OPTIMUM AND QUASI-OPTIMUM CONTROL OF THIRD AND FOURTH-ORDER SYSTEMS
Abstract
Pontryagin's maximum principle is used for computing the optimum control function u(t) for a given plant and a given performance criterion. If u(t) is bounded, the control is of the bang-bang type in many cases. If u(t) is expressed as the function of the state variables, that means, u(t) = sgn f(x to the ith power), the equation f(x to the ith power) = 0 determines the switching surface in the state space. In general these surfaces are not given by simple analytic functions, in particular not if the transfer function of the plant contains complex poles. If the desired final state is given by error and error derivates being zero, this surface goes through the origin of the phase space. Based on experiences with second-order plants, a systematic attempt has been made to approximate the exact switching surfaces for third-order plants. There is an approximation of the surface portion close to the origin (the so-called 'inner' surface) and an approximation of the larger portion of the switching surface which is not close to the origin (the 'outer' surface). Examples show the use of these surfaces; their results are compared to results with exactly optimum switching. They agree well. The extension to fourth-order systems is indicated.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 01, 1962
- Accession Number
- AD0621137
Entities
People
- Harold A. Titus Jr.
- Irmgard Fluegge-lotz
Organizations
- Stanford University