Elmo HARmonica, HARSFEN0602 software manual 202, Automatic Controller Gain-Scheduling

ElmoHARSFEN0602HARmonicaSoftwareManual PRELIMINARYDRAFT

Table 15-3: Programming sets of controller parameters for gain schedulilng

Only subset the controller parameters can be schedualed.

The KG[] parameters can program sets of KP,KI gains, as well as one scheduled double-lead block at the high order filter.

The other elements the high order filter cannot be gain scheduled.

The scheduling is automatic for GS[2]=64.

GS[2]=0 selects the controller parameters of KP[2],KI[2],and KP[3].

For other values of GS[2], the value of GS[2] selects directly which of the available sets of controller parameters is used.

Example:

If GS[2]=1, the proportional gain of the speed loop will be SpeedKpTable[1].By Table 15-3, SpeedKpTable[1]=KG[64].

202

15.6Automatic Controller Gain-Scheduling

The speed reference controls the controller gain scheduling. The goal of the algorithm is to decrease the gains when the speed is low, since when speed is low, large delay is added to the encoder measurement, forcing low bandwidth.

The gains are scheduled according to the reference speed. If the desired speed is high, then the encoder data is updated at high rate, so that the speed sensing delay will be low. If the desired speed is low, then encoder pulses shall be slow. For example, suppose that a speed of 200 count/sec is required. Then we have a new encoder count once per 5 msec. The calculated speed will have an average of 2.5msec delay that may kill the stability of the control algorithm. For that reason, if the speed is low, the controller bandwidth must be narrowed, so that the extra sensing delay becomes tolerable.

The speed command is filtered, and the filtered value of the speed command serves to fetch the relevant controller scheduled parameters, KP and KI and some of the advanced filter parameters, from a table.

The filtering is required to avoid abrupt changes of controller parameters, since abrupt changes can spoil the guaranteed stability of the gain-scheduled controller (Assuming that each of the selection sets of speed controller parameters is stable controller for its goal speed)

The speed range where the scheduling is effective is about 0..20000 count/sec.

The tabulated gains are not tabulated linearly by the commanded speed, since the dependence of the parameters in the speed is very nonlinear. The controller parameters are very sensitive to the command speed about the zero speed (At zero speed the feedback delay approaches infinity). Close to the upper end of the table, at about 20000 count/sec, the controller parameters become insensitive to the speed. For this reason, the speed command does not index the gains table directly. Instead, the parameter tables are indexed by a nonlinear, monotone, function of the commanded speed. This indexing function is tabulated in the vector SpeedIndexTable(0:63).

The actual parameter indexing process goes as follows:

Saturate speed command	X = max(	speed reference		,20000 count/sec)
Filter commanded speed.	Y (m + 1) = β ⋅ Y (m) + (1 − β )X
Note that the filter does not	where
respond symmetrically to rising
	GsFilterUpGain, if		X ≥ Y (m)
and falling speed commands.
	β = GsFilterDnGain, if		X < Y (m)
High-speed commands are
responded immediately, for swift
response, where as low speed