Abstract
Specific problems arising, when Von Neumann type computer is used as feedback element, are considered. It is shown, that due to specifics of operation this element introduce pure lag into control loop, and lag time depends on complexity of algorithm of control. Method of evaluation of runtime between reading data from sensors of object under control and write out data to actuator based on the theory of semi- Markov process is proposed. Formulae for time characteristics estimation are obtained. Lag time characteristics are used for investigation of stability of linear systems. Digital PID controller is divided onto linear part, which is realized with a soft and pure lag unit, which is realized with both hardware and software. With use notions amplitude and phase margins, condition for stability of system functioning are obtained. Theoretical results are confirm with computer experiment carried out on the third-order system.
Highlights
Including Von-Neumann type computer to digital control loops born many problems, main of which is the problem of gap from emergence a situation, which requires an adequate control system response, till the real action, affected onto the controllable object [1,2,3]
Control algorithms have specific features, which had been studied by several authors [4,5,6]: algorithms are a cyclic ones, i.e. they have start operator, but does not have the end operator; quest of peripherals is realized by means of inclusion into algorithm special transaction management operators; for an external observer selection of branch in places of algorithm ramification is a stochastic one, and probabilities of branching depend on a distribution of data processed; for an external observer algorithm operators’ run-time is, a random one, distribution function of time of operator execution depends on distribution of data processed
Let us consider an influence of lag time fsa (t) on the stability of digital feedback control system, shown on the Figure 1 for the case, when model of object under control is the linear one
Summary
Including Von-Neumann type computer to digital control loops born many problems, main of which is the problem of gap from emergence a situation, which requires an adequate control system response, till the real action, affected onto the controllable object [1,2,3]. Time lag depends on a number of factors, such as computer architecture, clock frequency, instructions structure, operating environment, scheduling discipline, transactions order, mathematical foundation of control algorithms, etc. A process of a deterministic algorithm interpretation with Von-Neumann type controller for external observer by several authors [5, 7, 8] is regarded as semi-Markov process with continuous time. Operators of an algorithm are considered as states of semi-Markov process. Interpretation of algorithm may be considered as sequence of state switches or wandering through the states of semi-Markov process. Time intervals between semi-Markov process states, which are abstract analogues of operators mentioned and influence of intervals onto the quality of control in linear control systems is subject of following investigations
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