Nonlinear Feedback Control Theory

Hassan K. Khalil | |


Nonlinear feedback control theory has seen remarkable progress in the past few decades. The Nonlinear Feedback Control Theory group at Michigan State University (MSU) has worked on robust and adaptive control of nonlinear systems for over 25 years. The main emphasis of the research has been on high-gain observers. This is a tool that was invented at MSU and has been advanced over the years by the contributions of 16 PhD and some MS students and post docs. Khalil and coworkers have developed the high-gain observer theory in a number of directions, covering stabilization, sliding mode control, regulation, adaptive control, separation principle, logic-based switching, robustness to unmodeled dynamics, sampled data control, effect of measurement noise, disturbance estimation, and connection with Extended Kalman Filter. High-gain observers were experimentally applied to the control of mechanical systems, electric drives and smart-material actuated systems.

Recent Research on high-gain observers has focused on three issues:

  • The first issue is how to modify the observer design to better handle the effect of measurement noise. Because high-gain observers have high bandwidth, they are more sensitive to measurement noise. It was demonstrated that such effects are more dominant during the steady state as opposed to the transient period. This led to ideas to change the observer gain between the transient and steady state periods. Two techniques were investigated, one based on switching the gain while the other uses nonlinearities to change the gain.
  • The second issue is expanding the high-gain observer tool to the so-called extended high-gain observer. This observer estimates disturbance signals in addition to estimating the state variables of the system, which facilitates the compensation for such disturbances and the design of nonlinear feedback controllers that meet performance specifications.
  • The third issue is the design of observers and feedback controllers for nonlinear non-minimum phase systems. Non-minimum phase systems pose a challenge to the design of feedback controllers, even for linear systems. In recent work we have used extended high-gain observers to design feedback controllers for this class of system.

Collaborative Research with MSU College of Engineering faculty has provided experimental test beds to validate the theoretical work on nonlinear feedback control. Three areas have been pursued:

  • Electric Drives: In collaboration with Dr. E. Strangas, the group has worked on nonlinear control of induction motors without the use of mechanical sensors (so called sensorless control). New observers were developed and their use in feedback control was justified theoretically. Currently they working on sensorless control of permanent magnet synchronous motors
  • Smart Material: In Collaboration with Dr. X. Tan, the group has studied nonlinear control of smart material, such as piezo-electric actuators, which are characterized by the presence of hysteresis. High-gain observers in multirate sampled-data control and nonlinear control of nano-positioners have been investigated.
  • Mechanical Systems: In collaboration with Dr. R. Mukherjee, the group has extended the dynamic inversion technique to uncertain nonlinear systems and applied the results to an inverted pendulum on a cart and a helicopter model.