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Peng Song, Guo-kai Xu, Xiu-chun Zhao, "Discrete Model Reference Adaptive Control System for Automatic Profiling Machine", Journal of Control Science and Engineering, vol. 2012, Article ID 964242, 5 pages, 2012. https://doi.org/10.1155/2012/964242
Discrete Model Reference Adaptive Control System for Automatic Profiling Machine
Automatic profiling machine is a movement system that has a high degree of parameter variation and high frequency of transient process, and it requires an accurate control in time. In this paper, the discrete model reference adaptive control system of automatic profiling machine is discussed. Firstly, the model of automatic profiling machine is presented according to the parameters of DC motor. Then the design of the discrete model reference adaptive control is proposed, and the control rules are proven. The results of simulation show that adaptive control system has favorable dynamic performances.
Automatic profiling machine is a movement system which has a high degree of parameter variation and high frequency of transient process, and it requires an accurate control in time. The traditional linear control methods, such as PID, cannot meet present needs or requirements of advanced performance. The adaptive control not only solves the problem that the control plant cannot be observed directly, but also improved the abilities of resisting interference . The applications of adaptive control to movement system are widespread [2–4], but it is infrequent in automatic profiling machine. A practical adaptive controlling scheme is proposed for automatic profiling machine in . In this paper, a discrete model reference adaptive control (MRAC) method is applied to automatic profiling machine. The discrete control method is convenient for program and contributes to application of adaptive control theory in practice.
2. The Mathematics Model
The control system is double closed-loop control system whose current loop is PI control and speed loop is MRAC. The DC motor parameters  of automatic profiling machine are shown in Table 1. The equivalent plant of speed loop is consisted of current loop and motor, and the transfer function is
3. The Design of MRAC System
The difference equation of the plant is where and are the output and input of the plant, respectively; is delay operator; is the discrete-time variable.
The difference equation of the reference model is where and are the output and input of the reference model.
The output error and its prediction are given by where and the other variables with “∘” represent the predictions.
The structure of the adaptive control system is shown in Figure 1 where
From Figure 1, the following relationship can be obtained
According to the Hyperstability theory, the discrete system control laws  are where where where
cannot be found directly in the operations above, so it can be replaced by . According to (10), becomes
The prediction error can be gained:
4. Simulation Studies
The reference model takes the form as follows:
The simulation results are shown in Figures 3–5. To make a calculation, the percentage overshoot is 6%, the rise time is 1 s, the settling time is 2 s (). Figure 3 is shown that the maximal error value is less than 40 r/min, so the control plant could better track reference model. Input the interference signal into the front of plant transfer function between 10 s and 20 s. The simulation results (in Figure 4) indicate that the control plant could be stable in 2 seconds. Input white noise into the reference input of plant not the reference input of model, and the result is shown in Figure 5. Obviously the figure has no visible variation. So the control system has better abilities of resisting interference.
(a) Reference model
(b) Control plant
(c) Error figure
(a) Control plant
(b) Interference signal
(c) Error figure
The discrete model reference adaptive control system of automatic profiling machine is discussed in this paper. The results of simulation show that adaptive control system has favorable dynamic performance. The discrete design method is easy to realize by computer. The work in this paper will lay a foundation for the application of adaptive control in practice.
This paper was supported by the National Science and Technology Support Program Project (2009BAH41B05) and the Fundamental Research Funds for the Central Universities.
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Copyright © 2012 Peng Song et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.