Using genetic algorithm for tuning controllers

Question

I've read some papers for controlling nonlinear systems (e.g. nonlinear pendulum). There are several approaches for targeting nonlinear systems. The most common ones are feedback linearizaing, backstepping, and sliding mode controllers.

In my case, I've done the theoretical and practical parts of controlling nonlinear model of a simple pendulum plus other manipulators problems in C++. For the pendulum, I've utilized a backstepping controller for solving the tracking task for the angular displacement and velocity. The results are

$$ \ddot{\theta} + (k/m) \dot{\theta} + (g/L) \sin\theta= u $$

where $m=0.5, k=0.0001, L=.2$ and $g=9.81$.

The results are good. However, tuning the controller is time consuming. The majority of papers use genetic algorithms for tuning their controllers such as PD, PID, and backstepping controllers. I'm clueless in this field and I hope someone sheds some light on this concept, preferable if there is a MATLAB sample for at least controlling a simple pendulum.

So far I've designed a simple GUI in C++/Qt in order to tune the controller manually. In the below picture, the response of the controller for step function.

Answer 1

Using evolutionary methods (GA is one of them) for parameter tuning is indeed a common method [1] in the control domain. Especially for non-linear systems, the analytic solutions for optimal parameters can be difficult to find. Evolutionary methods are one way to efficiently perform a search for near-optimal parameters.

A very successful and universal method that is widely used is CMA-ES. There are a large number of implementations out there, including for MATLAB. I know that pole balancing in its various forms is often used as a benchmark.

Applying the algorithm is usually not that difficult. Rating the performance of your result - this is called the fitness function in EA - is usually the most involved part.

[1] P.J Fleming, R.C Purshouse, Evolutionary algorithms in control systems engineering: a survey, Control Engineering Practice, Volume 10, Issue 11, November 2002, Pages 1223-1241, ISSN 0967-0661, http://dx.doi.org/10.1016/S0967-0661(02)00081-3.

Answer 2

Genetic algorithms are a machine learning technique to remove the need for a user to 'fine tune' a system, and instead allow a computer to figure out how to tune the system. The benefits of this approach are that it frees up the researchers/users time and often can lead to a system that is tuned better than what the researcher/user would have been able to achieve themselves.

The general idea of using a genetic algorithm would follow some basic control flow as follow:

Create_X_Number_Of_Random_Controllers()
while (Not_Yet_Satisfied_With_tuning)
    Score_Each_Controller_Based_On_Performance()
    Remove_Lowest_Performing_Controllers()
    Create_New_Controllers_By_Mixing_Best_Performers()
    Add_Slight_Randomness_For_Evolution()
Display_Top_Performer()

The best example I can easily show of this principle in practice is this 'game' that uses genetic evolution to design vehicles that are capable of driving over a course. The same idea applies to any system you want to fine tune without having to actual do any tuning yourself. Example: http://rednuht.org/genetic_cars_2/

Answer 3

I am confused by what you are calling a genetic algorithm. The PD, PID, etc., controllers are not heuristic nor stochastic methods, and they are not based on evolutionary algorithms. They are, instead, deterministic algorithms intended to allow placement of poles and zeroes of a system response to provide desired performance (error minimization, speed of response, settling time, stability, and disturbance rejection). A good learning reference, in my opinion, is Kuo's Automatic Control Systems book. You can find a less rigorous treatment in Raven's Automatic Control Engineering book.