Position error controller

Based on the FRF data, a position error (PERR) controller is designed. This bilateral control architecture can be found in for example [32, 47]. The minimum bandwidth must be at least 60 Hz as kinesthetic and proprioceptive force sensing go up to about 30 Hz. As visible in figure 4.13, the PERR controller is based on two individual control loops, one for the master and one for the slave. The rotation of both setups is measured and subtracted from each other. This error is used as setpoint information for the lead/lag control loops. The input to the master controller is inverted to create a reaction force, which has an opposite sign with respect to the slave.

The controller is based on a lead/lag scheme, so as to limit the gain at high frequencies. Experiments have revealed that the lead/lag architecture can be tuned for a bandwidth up to 100 Hz in combination with a TUeDACS and a sample frequency of 1 kHz. To increase robustness, it is limited to 80 Hz. Additional filters, like a low pass filter to deal with high-frequency noise or a notch filter to suppress resonance peaks are not implemented. The scaling factor between master and slave motion is set via the position scaling gain. The force feedback at the master can be disabled via the force feedback off/on switch. The force scaling switch allows to choose two different scaling levels. For the situation as drawn in figure 4.13, the master and slave make use of an identical control algorithm. This means that the two setups have the same servo stiffness. When

0 1 -1 position scaling lead/lag 60Hz slave lead/lag 80Hz master lead/lag 80Hz slave P 60Hz P 80Hz P 80Hz ffw master ffw slave force feedback off/on force scaling master + slave offset master offset slave

Figure 4.13 / Position error (PERR) control architecture with feedforward. The position error between master and slave is used as the input for the master and slave controller. Position scaling and force scaling are implemented.

the end effector of the slave comes in contact with the environment, e.g. a rigid post, then the slave is not able to follow the movement of the master anymore. A position error between the master and slave is the result. This error times the servo stiffness results in the interaction force, which is identical for master and slave.

When the bandwidth of the slave is reduced to 60 Hz, then the slave will have a lower servo stiffness than the master. In this case, the interaction force between slave and environment is smaller than the the interaction force between master and user: the forces are scaled upwards. The scaling ratio depends on the ratio between the two gains (P 60 Hz and P 80 Hz).

The friction is partially compensated via a friction feedforward (FFW) loop (figure 4.13). The direction of rotation is determined via a sign function (-1 or 1) out of the angular velocity of the setup. Depending on the direction of rotation, the amplifier is provided with a positive or negative offset voltage. A friction reduction of 90% is possible without causing limit cycling. As the desired trajectory is not known in advance, there must be first a rotation of the motor shaft before the friction can be compensated. This is in contrast with setpoint based servo control. The offset master block and offset slave block are added to deal with the asymmetric friction level in CW and CCW direction. Furthermore, it is used to compensate for the offset voltage of the amplifier to get an output current of 0 A.

The servo stiffness is determined by measuring the position error after applying a specific load on the end effector. For 80 Hz, it is 6.8 · 103

N/m or 38 Nm/rad, for 60 Hz it is 3.9 · 103

N/m or 22 Nm/rad. Also some initial measurements are done to reveal the forces during operation of the setup. Figure 4.14 gives the results of one of these

measurements. Successively a spring with a stiffness of 3.0 · 102

N/m, 1.2 · 103

N/m and a rigid post are placed under the end effector of the slave. The first peaks in each series are forces that a user can exert for a long period of time. The last peak in each series is the maximum force. A user can exert this force only for a short period of time.

0 5 10 15 20 25 30 35 40 45 0 2 4 6 8 10 12 14 16 18 time [s] force [N] 3.0⋅102 N/m 1.2⋅103 N/m rigid

Figure 4.14 /Typical forces during operation of the setup. Successively three objects with an increasing stiffness are placed under the end effector of the slave. There is no scaling in force or position between master and slave.

The exerted forces are lower than stated in the requirements. The maximum force can be reduced from 30 to 15 N and the continuous force from 10 to 5 N. For a very compliant environment, it is possible to work with a maximum force of 10 N and a continuous force of 3 N.