With the rapid development of national economy, a higher requirement is put forward for the dimension accuracy of thin plate. Because of the time lag in the thickness control system of rolling mill, the traditional PID regulation can no longer meet the technical requirements of thin plate. Smith predictor is used to compensate the measured lag, and the Smith predictive control system is designed by internal model design method. Simulink simulation software is used to analyze and compare the influence of Smith predictor and PID control mode on the system. The sheet and strip products of tandem cold rolling mill have the advantages of good surface technical index, high dimensional accuracy and good mechanical and technological properties. They are widely used in aerospace technology, manufacturing, food packaging, household appliances, chemical industry, light industry, instrumentation and civil small metals and other sectors of the national economy. With the rapid development of various industries, higher requirements are put forward for the dimensional accuracy of sheet products. The dimensional accuracy is required to be in the millimeter and micron scales, while the thickness deviation is only a few microns. Therefore, improving the dimensional accuracy index of sheet and strip products in tandem cold rolling mill is an important direction topic. In production practice, there is a certain distance between the test position of the gauge gauge of rolling mill system and the rolling mill running, which brings a pure lag link to the gauge control system.
For the pure lag link, the traditional PID feedback control system can not feedback through the feedback loop in time, so it can not achieve good control and regulation effect. Smith predictor has a good compensation effect among the pure delay compensation methods currently used. Its application in the automatic control system of rolling mill sheet can improve the control index of the delay system [2]. For open-loop control, as long as the accuracy of controller C (s) and object G (s) is improved, the accuracy of output can be guaranteed. But its shortcoming is that it can’t do anything to adjust the object when it changes or disturbance is added. For the closed-loop system with feedback, although it can send the change of control object and the influence of interference back to the input of the system for adjustment, so as to improve the control accuracy, there are also problems. Because the feedback signal is taken from the output of the system, the feedback signal = unmeasurable interference other factors, unmeasurable interference is mixed with other factors. It can not be distinguished, and even may be flooded by other quantities without timely compensation, thus affecting the regulation effect. Then, if we transform it into an equivalent internal model control design, as shown in Figure 1, in a system with internal model control, the feedback has changed from the original output feedback to the disturbance feedback, so that the disturbance can be compensated in time. When the model Gm mismatches the object G, the feedback information contains disturbance model mismatch information, which is helpful to improve the anti-jamming effect of the system and enhance the robustness of the system. At the same time, the design of the controller also reduces the difficulty. When model matching (Gm = G), the closed-loop system in Fig. 1 is equivalent to the open-loop system. It can be designed according to the open-loop method, which is simple and easy to implement.
It can be seen that the internal model design method has the advantages of both open-loop and closed-loop. The design is simple and feasible, and ultimately achieves a relatively ideal dynamic index. At the same time, robustness is an effective design method, taking into account the function of system regulation and control. Thickness closed-loop system uses Smith predictor based on internal model control structure, as shown in Figure 2. In Figure 2, the controller C is combined with the predictor which does not contain pure delay. Among them, C (s) – controller, G (s) – actual control object, Gm (s) – model, Gm0 (s) – model do not contain pure lag part, dynamic link of Gf (s) – feedback loop.
In the thickness system, the thickness gauge with feedback link is a first-order small inertia link, so the structure of Smith predictor used in this design adds a Gf (s) dynamic link, Gf (s) = 1/(Ths 1), Th is the lag time of thickness gauge and data processing, Th = 0.05s. From the traditional point of view, Smith predictor and PID controller are two different kinds of controllers. Smith predictor is superior to PID controller in that it can be applied to the regulation of large time-delay objects. However, they are equivalent under given conditions, as shown in the feedback control loop shown in Figure 3. The structure of K(s) is an incomplete differential PID controller.
MP in the controller corresponds to the delay time in Smith prediction model, and lambda is an adjustable coefficient.
In the rolling process, the lag time_p varies. The lag time P in the closed-loop system of thickness is a variable with wide range variation. The closed-loop system of thickness is limited: when the rolling speed is low, closed-loop control is not put into operation. The speed of low-speed is limited to V0=0.4m/s, and the maximum rolling speed is Vm=10m/s. According to p=L/V, p=0.16-4s can be obtained. From figs. 4 and 5, it can be seen that the Smith predictor has smaller overshoot and shorter adjustment time than the step response of the PID controller in ideal state, reflecting better dynamic indicators. The main disadvantage of using Smith predictor is that it is difficult to construct an accurate mathematical model. Although we can get the lag time by measuring the rolling speed, thermostatic element and then dynamically track and revise the lag time parameters in the model, it takes a certain time for the process from measuring speed to modifying the parameters in the model, so it is relative to thickness measurement. There is a lag error between the lag time in the model and the actual lag time caused by the position of the instrument.
When the model mismatches, P = 0.16 0.1 = 0.26s, and lambda = 0.3, the step response of the system is shown in Fig.
6 when Smith predictor and PID controller are used. When using the PID controller, the adjustment time is 2 seconds and the overshoot is 16%, while when using Smith predictor, the adjustment time is 1.
5 seconds and the overshoot is 14%. When P = 4S and lambda = 1, the step response of Smith predictor and PID controller is shown in figure 7. From the comparison of figs. 6 and 7, it can be seen that the Smith predictor has smaller overshoot and shorter adjustment time than the step response of the PID controller under the model mismatch state, which also reflects better dynamic indicators.
Aiming at the time lag problem in the closed-loop feedback control system of thickness, a Smith predictor is designed to compensate the system error caused by the measured time lag.
The Smith predictor of the system is designed and the closed-loop transfer function of the position inner loop is equivalent to a typical second-order link system. From the simulation data waveform, it can be seen that Smith predictor controller has better dynamic index than traditional PID controller.