Force-feedback control of steering wheels

Transcription

1 Scuola universitaria professionale della Svizzera italiana Dipartimento Tecnologie Innovative Mechatronics laboratory Force-feedback control of steering wheels Scope Tasks Keywords Force-feedback control implementation with torque sensors - Angle control - Bilateral servo simulation and implementation - Improvement with the help of torque measurements bilateral servo, force-feedback Prerequisites - References - Time 8 hours Appendices - Contact Silvano Balemi

2 Force feedback control SUPSI-DTI 1 Presentation The steering system consists of two identical platforms composed of a brushless motor, an encoder, a gear, a torque sensor and a steering wheel. The objective of the control is to keep the two steering wheels at the same angular position and to transmit the torque from one wheel to the other. Different torque and/or position ratios should be implemented in order to simulate a bilateral servo with increased positioning accuracy or torque amplification. The controller has to be implemented in Simulink and connected to the hardware via the CAN bus. Historical note This system is similar to a device called Selsyn (or Synchro) developed around 1925 and extensively used during the Second World War. In this system a generator and a motor are electrically connected with the aim to reproduce the angular position and to transmit the respective torques. The motor (receiver) differs only mechanically from the generator (transmitter) in that a mechanism for dampening oscillations is mounted on the rotor shaft. Electrically, they are identical. 2 Set-up 2.1 Necessary material Given are following items Two identical mechanical systems each with a brushless motor, an encoder, a gear, a torque sensor and a steering wheel. The systems can be addressed through the CAN bus at the speed of 1 MBit/s. Figure 1.1 shows a block diagram representation of the system. Motor w 1 Gear w 2 Torque sensor Steering wheel Figure 1.1: Block diagram of one system The transfer function between the motor torque T and the motor angle φ is Φ(s) T (s) = s (s ) (1) 2 Dario Bralla, Silvano Balemi

3 SUPSI-DTI Force feedback control and the transfer function between the torque T u that the user applies to the steering wheel and the motor angle φ is Φ(s) T u (s) = s (s ) (2) Under the assumption that the inertia and the damping coefficient of the steering wheel are negligible it is possible to set the torque sensor signal T s equal to T u. A first order low pass filter with 100 Hz cut-off frequency can model the torque sensor dynamics. The gear ratio N between shaft and wheel is already included in the transfer functions (1) and (2) and is 80:1. The relationship between current and torque can be considered to be linear according to the relation T = k t I where the torque constant is kt = Nm/mA. A parallel port to CAN dongle from Peak Systems with 120 Ω terminator. Two serial cables connecting the dongle to the two mechanical systems and an additional 120 Ω terminator. A simulink block with interfaces managing the data flow between the computer and the electromechanical system via the CAN bus. Figure 1.2 shows the block with the associated connections. It provides two input and two output signals. Their meanings are explained in Table 1.1. Table 1.2 defines the sign conventions of the provided block assuming that the observer is in front of the steering wheel (like when driving a car). current[ma] phi1[rad] 5000 enable Wheel1 Figure 1.2: Interfaces block Ts1[Nm] Dario Bralla, Silvano Balemi 3

4 Force feedback control SUPSI-DTI Current Enable Table 1.1: Signals Inputs Sets the motor current reference in the Maxon current driver. The current reference is expressed in ma and the maximum value is 5000 ma. Resets the torque value when a rising edge is detected. Outputs Position Reads the motor shaft position. The position is expressed in radiants. Torque Reads the torque applied to the steering wheel shaft. The torque is expressed in Nm. Current Position Torque Table 1.2: Sign conventions A positive current causes the steering wheel to turn clockwise A negative (clockwise) rotation causes the encoder reading to increase A positive (counter-clockwise) torque applied by a person on the steering wheel is positive for the sensor. (A positive current when holding the steering wheel produces a positive reading of the torque.) 2.2 Steps to be followed The Simulink template of Figure 1.2 can be downloaded from the web at the page smt/courses/steer template.mdl. 2.3 Hints Limit the angle reference value for the steering wheel to ±0.5 π radians in order 2 to respect the mechanical rests. Take into account the gear ratio N between shaft and wheel. The motor encoders are incremental and the interface block control sets the initial angle measurement to zero. Remember to bring the steering wheel to the central position before starting the real-time control program. 4 Dario Bralla, Silvano Balemi

5 SUPSI-DTI Force feedback control 3 Assignment tasks 1. Create the model block of the system which respects the sign conventions of Table 1.2. Test the model behaviour by applying current and user torques. 2. Design a discrete-time state-feedback controller with full-state observer and precompensation that controls the position of a single steering wheel. Use a 200 Hz sampling frequency, the motor encoder measurement as a feedback and the current as actuation signal. Apply a periodic reference signal with 10 seconds period; its amplitude must be in the range ± π radians. Consider 4 the gear ratio N between shaft and wheel. Apply realistic user disturbance torques. Simulate the closed-loop. 3. Replace the mathematical model with the interface block, compile and execute the control application. Apply a torque on the steering wheel when it is still to check the stiffness. 4. In the simulation connect the two steering wheel models together in such a way that the position of the first is the reference position of the second and vice-versa. Simulate. 5. In order to achieve a movement towards the zero point of both wheels, condition the reference signal of each steering wheel in a suitable way. Simulate. 6. Check the behaviour of the mechanical system by executing the new control application. 7. In order to reduce the viscous damping effect use a cross-velocity feed-forward. Pay attention to choose a suitable gain and bandwidth limitation of the differentiated signals which estimate the speeds from the angles. Check the benefits on the mechanical system. 8. Find a strategy to improve the stiffness between the two steering wheels using the torque sensors. Check the benefits on the mechanical system. Dario Bralla, Silvano Balemi 5