A Unified Approach to Model-Reference Adaptive Systems Part I: Theory

A unified approach to model-reference adaptive control systems is presented. A linearized error equation for each adaptive system is derived about some operating point and converted into the standard form for plotting root loci. The contribution made here is to convert the selection of an adaptive technique and the choosing of adaptive coefficients for some desired system performance from a "mystical art" to standard control techniquess.     

A Unified Approach to Model-Reference Adaptive Systems Part II: Application of Conventional Design Techniques

The use of linearized error equations in the design of model-reference adaptive systems developed by Part I is illustrated. Using standard control specifications on the system error (e.g., percent overshoot, rise time, etc.), a set of desired root locations on the root loci can be obtained. Then constants in the adaptive scheme can be chosen to obtain the desired root locations. Simulation results are given to illustrate the validity of the linearized error characteristic equation design procedure.     

Discontinuities in the solar wind

The nonuniform emission of the solar wind from the sun means that conditions are established which favor the development of discontinuities in the plasma parameters. Since the solar wind is in rapid proper motion with respect to the sun and the earth, examination of these discontinuities requires that the wind velocity be transformed away. Then it is found that they satisfy the conditions of magnetohydrodynamics and can be treated as shock waves and the stationary contact surfaces consisting of either tangential or contact discontinuities. The collision-free structure of the solar wind suggests that the tangential discontinuity is the more likely contact surface as it is more capable of inhibiting diffusion which is required for a lifetime sufficient for the structure to be carried to the neighborhood of the earth.Either the shock wave or the contact surface can create signals that are detectable at the surface of the earth. The simplest surface signal to detect is the sudden impulse (SI) but other signals may be found. The existence of a field of MHD discontinuities in the solar wind should make possible the generation of ensembles of shocks and contact surfaces. Various possibilities are explored and these are discussed from the standpoint of combinations of sudden impulses at the earth's surface which are both positive and negative. Some of these are recurrent with a 27-day period; the interplanetary M region shock ensemble associated with this is discussed and the development of these structures in space is reviewed.Lastly observational evidence for interplanetary shock waves is given together with the analytic technique for establishing their geometry and comparing the derived and measured jump parameters. The applicability of the geometrical construction of the general class of MHD discontinuity to their analysis is indicated and shows the way in which the structural content of the solar wind can be classified by the use of magnetometers and plasma probes. A parametric study of the jump conditions through a shock wave can be used to verify the correctness of field measurements because of the redundancy in measurements. This also allows the details of shock structure to be examined including the intrinsic partitioning of the internal energy of the shocked plasma.