A method for operating a linear compressor includes substituting a first observed velocity, a bounded integral of the first observed velocity, an estimated clearance, an estimated discharge pressure, and an estimated suction pressure into the mechanical dynamic model for the motor, calculating an observed acceleration for the piston with the mechanical dynamic model for the motor, calculating a second observed velocity for the piston by integrating the observed acceleration for the piston, calculating an observed position of the piston by integrating the second observed velocity for the piston, and updating an estimated clearance, an estimated discharge pressure, and an estimated suction pressure based upon an error between the first and second observed velocities and an error between the bounded integral of the first observed velocity and the observed position.

A method for operating a linear compressor includes substituting a first observed velocity, a bounded integral of the first observed velocity, an estimated clearance, an estimated discharge pressure, and an estimated suction pressure into the mechanical dynamic model for the motor, calculating an observed acceleration for the piston with the mechanical dynamic model for the motor, calculating a second observed velocity for the piston by integrating the observed acceleration for the piston, calculating an observed position of the piston by integrating the second observed velocity for the piston, and updating an estimated clearance, an estimated discharge pressure, and an estimated suction pressure based upon an error between the first and second observed velocities and an error between the bounded integral of the first observed velocity and the observed position.