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If it only goes down in all directions, he has arrived at a summit.The Twiddle algorithm is used for auto tuning of PID parameter. First of all, parameters can be tested with a manual tuning with a potentiometer. Auto Tuning Pid Arduino Kit Tune a single-loop PID controller in real time by injecting sinusoidal perturbation signals at the plant input and measuring the plant output during an open-loop experiment. Powered by Create your own unique website with customizable templates.
Auto-tune is a common feature for standalone PID temperature controllers, as tuning a temperature control loop can be a very time consuming effort as process feedback is usually very slow in many applications so it's hard/fustrating/timeconsuming to manual tune such controllers. Dr.Abdul-Kareem Z. Mansoor, Dr.Thair A. Salih, Mohamed Y. Hazim, “Self-tuning PID Controller using Genetic Algorithm”, Iraqi Journal of Statistical Science (20) 2011 Jin-Sung Kim, Jin-Hwan Kim, Ji-Mo Park, Sung-Man Park, Won-Yong Choe and Hoon Heo, “Auto Tuning PID Controller based on Improved Genetic Algorithm for Reverse Osmosis Plant. From what I remember when I was designing PID, the proportional gain was usually less than 0.01 for me.(That being said it depends on the application) I don't know about arduino auto-tuning but you can tune your variables using matlab, transfer function of the system or using Nyquist plot.
You don’t want to manually tune the PID gains of your motor controller anymore? Well, use genetic algorithms! To fully understand “how does genetic algorithms work?”, I decided to build a small demonstrator/simulator of an auto-tuned PID controller using a genetic algorithm.
Let’s assume the following system:
The output of this system is an angular velocity for a given reference value as input. The angular velocity of the shaft of the motor should be as precise as possible. To ensure this, the feedback sensor measure the actual rotational speed of the shaft. The measured speed is substracted from the reference value and give the error value. The error value feed the PID controller which compute the correction factor. The PID controller consists of three gains:
- Proportional : the actual error is multiplied by the Kp gain.
- Derivative : the derivative error is multiplied by the Kd gain.
- Integral : the integral error is multiplied by the Ki gain.
The main problem is to find the value of each gain. Those values should optimise 3 characteristics : stability, accuracy and response time. First and foremost, let’s try to simulate a motor.
The motor can be modeled as a 2nd order low-pass filter. In the Laplace space, its transfer function is:
For simulation purpose, this continuous transfer function must be sampled. Therefore, the bilinear transform (aka Tustin’s method) should be used in order to find the respective digital filter. The bilinear transform aproximate . Applying this transform on the continuous transfer function gives:
Well, the hard work is done! The inverse Z transform leads to the following output equation:
The coefficients C1, C2, C3, C4 and C5 are computed according to the transfer function found on this page. To make it simple, I also used a fixed sampling period (1ms).
Now we are ready to implement the filter! For further details, please have a look to https://github.com/Kev-J/PID-autotune/blob/master/src/DummyMotor.cpp.
The digital PID formula used in this project is as follow:
With y(n) the output function and x(n) the input function. Let’s try to find the best Kp, Kd and Ki gains thanks to a genetic algorithm.
Basically, a genetic algorithm is inspired by natural selection.
Diagram of the genetic algorithm used in this project.
Arduino Pid Autotune
On this project, each “genome” have three “genes” : Kp, Ki, Kd. The genetic algorithm try to find the best genome, thus, the best PID controller by following these steps:
- First and foremost, the population of genome is generated randomly. The genes are bounded to some user defined minimum and maximum limits.
- Each genome are evaluated by the fitness function. This function simulate a closed loop containing the PID controller and the motor. The fitness ratio is computed by the squarred error.
- The population is sorted according to the fitness function output : the fitness ratio.
- If the EliteNumber variable is greater than zero, then the EliteNumber best genomes are copied to the next population.
- As in natural selection, 2 parents are selected to give birth to offsprings. The parents are selected according to there fitness ratios.
- The arithmetic crossover operator generates offspring from pairs of parents by mixing their genes. All offspring’s genes are generated by choosing a random point between the first parent’s genes and second parent’s genes.
- In order to add more “random” to the genetic algorithm’s exploration, a gaussian mutation operator is applied on the new generated offspring.
- Finally, the offspring is added to the next population.
- The algorithm iterate until the user decide to stop it.
Please note that the crossover and mutation operator are applied with a crossover/mutation probability. If crossover does not occurs, the parents are simply copied in the next population.
Here is a short video of the program:
Wanna give it a try? Please have a look at https://github.com/Kev-J/PID-autotune
Arduino Pid Motor
Do not hesitate to contact me for mistakes/bugs report.
Pid Auto Tuning Algorithm
- Dr.Abdul-Kareem Z. Mansoor, Dr.Thair A. Salih, Mohamed Y. Hazim, “Self-tuning PID Controller using Genetic Algorithm”, Iraqi Journal of Statistical Science (20) 2011
- Jin-Sung Kim, Jin-Hwan Kim, Ji-Mo Park, Sung-Man Park, Won-Yong Choe and Hoon Heo, “Auto Tuning PID Controller based on Improved Genetic Algorithm for Reverse Osmosis Plant”,World Academy of Science, Engineering and Technology Vol:2 2008-11-28