Control Design for Flexible Manipulator Model with Nonlinear Input and State Constraints Based on Symmetric Barrier Lyapunov Function

Flexible manipulators are widely applied in many fields. Here, the control design for a simplified flexible manipulator model with nonlinear inputs and state constraints is studied. The impact of two inputs and disturbances on the system was considered. One torque input comes from the joint motor, and the other input force comes from the linkage actuator tip. The input constraints of a dead zone are applied to both inputs to the manipulator. To offset the effect of the nonlinear input, we first linearize the dead zone and convert it into a linear-input characteristic and a finite error value. Then, the adaptive rate is designed to compensate for the effects of the nonlinear input. For the state constraints, an adaptive controller is proposed based on a symmetric tangent-type barrier Lyapunov function which can operate under closer constraint conditions, and parameter tunability offers flexibility in balancing the constraints’ tightness and performance. The stability proof ensures that all states are within the given constraint range. The provided simulation results indicate that the system is not sensitive to the initial values, and when the initial values are taken to be between open intervals (−0.4, 0.34), this ensures the stability of the system and does not violate the constraint bounds.