Tracking system design for a single-link sensorless manipulator under nonsmooth disturbances

The controlled plant is a single-link manipulator having an elastic connection to a DC motor and operating under uncertainty and incomplete measurements. The problem is to design a discontinuous feedback control for tracking a given reference signal of the plant's angular position. The angular position and velocity of the manipulator are not available for measurements; the sensors are located only on the drive; parametric and exogenous disturbances affecting the manipulator are nonsmooth and cannot be directly suppressed by control applied to the actuator. Within the block approach, a decomposition procedure is developed to design a nonlinear local feedback control. This control ensures the controlled variable's invariance with respect to uncertainties unmatched with the control action. A state observer of reduced order is constructed to estimate the angular position and velocity of the manipulator required for feedback design. The state variables in this observer are estimated using the principle of restoring exogenous disturbances by their action on the controlled plant. With this principle, a dynamic model of exogenous disturbances is not needed. In both problems (control and observation), S -shaped bounded continuous local feedbacks are used (smooth (sigmoidal) and nonsmooth (piecewise linear) local feedbacks, respectively). These local feedbacks suppress bounded disturbances acting with them through the same channel. The algorithms developed below do not require real-time identification of parametric and exogenous disturbances. However, they stabilize the observation and tracking errors with some accuracy. The effectiveness of the dynamic feedback is validated by the results of numerical simulation.