Output Tracking For Non-minimum Phase Systems Based On Trajectory Redefinition

Non-minimum systems are common in engineering applications.Flexible link manipulator(FLM)is known to be a classical non-minimum system which being widely used in aerospace and complicated manufacturing.There is no causal stable inversion for non-minimum systems due to the existence of unstable zeros,thus usual feedback controllers are not applicable.The traditional un-causal stable inversion method is the essential way to achieve output tracking precisely.Yet it has to be pre-actuated for an un-finite long time period,which is unpractical in real operation situation.Also it is not suitable for systems having zeros on imaginary axis,which is known as non-hyperbolic systems.Considering the requirements of both practicability and tracking accuracy,this paper put forward an approximated linearized method by redefining output trajectory with exponential form,aiming at realizing causal inversion control at a limited time period.The main work of this paper is presented as follows,(1)To solve the impracticability caused by infinite long time pre-actuation process,a method of redefining the output trajectory to replace the infinite pre-actuation process is proposed in this paper.Consequently,the desired Stable Initial State can be reached from the actual state after a fixed time period control.Then using the unstable inversion method to track the desired output trajectory precisely.The redefined trajectory is well designed with exponential form.Using a search algorithm,the most optimal one is searched in a family track.To verify the effectiveness of this new scheme,a simulation result is demonstrated for a tip trajectory tracking of a one-link flexible manipulator system.The simulation results are favorable to our research.(2)To design the control algorithm for generalized non-minimum systems,while improving the tracking accuracy at the same time,a piece-wise causal inversion controller is proposed in the following chapter.The whole output track is redefined with exponential form.What is mentioned especially is the redefined output trajectory must be designed as accurately as possible with the desired one.Meanwhile eliminating the influence of the unstable zeros.The desired trajectory is divided into several parts to be tracked respectively.New controller must satisfy the continuity of the redefined output,input and the inner states signal.New designed controller is applied in a real single flexible manipulator system.And the simulation results can approve the effectiveness well.(3)Experiment verification,the causal piece-wise casual inversion method is applied in a classical non-minimum system—flexible single manipulator.The system model is identified by least square method.Input signal is calculated off-line.Given the specified input signal being imported into the system,we record the corresponding output to make a comparison with the desired output trajectory.And the experiment result is obviously sustaining to new control scheme.