Designing a controller that balances two links adds an extra challenge when compared to the single inverted pendulum system. The additional challenge of a second pendulum can be used to demonstrate advanced controls concepts, or as a basis for research.
Linear Double Inverted Pendulum
The double inverted pendulum represents a complex challenge with real-world applications that include stabilizing the takeoff of a multi-stage rocket and modeling the human posture system.
Same as the physical QUBE-Servo 2, the virtual system features a DC motor with the inertia disk and inverted pendulum modules. Rotary encoders measure the angular position of the DC motor and pendulum. The motor angular velocity is measured through a software-based tachometer.
Same as the physical Ball and Beam, the virtual system features a track on which a ball is free to roll. The track is effectively a potentiometer, outputting a voltage proportional to the position of the ball. The tilt angle of the track is controlled by the Rotary Servo’s DC motor.
Same as the physical Coupled Tanks, the virtual system features a single pump and two tanks. Each tank is instrumented with a pressure sensor to measure the liquid level. The different outflow valves configurations allow to direct the flow of the liquid, while the flow rate can be changed by using outflow orifices of different diameters.
QLabs Controls is a collection of virtual laboratory activities that supplement traditional or online control systems courses. The virtual hardware labs are based on Quanser QUBE-Servo 2 and Quanser AERO systems which allows you to combine physical and virtual plants to enrich lectures and in-lab activities and increases engagement and students’ learning outcomes in class-based or online courses.
The Double Inverted Pendulum module is composed of a rotary arm that attaches to the Rotary Servo Base Unit, a short 7-inch bottom blue rod, an encoder hinge, and the top 12-inch blue rod. The balance control computes a voltage based on the angle measurements from the encoders. This control voltage signal is amplified and applied to the Servo motor. The rotary arm moves accordingly to balance the two links and the process repeats itself.
The force between electromagnet and ball is highly nonlinear. Further, the electromagnet itself has its own dynamics that must be compensated for. The challenging dynamics of the system make it perfect for teaching modeling, linearization, current control, position control, and using multiple loops (i.e. cascade control). It could also be used to test and implement more advanced control strategies, such as multi-variable, gain scheduling, and nonlinear control.
The 2 DOF Ball Balancer module consists of a plate on which a ball can be placed and is free to move. Two Rotary Servo Base Units are connected to the sides of the plate using 2 DOF gimbals. The plate can swivel about in any direction. By controlling the position of the servo load gears, the tilt angle of the plate can be adjusted to balance the ball to a desired planar position. The digital camera mounted overhead captures two-dimensional images of the plate and track coordinates of the ball in real time. Images are transferred quickly to the PC via a FireWire connection. Students can make the ball track various trajectories (a circle, for example), or even stabilize the ball when it is thrown onto the plate using the controller provided with the experiment.
The Active Suspension consists of three masses that along stainless steel shafts using linear bearings and is supported by a set of springs. The upper mass (blue) represents the vehicle body supported above the suspension, the middle mass (red) corresponds to one of the vehicle’s tires, and the bottom (silver) mass simulates the road. The upper mass is connected to a high-quality DC motor through a capstan to emulate an active suspension system that can dynamically compensate for the motions introduced by the road. The lower plate is driven by a powerful DC motor connected to a lead screw and cable transmission system.