# Considerations for the Design of a Wheelchair Dynamometer Concerning a Dedicated Braking System
## 2 Materials and Methods
### Measurement Methodology  
An electric drive wheelchair was placed on the test stand to enable measurements. This enabled the generation of drive with the set rotational speed. Figure 4 presents the measurement scheme in the form of a block diagram for the sake of clarity. Measurements were conducted for five different rotational speeds (\(n=72\), \(109\), \(148\), \(184\) and \(226\) rpm). The \(m\) parameter values correspond to the degree of brake release and may be defined in the control programme as a variable. A value of \(m=14\) indicates that the brake is fully released (no braking torque). Values lower than \(14\) indicate the progressive clamping of the brake shoes, thus generating a braking torque \(M_{H}\) (proportional to the set value of \(m\)) that had to be overcome by the wheelchair's electric drive.  
Figure 4: Measurement scheme.  
Figure 3: Design schematics for the brake control system in the wheelchair test stand.  
The measurement algorithm was as follows (see Figure 4): the selected rotational speed of the wheels was set and the brake was released completely (\(m=14\)). During this, the value of the torque was measured for 30 s; afterwards, the parameter value was reduced by \(\Delta m=-0.5\), and then the measurements were once again taken for 30 s. This procedure was repeated until the value \(m=10\) was obtained. Once the measurements for this value were taken, the cycle was reversed and the m value was increased by \(\Delta m=+0.5\). Measurements were subsequently taken cyclically until the value \(m=14\) was once again reached. The hysteresis of the brake system was thus determined by taking measurements during the gradual increase and subsequent decrease in the braking force (the measurements were taken for values \(m=14\) to \(m=10\), and then back to \(m=14\)). This cycle of measurements was then repeated for each of the five planned rotational speeds.  
Up to the value of 10, the brake shoe release was so small that the braking torques generated were higher than the wheelchair's electric drive power, which caused its wheels to stop. This was the final value because, although the brake was able to generate a greater braking torque, the electric drives of the wheelchair were unable to generate a mechanical power of such a high value. The measurements were taken as part of the system presented in Figure 1, using the T22/10 NM torque gauge (Hottinger Bruel & Kjaer GmbH, Darmstadt, Germany) and the HY38-500 incremental encoder (Termipol, Lublinicc, Poland).  
Processing the data involved the smoothing of the signals measured by the encoder and the torque gauge. The 15 measurement points for each brake setting \(m\) and the rotational speed of the wheelchair's wheels \(n\) were defined. The average value of the measured braking torque \(M_{H}\) was taken as the estimator of the value sought. The standard deviation of the arithmetical mean was adopted as the error of the sought value. The view of the braking system tested is presented in Figure 5. In order to improve data processing, the use of virtual-vector-based robust predictive current control is worth considering. As reference [26] shows, this makes it possible to increase the resistance of the system due to the various mismatches of the parameters. As is presented here, the concept of a virtual vector depends on the structure of a positive vector in the \(\alpha\beta\) subspace and a zero vector in the xy subspace, thanks to which we eliminate the influence of disturbances that occur in only one space [26].