Figure 4.13: Measured and simulated velocity of the USM
4.3
USM control algorithm
In the last decade, various publications demonstrate that the USM can be controlled with: PI control models in speed, position or torque [77] [78], fuzzy models [79], [80], models based on neural networks, or a combination thereof.
In this work, a cascade control model was designed, with two control loops for angular velocity, and angular position, each one with its own PI controller in func- tion of the equation 4.5. The primary loop is represented by the position controller (master) and the second loop (intern) is composed from a feed forward controller in parallel with the secondary controller in velocity. Using this type of control, has the possibility to control the actuator in position and velocity at the same time. This condition to control the actuator in position and velocity are primordial in rehabil- itation therapies. For this reason a cascade control is the more adequate choice to control independently position and velocity (limiting the velocity) for the USM.
Y = kpe(k) + ki
Z k
0
e(τ )dτ (4.5)
where Y is the controller output signal (velocity respectively voltage ) , kp is the
proportional gain, ki is the integral gain and e(k) is the error between the reference
and the output. The parameters of the PI controllers are presented in the Table 4.2. These parameters are obtained over simulation model with the aid of PID tuning tool of Matlab/Simulink R.
The cascade control systems are more complex than single-measurement con- trollers, requiring twice as much tuning. Then again, the tuning procedure is fairly straightforward: tune the secondary controller first and after the primary controller
Table 4.2: Cascade PI Controllers gains
Gain Kp Ki
Velocity controller value 0.02 0.0001 Position controller value 1.5 0.001
using the same tuning tools applicable to single-measurement controllers. The feed forward controller is based on the USM voltage-rotational speed characteristics pre- sented in [2].
The proposed control scheme consists of a relatively simple algorithm that meets the objectives, with an error in the position angle of 0.08 degrees and a low computa- tional power use. The control scheme is shown in Figure 4.14. The control algorithm was developed in Matlab/Simulink R and has been calibrated with the necessary PID
gains in the simulation, and tested in the test bench.
Figure 4.14: Control algorithm for USM based actuator
The control scheme uses the signals of two encoders: a relative encoder, positioned on the shaft of the motor to measure the actual speed of the actuator and one absolute encoder positioned on the shaft of the gear, to operate at lower speed and to calculate the real arm position.
4.3.1
USM based actuator control results
The operation of the USM is analysed with several experiments to check the correct performance of the prototype. Firstly, the actuator control algorithm was calibrated
4.3. USM control algorithm 67
and tested in the simulation environment and after that was implemented in the real plant. The real and the simulation model of the system it can be seen in Figure 4.15.
Figure 4.15: Real system and simulation environment
The USM answer in the test bench can be seen in Figure 4.16. The structure of the first device actuator tested is composed of the USM and the planetary gear. Due to the planetary gear tolerance, the error of control in position increases up to 0.7 degrees. In this case, the motor must follow the reference signal in position with a constant speed.
The objective of the actuator is to move an elbow rehabilitation device, exoskeleton where its movement ( in flexion and extension) needs to have a good response to the input signal, in position with one adequate speed. In this case, the proposed algorithm is able to maintain a constant speed despite of inertia and mass of the arm. Figure 4.16 highlights the output signal, from cascade control with the reference signal in position.
The first tests of the proposed actuator in the test bench were made by magnetiza- tion of the magnetorhelogical clutch with Neodymium magnet, allowing transmitting the necessary torque 1:1 (the torque of output shaft clutch is equal with the torque of the motor). In this case, the clutch is subjected to a magnetic induction of ap- proximately 0.8T. In the future, the necessary magnetic field will be produced by an electromagnet which will be able to provide independent control for the torque transmitted by the clutch just by changing the viscosity of the fluid.
Fig. 4.17 shows the response of the proposed actuator controlled in position when the magnetorhelogical fluid is magnetized, giving the possibility to transmit more than 5Nm. In this case, the USM has a constant speed of 200 degrees/second.
Figure 4.17: USM response with magnetized clutch
As can be observed in Fig.4.17, the clutch doesn’t change the performance of the control algorithm, the skating effect doesn’t appear for the inner disk.
Fig. 4.18 shows the actuator’s response to a step input reference where the clutch is not subjected to a magnetic field. In this case, the inner disk of the clutch skates leaving the output shaft of the actuator free. Then, the torque transmitted is close to 0N m. This test highlights the capacity of the actuator to leave free the forearm when the clutch is not subjected to any magnetic field.