Output feedback controller for systems containing a backlash

For the case of a single-input single-output control system with a backlash, the feedforward gain is determined. A control equation is applied to the original system. Because of the nonlinearity, the resulting feedback system often exhibits a limit cycle. In this case, the feedback gains are readjusted using the describing function method so that the limit cycle is eliminated. The block diagram for describing function analysis is given. It is shown that, when the controller is implemented, the steady state error is related to the sum k₀+k₁+k₂+. . .+k_n-1 of the feedback gains. Although the relationship is not linear, the larger the sum, the smaller the error becomes. In addition to satisfying the transient requirements, it is also necessary to choose the cost weighting matrices Q and R so that the sum of the feedback gains is sufficiently large and the steady state error is acceptably small