NOVEL ADAPTIVE METHOD OF SETTING PARAMETERS FOR MARSIK CONTROL ALGORITHM NOVEL ADAPTIVE METHOD OF SETTING PARAMETERS FOR MARSIK CONTROL ALGORITHM

An advantage of the algorithm is that controlled system identification and special signals introducting is not required. A control error only is calculated to define a new criterion type. The new criterion does nol lead to finding optimization function extremes as usual, so the adaptation goes as a common control on. The new criterion is an oscilation index that specifies the rate of control error and its first derivation cross the zero level [1][2]. The measure-controlled value must be properly filtrated from the high frequency noises that could influence the process of specifying oscilation coefficient negatively.


1.Introduction
An advantage of the algorithm is that controlled system identification and special signals introducting is not required. A control error only is calculated to define a new criterion type. The new criterion does nol lead to finding optimization function extremes as usual, so the adaptation goes as a common control on. The new criterion is an oscilation index that specifies the rate of control error and its first derivation cross the zero level [1] [2]. The measure-controlled value must be properly filtrated from the high frequency noises that could influence the process of specifying oscilation coefficient negatively.

How to change KappaZ adaptively
After analysing the KappaZ's influence on the control process quality, some relationship between KappaZ and the control loop response time has been discovered. It was made possible to either slow down by its decreasing. There is still a problem how to detect whether a process is "too slow" or "too fast".
A block diagram of Marsik algorithm is shown in Fig. 2. The blue line is showing the feedback to change KappaZ adaptively. Marsik algorithm also estimates the global time constant named Tau. Its value can be used to compute the KappaZ's changing time and direction. If the system output reaches the setpoint in time shorter than Tau it is supposed that process is "too fast" and there is a need to damp it by decreasing KappaZ (see Fig. 2 line 1) and vice versa, if the system output is significantly smaller than the setpoint at time KappaZ should be increased to speed the process up (see Fig. 2 line 2).

Simulations
From the set of benchmark systems recommended by Aström [3], three system types were chosen: a system with multiple equal poles, a non-minimal phase system and dead-time system. In the next three figures, performances of Marsik algorithm with and without KappaZ adaptation are depicted and compared to analytically tuned PID. [4]. The green line represents a Pid controller, magenta representing Marsik with adaptation and the blue one the algorithm can be changed in the future to be able to adapt KappaZ even during disturbancies from the steady state.
In Fig. 3 the main difference between On and Off Adaptation is that there are less oscillations and higher stability in the case with adaptation. It is visible how KappaZ changes the process behaviour at the points of red line step changes.
In Fig. 4, decrease of KappaZ in time is to be seen. The reason is that the process is more oscillating and the algorithm is trying  Fig. 5 shows that systems with non-minimal phase are harder to control by Marsik algorithm. Here, the influence of KappaZ to a controlled process can be seen clearly, esp. at points 1, 2, and 3. KappaZ changes the system dynamics, PID proves to perform best in the analytical PID control. Table 1   Table 1 shows that control process with adaptation has value of IAE smaller than process without adaptation in most cases. However smaller value of IAE criterion does not need to be always corespondent to better quality of control. For instance number of oscillations, their magnitude, number of overshoots and moreover, are also important.

Conclusion
It can be claimed that the KappaZ adaptation leads to a better performance at benchmarked systems but its adaptation itself has to be improved to adapt continually at every sample time period. The adaptation under disturbancies can be added as an improvement as well. Marsik algorithm is sensitive to great large changes of the sampling period. Algorithm tests on different systems and carrying out tests with disturbancies is planned and adding a filter for KappaZ adaptation as well. All the improvements may lead to a more robust algorithm insensitive to sampling period values.

Acknowledgment
This work has been supported by the institutional grant FRI 28/2003.