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ece6554:project_ballbeam [2019/04/20 20:14] – [Step 2: Full Linear System (An Almost Backstepping Approach)] pvelaece6554:project_ballbeam [2024/08/20 21:38] (current) – external edit 127.0.0.1
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 Incorporate adaptive control to correct for the unmatched uncertainty. Randomly perturb by about 15% the parameters.  Since the uncertainty is unmatched, you will have to work out a backstepping type of adaptive control law. The uncertainty hits the $\dot x$, $\dot \theta$, $\iota$ coordinates dynamics. Provide your derivation of the adaptive control law, the final set of equations, and simulations showing it in action. Incorporate adaptive control to correct for the unmatched uncertainty. Randomly perturb by about 15% the parameters.  Since the uncertainty is unmatched, you will have to work out a backstepping type of adaptive control law. The uncertainty hits the $\dot x$, $\dot \theta$, $\iota$ coordinates dynamics. Provide your derivation of the adaptive control law, the final set of equations, and simulations showing it in action.
 +
 +=== Tips: De-Coupled then Re-Coupled Adaptive Systems ===
  
 //Tip:// Designing a fifth-order backstepping method is going to be pretty nasty, especially because of the dependency structure of things.  Instead, decouple the system into two parts.  One is the subsystem from Step 1 and the second is the new motor dynamics subsystem.  Design a backstepping controller for the new motor dynamics subsystem independent of the ball subsystem.  You will have to treat the ball signal as an external input in the decoupled system.  Go ahead and do that when synthesizing the backstepping control policy for the motor subsystem.  Get it to work out, then add on the adaptive ball system from Step 1.  This is not 100% correct/ideal, but it is much simpler than attempting a full backstepping design that will end up with lord knows how many differentiated signals. //Tip:// Designing a fifth-order backstepping method is going to be pretty nasty, especially because of the dependency structure of things.  Instead, decouple the system into two parts.  One is the subsystem from Step 1 and the second is the new motor dynamics subsystem.  Design a backstepping controller for the new motor dynamics subsystem independent of the ball subsystem.  You will have to treat the ball signal as an external input in the decoupled system.  Go ahead and do that when synthesizing the backstepping control policy for the motor subsystem.  Get it to work out, then add on the adaptive ball system from Step 1.  This is not 100% correct/ideal, but it is much simpler than attempting a full backstepping design that will end up with lord knows how many differentiated signals.
 +
 +//Tip:// When designing the back-stepping type adaptive controller for the three new states, you should identify some candidate $x_1$ dynamics for the ball-beam part to be used in the motor controller. With $x_1$ specified in closed-form, the associated time derivatives can also be computed in closed form.  These should be used as exogenous signals in the linear, back-stepping type adaptive controller.  Later, when combining with the adaptive controller for the ball sub-system, you'll be trying to track the desired adaptive control law for the motor sub-system.
  
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-==== Step 3: Nonlinear Adaptive Backstepping ====+===== Step 3: Nonlinear Adaptive Backstepping =====
  
 **This Step should not be done for ECE6554 Spring 2019. Only complete Steps 1 + 2.** **This Step should not be done for ECE6554 Spring 2019. Only complete Steps 1 + 2.**
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 Translate the linear adaptive backstepping strategy to the nonlinear system. Start with the vanilla nonlinear backstepping method, then make it adaptive. Translate the linear adaptive backstepping strategy to the nonlinear system. Start with the vanilla nonlinear backstepping method, then make it adaptive.
  
-=== Nonlinear Model Inversion with Backstepping ===+==== Nonlinear Model Inversion with Backstepping ====
  
 Consider the nonlinearities of the system and identify a backstepping approach to controlling the system. Get the baseline backstepping method working.  It should resemble that of the linear controller from Step 2 but with nonlinear terms. Consider the nonlinearities of the system and identify a backstepping approach to controlling the system. Get the baseline backstepping method working.  It should resemble that of the linear controller from Step 2 but with nonlinear terms.
  
  
-=== Nonlinear Model Inversion with Adaptive Backstepping ==+==== Nonlinear Model Inversion with Adaptive Backstepping ====
  
 Add in adaptation to the backstepping controller, using the same 15% perturbed model. Add in adaptation to the backstepping controller, using the same 15% perturbed model.
ece6554/project_ballbeam.1555805672.txt.gz · Last modified: 2024/08/20 21:38 (external edit)