Page 32

the rest of the system dynamics. It was uncertain if the suggested control-scheme would be stable during these conditions. Instead a very simple extremum seeking control scheme was devised based on changing the control-signal in steps and observing the system response after the transients had settled. 3.4


The control algorithm had to fulfil a list of basic demands. •

It had to be able to find the optimum and follow it

It had to not overshoot the optimum too much

It had to be easy to explain to people with no background in control

It had to be simple to implement

A number of extremum-seeking algorithms was considered. However, since the shape of the relation between the control-signal and the output could vary (see Figure 6, page 12) methods like Newthon-Rapsons and similar methods risked overshooting the the optimum too much. Instead a fixed-step based method was used. This method is called the stepping method (Ma 1997, 10). The algorithm (Fig. 14) was based on two parameters, the step size of the control-signal  u and the time delay between steps  t. Initially the control-signal u was set to a starting guess based on a priori information. After the time period  t the controlled variable y was stored and the controlsignal was changed to u 1=u 0 u . After each following time period of the length  t, the following happened. First the difference in the controlled variable  y= y n − y n−1 was computed. Then the sign of  u was reversed if  y was negative,  u=sign y⋅ u . The control signal was updated by u n1=u n u and the value of the controlled variable was stored until the next iteration.