Synthesis of the Additive Terminal Control of Uniaxial Motion of Nonlinear Objects

A method for synthesizing the laws of terminal control of uniaxial movement of nonlinear dynamic objects is proposed. The problem is solved for the case when the control action is included in the scalar additive component of the nonlinear equations of the object. Target control laws meet the requirement to transfer an object from an arbitrary initial state toa specified final position with a specified final speed. The other parameters of the object’s state at the end time are generally not controlled. When assigning a zero final speed, the object’s "soft" transition to the specified position is achieved, which is necessary for many terminal systems. Due to the fundamental complexity of optimal synthesis in conditions where the control object has nonlinear properties, a purely terminal formulation of the problem is preferable. One of the most effective means of solving this problem is the methods of trajectory planning and solving inverse dynamics problems. This approach is adopted in this study. Using it together with additional analysis allowed us to write the control law in the feedback form for the case of a nonlinear mathematical model of the object. The developed synthesis method is characterized by simplicity of form and ease of practical implementation, for example, using embedded microcontrollers. Known general approaches are usually associated with a significant expenditure of time and technical resources of the control system in this case. The specified efficiency of the method is achieved by taking into account the features of scalar and additive control in the system. The use of the method is illustrated by an example of "soft" turn of the sequential excitation electric motor shaft at a given angle with zero final speed, which does not require the use of rigid stop. The latter circumstance means a significant improvement in the quality of terminal control. Under this condition, the organization of positioning of mobile executive bodies of various industrial equipment is significantly simplified.

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