Integrator Backstepping and Related Techniques

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Integrator Backstepping and Related Techniques

von Ellenrieder, Karl Dietrich

The concepts involved in the use of integrator backstepping techniques are introduced one-at-a-time, starting with simple single input, single output systems, then moving to systems in strict feedback nonlinear system form, and gradually building up to multiple input multiple output vectorial integrator backstepping for marine systems. Related concepts, such as the use of stabilizing functions and the use of added nonlinear damping to counter unmodeled nonlinear dynamics are examined along the way. Backstepping methods are fairly complex and there are several related implementation issues, such as the required smoothness of desired trajectories and how to perform the real-time differentiation of stabilizing functions. Several methods for handling these issues are reviewed. The use of dynamic surface control, in which the real-time differentiation of terms in the control law are computed in real time using first order linear filtering is presented. Techniques for including the effects of actuator rate- and magnitude-limits are discussed. Lastly, the use of nonlinear disturbance observer based control, which can make a backstepping controller more robust to exogenous disturbances, is illustrated.