ensuring control processes quality in relay system without speed sensor
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Abstract
The paper considers topical issues of constructing relay systems to control spacecraft attitude and stabilization with no speed sensors (SS) owing to use of internal feedback (IF). To research this system by point methods, e.g. a point mapping method, is difficult because of the need to solve the transcendent equations containing parameters both of control object and of IF. We propose the “diagram of superimpositions" (DS) method based on topological transformations of the phase space and introduction of a relative time, which enables us to solve engineering problems in analysis and synthesis effectively.
The concept of the method is based on the assertion that there is an unambiguous dependence between quality of dynamical regimes in the control system and characteristics of IF transition function. To justify the method a simplified mathematical model of spacecraft motion is applied. The following conditions are accepted: perturbations can be neglected; when the control function is activated, the signal of IF is equal to zero. To the phase surfaces are applied topological symmetry transformations, alignment and projection onto the plane with one of its coordinates being the relative time.
The paper gives specific examples of systems with aperiodic feedback (AF) for two versions of parameters to satisfy the requirements: I – in quality of self-oscillation mode (by pulse width in the limit cycle); II – in quality of transition process (lack of sliding modes). It is shown that the requirements II and I are contradictory for the system with AF while the sliding modes are unacceptable.
It is shown that DS can be used to synthesize the IF to meet requirements of both steady and transient processes consistently. Using the IF it is possible to implement the shutdown laws of the control action on the DS without SS, the same as in case of using the SS. It is shown that in sliding modes transient processes poor in quality can be completely eliminated by choosing the proper form and parameters of the transition function of IF.
The DS topological structure features representing object and IF parameters separately are advantages of the method. A character of the transient process and its quality characteristics are defined by the views and parameters of the curvilinear stairs to DS, squeezing into the limiting cycle. An available binary field of curvilinear coordinates makes it easy to do geometric constructions. DS is of great value for analytical solution of problems concerning IF analysis and synthesis.
| Reference Key |
simonyants2014naukaensuring
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| Authors | ;R. P. Simonyants |
| Journal | BMJ open |
| Year | 2014 |
| DOI |
10.7463/1014.0729606
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| URL | |
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