Download e-book for iPad: The Reaction Wheel Pendulum by Karl Astrom

By Karl Astrom

ISBN-10: 1598291947

ISBN-13: 9781598291940

This monograph describes the response Wheel Pendulum, the latest inverted-pendulum-like gadget for keep watch over schooling and examine. We speak about the historical past and history of the response wheel pendulum and different related experimental units. We boost mathematical versions of the response wheel pendulum extensive, together with linear and nonlinear versions, and versions of the sensors and actuators which are used for suggestions keep an eye on. We deal with a variety of features of the keep an eye on challenge, from linear regulate of themotor, to stabilization of the pendulum approximately an equilibrium configuration utilizing linear keep watch over, to the nonlinear keep an eye on challenge of swingup keep watch over. We additionally talk about hybrid and switching regulate, that's beneficial for switching among the swingup and stability controllers. We additionally speak about very important functional matters similar to friction modeling and friction reimbursement, quantization of sensor signs, and saturation. This monograph can be utilized as a complement for classes in suggestions keep watch over on the undergraduate point, classes in mechatronics, or classes in linear and nonlinear nation area keep watch over on the graduate point. it may possibly even be used as a laboratory guide and as a reference for study in nonlinear keep watch over.

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Extra resources for The Reaction Wheel Pendulum

Example text

Let the angular velocity of the wheel be ω = d θr /d t. It follows from Eq. 13) The proportional feedback gives a closed loop system characterized by de + k dr b r e = b r F dt where e = ωr − ω is the error. With the chosen control law the angular velocity will follow the reference value ωr , with a steady state error. ess = F k dr The time constant of the closed loop system is Tω = 1 k dr b r book Mobk073 34 May 30, 2007 7:38 THE REACTION WHEEL PENDULUM The response time of the system will decrease with increasing feedback gain k dr .

For initial conditions too far away from the equilibrium, or for large disturbances which move the system too far away from the equilibrium the pendulum will fall down. In the next chapter, we consider the problem of starting the pendulum and wheel in arbitrary initial conditions. This problem requires consideration of nonlinear control theory. 1 NONLINEAR CONTROL So far we have discussed the identification of the parameters needed in the dynamic description of the Reaction Wheel Pendulum, we have discussed stabilization of the motor position and velocity, and stabilization of the pendulum angle in both the downward and the inverted positions using the linear approximation of the nonlinear dynamics.

We then considered the problem of controlling all four states. We showed that the fourth-order system is controllable from the single input available and we considered the effect of disturbances on the system response. The controllers in this chapter are local in the sense that the initial conditions must be sufficiently close to the equilibrium point for the closed loop system to be stable. For initial conditions too far away from the equilibrium, or for large disturbances which move the system too far away from the equilibrium the pendulum will fall down.

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