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.


Introduction
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 [1].The applications of adaptive control to movement system are widespread [2][3][4], but it is infrequent in automatic profiling machine.A practical adaptive controlling scheme is proposed for automatic profiling machine in [5].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.

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 [6] of automatic profiling machine are shown in

The Design of MRAC System
The difference equation of the plant is where y(k) and u(k) are the output and input of the plant, respectively; z −1 is delay operator; k is the discrete-time variable.
The difference equation of the reference model is where where e • (k) 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 Introduc ( 8) into (4): Subtract ( 9) from (2): According to the Hyperstability theory, the discrete system control laws [1] are where where where Zero-order hold5 Zero-order hold4 Zero-order hold3 Transfer Fcn2 E(k) cannot be found directly in the operations above, so it can be replaced by e • (k).According to (10), e(k) becomes The prediction error can be gained: Subtract ( 16) from ( 15) and link (11)∼(13); the function becomes Equation ( 17) becomes (18) by calculating,

Simulation Studies
The reference model takes the form as follows: Make simulation according to the analysis above by SIMULINK.The structure of the adaptive control system is shown in Figure 2, and the parameters value are shown in Table 2.
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 (Δ = 0.02).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.

Conclusion
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.

Figure 2 :
Figure 2: Simulation block diagram of MRAC system.

Table
. The equivalent plant of speed

Table 1 :
The parameters of DC motor.
m (k) and r(k) are the output and input of the reference model.The output error and its prediction are given by

Table 2 :
Parameter values of MRAC system.