observer and state error feedback control law.
For motor speed control, the input of the tracking differentiator is the target speed; The output is tracking speed and tracking acceleration. The tracking speed is equal to the target speed, and the tracking acceleration is the target acceleration.
The inputs of the extended state observer are: the product of the actual speed, the output voltage U and the coefficient B0; The outputs are observation speed, observation acceleration and observation disturbance respectively. The observation speed is equal to the actual speed, and the observation acceleration is equal to the actual acceleration. The observation disturbance is the total disturbance inside and outside the system. After it is divided by B0, the voltage U0 output by the state error feedback control law is subtracted to obtain the voltage u to the motor.
The state error feedback control law outputs the voltage U0 according to the speed error (tracking speed - observation speed) and acceleration error (tracking acceleration - observation acceleration). If both errors are zero, U0 is zero. The coefficient B0 is a roughly set parameter, where it represents how many V voltages correspond to how many rpm. Regardless of the true relationship between voltage and speed, ADRC only controls according to its own set B0. It believes that the current voltage is u and the speed should be u * B0. If the actual speed is different, the deviation is considered as disturbance (observation disturbance), which may be caused by the change of external resistance or inaccurate estimation of internal parameters of the motor. After dividing the observed disturbance by B0, it is directly compensated to the U output. Therefore, ADRC is capricious. It does not need to specially measure disturbance. "He is cruel to himself, he is evil to himself, and I am really angry.".
In addition, if the system specifies the target velocity and target acceleration at the same time, the tracking differentiator can be omitted and the two quantities can be input directly.
Figure 7 ADRC speed control
5、 Characteristics of ADRC
1. Almost independent of the model
ADRC is applicable to any situation from knowing nothing about the object model to fully mastering the object model. As shown in Figure 7, roughly set the relationship B0 between voltage and speed. Of course, if this relationship can be accurately captured, the work intensity of ADRC will be reduced and the effect will be better. For example, we are studying how to accurately estimate the motor parameters and reconstruct the motor model B0 by using AI Artificial Intelligence neuron technology without injecting additional measurement signals (try not to affect the motor operation), In this way, the performance of ADRC will be further improved.
2. Quick response
Traditional PID control can not compensate the control until the error occurs, while ADRC compensates the observed disturbance to the output at the first time. Moreover, although the differential term D in PID has the prediction function, it only subtracts the error of the last time from the error of this time to obtain a very poor differential result, while ADRC uses the tracking differentiator to accurately track the differential of the target value (the tracking acceleration in Fig. 7) and the differential of the actual value (the observed acceleration in Fig. 7) with the extended state observer, Two subtractions are the exact error differential.
Figure 8 is the motor speed diagram of a product popular in JD. It adopts FOC technology based on PID. The motor keeps accelerating and decelerating. The yellow line is the target speed and the red line is the actual speed. The actual acceleration and deceleration are still very fast, and the tracking effect is OK. This effect is already leading in the industry. Once upon a time, we thought that if we did not change the motor, the effect could not be better.
Figure 8 PID based foc
But one day, as shown in Figure 9, we directly replaced the PID code in FOC with ADRC, and there was an amazing scene. The two lines of target speed and actual speed almost coincide, with almost no overshoot, vibration and static error. Moreover, the acceleration and deceleration are increased by more than 30%, the noise is reduced 2dB and the energy efficiency is increased by 5%!
Figure 9 FOC based on ADRC
3. Ease of use
Although the performance of ADRC was amazing when it was first launched, there are many parameters to be debugged and it is not easy to use. However, with the theory of scaling and bandwidth parameterization, the adjustment of ADRC parameters becomes much simpler. For example, Zhou Ligong's ADRC library can be roughly adjusted as long as the bandwidth of the extended state observer and the bandwidth of the state error feedback control law are adjusted step by step.
4. Flexibility
ADRC is developed under the inspiration of PID. Generally, wherever there is PID, ADRC can be directly replaced.
6、 Application of ADRC
At present, ADRC has been used in many fields, such as hypersonic aircraft, magnetic levitation, superconducting particle accelerator, large radio telescope, tank fire control system, nuclear power plant cooling system, etc., as well as industrial robot, servo motor driver, UAV flight control system, floor sweeping robot, and even website search engine.
Figure 10 hypersonic vehicle
In addition, Zhou Ligong's unmanned electromechanical regulator, industrial motor driver, automobile water pump electric regulator, automobile wind electromechanical regulator, special control chip for brushless motor, multi motor FOC scheme based on NXP i.mxrt, etc. are built with self-developed and efficient ADRC algorithm.
Fig. 11 s32k FOC automotive electric regulator with built-in ADRC algorithm. Read the full text. Original title: ADRC 01: why will ADRC become the successor of PID algorithm for a century?
The source of the article: [micro signal: Zlgmcu7890, WeChat official account: Zhou Li Gong SCM] welcome to add attention! Please indicate the source of the article“
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