Ever wondered how a helicopter works? How it translates and has access to various freedom of motion? Credits to the mechanically complex swash plate mechanism. The swash plate mechanism allows the pilot to control the pitch of the propellers mechanically which in-turn allows then to control the helicopter
Now coming to multirotors these are electronically complex devices whose motion is controlled majorly through control system that are electronics heavy.
This is a newly developed concept of imaginary swash-plate which combines these two control system and provide a controlled flight using just 2 counter rotating props and a cleverly designed control system., without any mechanical complexity. This new concept of wingless flight fascinated us to study more about it in detail.
Single rotor helicopters and coaxial helicopters use the main lifting rotor(s) both to generate thrust for flight and to regulate the vehicle’s orientation in roll and pitch. This is conventionally achieved through a technique referred to as cyclic control in which the pitch of the rotor blades is manipulated within each revolution.
This is controlled by using only two counter rotating Propellers and freely hinged rotor head without using any servos or solenoids. When the speed of the motor is increased and decreased several times, the motor blades lag behind which causes the angle of one blade to increase and the other to decrease. The motor accelerated for the first half of the rotation and decelerates for the next half causing the blades to lead and lag at the perfect positions. The positions at which the blade should take high Pitch is derived from Gyroscopic Precession and is calculated by using Magnetic sensors with the motor. This achieves the same control system as a helicopter without a Swashplate.
A downward force applied to the disk at point A results in a downward change in disk attitude at point B. And upward force applied at Point C results in an upward change in disk attitude at point D. when a force is applied to a spinning object, the maximum reaction occurs approximately 90 degrees later in the direction of rotation. this phenomenon is called as Gyroscopic Precession. If we need to move the system forward, the pitch of the propellers should be in such a way that it creates a lift on the left side of the system.
The method is to kinematically induce a lag-pitch coupling through the combination of a conventional flap hinge and a skewed lag-pitch hinge. Figure 1 illustrates the physical device consisting of the hub, cross, blade grip, and blade bodies. The hub is attached to the cross by a flap hinge pin joint. The cross connects to the blade grip by a skewed lag hinge pin joint, and it is this skew angle that controls the degree of lag-pitch coupling. To this end the hub design is antisymmetric with a positive lag-pitch coupling imposed on one blade and a negative coupling imposed on the opposite blade. As a consequence, when a driving torque excites synchronous lead-lag motions in the two blades the pitch responses will be 180◦ out of phase with each other.
Figure 2 depicts rotor mounted above the centre of mass and a second counter rotating rotor mounted below the centre of mass. The figure conceptually illustrates that the force vectors f1 and f2 can be directed counter to each other in order to produce a net pitching moment about the vehicle’s centre of mass while maintaining zero net lateral force. Alternatively, the force vectors can be pointed in similar directions, yielding a net lateral force on the aircraft while maintaining zero net moment.
Two blades are attached to a hub with skewed lag-pitch hinges, as shown in Fig. 2. As the hub accelerates forwards the positive blade tip lags backwards relative to the hub and the kinematics require the pitch of the blade tip to increase. At the opposite station, 180◦ later, the positive blade tip now leads forwards relative to the hub and the pitch of the blade is instead depressed. The complementary geometry of the negative blade yields the opposite response, so that an appropriate input can induce both blades to, for example, elevate pitch while passing across the nose and decrease pitch while passing across the tail of the aircraft. Such smooth oscillation through every revolution bears a strong resemblance to conventional cyclic pitch control, but it is now achieved merely by electronically altering the amplitude and phase offset angle of the sinusoidal drive component.
The motor torques driving the gross propeller rotation as well as the cyclic blade pitch and flapping response are a result of modulating the applied motor voltage. The applied voltage V is the sum of two parts: a proportional-integral control on error between the observed rotor speed ψ˙ and desired speed Ω with gains KP and KI, and an additional voltage modulation V* used to excite the lag-pitch mode.
V = −Kp (ψ˙ − Ω) − KI ꭍ(ψ˙ − Ω) dt + V *
Magnetic encoders like AS5047 can be used with Motors to calculate the angle of rotation of motors. The main challenge is to configure the code. After the FC receives the pitch and roll input from the transmitter, the throttle output is calculated from the equation below and fed to the FC which runs the PID loop to control the system.
Output = throttleIN + [ (pitchCTRL * cos (motor angle)) + (rollCTRL * sin (motor angle)]
But, when the rpm of the motor increases, the frictional force between the hinges of the motor head increases, which decreases the control output. We will not be able to control the pitch in higher RPMs. This can be resolved by modifying the code which can add a dead band to the bottom of the control output (till the maximum value of the friction)
listed below are the sources from which content was taken:
More info + research papers: https://www.modlabupenn.org/2014/10/23/underactuated-rotor/
credits to tomstation and james for the sources.