Outline Introduction Reaction Wheels Modelling Control System Real Time Issues Questions Conclusions

The Plant Pendulum Reaction Wheel Motor Encoders TI Digital Signal Processor PWM Motor Driver

Reaction Wheel Wheel acceleration by torque from motor Torque on motor from wheel inertia Torque is transferred to the whole pendulum

Satellite adjustment Motorcycle mid-jump correction Applications of Reaction Wheels

Three states – Model derived by laws of physics and measurements Model Derivation

Validating the Model

Hybrid Automaton Two discrete states –Swinging State –Balancing State

Swing Up Controller Bang-bang energy control Energy of pendulum W total = W potential + W kinetic Reference value is the potential energy at the upright position The pendulum will reach the catch angle with the right amount of speed

Two Approaches of Controller Design 1.Design in Continuous Time 2.Design in Discrete Time Continuous time Plant Discretized Plant Continuous time Controller Discrete Controller h h

1.Design in Continuous Time Design of a State Feedback Controller Investigate PD controller: Controller Process State observerState Feedback

1.Analysis of the Root Locus Root locus : closed-loop pole trajectories as a function of

1.A Stable Closed-loop System  necessity of a feedback on

1.Sampling of the controller Discrete transformation of the derivatives in using backward difference Filtering of the velocities and  First order low pass filter State observerState Feedback holdsample

1.Performance of the PD- controller Higher overshoot in reality (Nonlinearities such as dry friction) High rising time (>1.5s) Open loop plant has 3 poles : 8.82, -8,72, turns around -1  stable closed loop

1.LQ-controller How to choose for optimal results? Computed from the continuous plant state matrices With, and gives optimal solution

1.Performance of the LQ- controller No overshoot. Phase margin 60 degrees

1.Performance of the LQ- controller Demo of the continuous LQ…

2.Design in Discrete Time Plant is sampled with a zero-order hold approximation. LQ controller derived with the discrete plant state matrices : with Gives optimum solution for any sampling period h : State observer Discrete Plant

2.Performance of the Discrete LQ-controller Demo of continuous and discrete LQ…

2.Deadbeat Control Use a state feedback The strategy: drive the state into the origin in at most 3 steps Possible if Cayley-Hamilton theorem states that if the desired closed loop poles are put at the origin,

2.Performance of the Deadbeat Controller Demo of the Deadbeat Controller…

Embedded behaviour CPU time 2%  no pb with deadlines not met Sampling frequency VS control performance Maximum sampling period h=150 ms according to rising time of motor

Conclusion Energy controller for swinging up the pendulum gives good results. Continuous LQ works fine with high sampling frequency For lower sampling frequencies, discrete design of controller needed. Deadbeat controller does not work because of voltage limitations

Questions?