An Improved 2-DOF Proximate Time Optimal Servomechanism

The proximate time optimal servomechanism (PTOS) is a well established algorithm for the control of linear systems where control bounds and the speed of response are important. The PTOS approach modifies the time-optimal switching curve by including an unsaturated "slab" region that leads to a linear control regime for small errors. The control parameters are required to satisfy the continuity and the stability constraints resulting in only a single independent design parameter. In this note, the PTOS theory is reviewed and the stability conditions are derived. An improved version of the PTOS algorithm, called the MPTOS, is presented that results in a performance improvement over the original PTOS by providing two independent control parameters in the design. As a result, the system response can be shaped in a more efficient way in both continuous and discrete time domains. The stability conditions are derived for the proposed MPTOS scheme for continuous and discrete time implementations. Further extensions are discussed including a new discrete algorithm suitable for systems with slow sampling and a model reference tracking method also known as a feedforward/feedback structure for reducing the response of flexible modes. The latter method can be extended to dual actuator systems as are being introduced to the disk drive read/write head assembly fabrication and control. An approach is also presented for combining the vibration reduction filters with the model reference structure to further enhance the performance.