Adaptive Control of Systems with Hard Nonlinearities

Project Summaries

• Robust and Adaptive Control of Systems with Backlash and Flexibility
  
  This report summarizes our recent work on control of gun-turret systems with backlash and flexibility. In the first part of the report, we formulate the control problem and propose two control schemes for a rigid gun-turret system which has backlash between a driving gear and a driven gear. The first scheme is for the system with known parameters and the second scheme is for the system with unknown parameters. Both schemes have a backlash compensation design to cancel the undesirable backlash effect for improving system tracking performance.
  
  In the second part, the assumption of a rigid system is relaxed and the effects of flexibility on system performance and stability with and without backlash are analyzed. Utilizing a root-locus and partial state-feedback approach it is shown that with the proper choice of feedback gains, the designs of Part I for known and unknown parameters can be made robust with respect to flexibility.
  
  
• Optimal Control of Tracking Systems with Backlash and Flexibility
  
  A system with backlash and flexibility is compensated with an optimal control law combined with a linear partial-state feedback law. The compensation of backlash is treated as a rendezvous problem in optimal control, while the linear controller for flexibility is designed using techniques from classical control theory and singular pertubation theory. Simulation results show significant improvements in system tracking performance when backlash compensation is active.
  
  
• Adaptive Control and Identification of A Flexible System with Friction and Backlash
  
  In control of a real-life system consisting of two mechanical bodies with flexibility, backlash and friction, there are several important issues such as design of low-order adaptive controllers, friction compensation in the presence of flexibility, and backlash compensation.
  
  An adaptive state feedback control scheme is developed for systems with unknown parameters in non-canonical forms, by employing static state feedback for pole placement and dynamic output feedback for parameter adaptation. The developed control scheme does not need a restrictive state space model matching condition for an adaptive state feedback design. The adaptive parameter update law is derived based on a desirable linear output tracking error equation. Such an adaptive control scheme, whose order is considerably lower than an output feedback design, ensures closed-loop stability and output tracking.
  
  The developed model reference adaptive control scheme is then applied to the control of a two-body system with flexibility and damping. Simulation results indicate that the adaptive state feedback model reference control scheme ensures desired tracking performance in the presence of parameter uncertainties.
  
  An extended model reference adaptive control scheme is developed for control of the two-body system with nonlinear friction compoments. New parametrization schemes are proposed for adaptive friction compensation in the presence of flexibility which imposes some new challenge.
  
  In the presence of backlash, a two-body system operates in two modes: a backlash mode and an impact mode. While an adaptive controller can be used for a system in impact mode, optimal control designs are favorable for a system in backlash mode. Several such optimal controllers are compared. Backlash compensation in the presence of friction is also addressed. Finally, algorithms are developed for identifying system parameters needed for backlash compensation.