Genetic Algorithm based gain scheduling

We designed a feedforward control law that greatly decreases the load sway of a shipboard crane due to ship rolling. This feedforward control uses measurements of ship rolling angle at each instant. At different operating points the optimal feedforward gain changes while is numerically computable. Here, we endeavor to bring forth the utility of the use of a Genetic Algorithm (GA) based approach to optimize the mapping of feedforward gain in four dimensional space. The process is based on the numerical calculation of the optimal feedforward gain for any rolling angle (rho), and length of the rope (L), and luffing angle (delta(0)). The optimal gain is calculated for a group of points in the working space and then fit a function of order n to these points in a four dimensional space. Our choice for this problem includes real value GA with a combination of different crossover methods. The cost function is the sum of squared errors at selected points and we aim to minimize it. Since moving the load to another location also changes the optimal gain, the new improved gain scheduling further reduces the swinging within the whole working space. GA is a directed serach method and is capable of searching for variables of functions with any desired structure. The major advantages of using GA for function mappings is that the function does not have to be linear or in any specific form.