X-Y tables are widely used in machining processes such as lathe, milling machine, and SMD mounter in the manufacturing fields. Since an X-Y table can be regarded as a linear system in a global sense, it can be controlled with reasonably good performance by the conventional linear control scheme like the PID (Proportional-Integral-Derivative) controller. The control precision and time domain specifications of X-Y tables vary depending on their application. Nowadays, as machines are used for precise operations in manufacturing fields, fast and precise control of X-Y table are required. For high-precision control, the conventional control schemes are not suitable because the mechanical systems being controlled will have several nonlinearities including friction, backlash, hysteresis, actuator saturation, etc. Actuator saturation primarily affects the transient performance, while stiction may cause steady-state error or limit cycle near the reference position in case of conventional linear control of positioning systems.
Various high-precision position control techniques have recently been suggested. We can divide them in to two category. The first falling into the model based scheme and the other into non-model based scheme. Model based schemes use a nonlinear model of the controlled system. It is, however, difficult to identify the nonlinear model. Moreover, the nonlinearities change with respect to time and system position. Non-model based schemes don't need a complicated nonlinear model. For example, in case of adaptive pulse width control, the controller applies a pulse and waits for the system to settle, and then calculates a pulse width as the next control input. Thus, too much time might be needed for the system to reach the at a goal point. These schemes might not be suitable for systems which should settle down quickly.
On the other hand, fuzzy-based control methods are useful when precise mathematical formulations are infeasible. Moreover, fuzzy logic controllers often yield superior results to conventional control methods.
In this work, a high-precision controller based on a two-layered controller structure for the X-Y table under the influence of friction, actuator saturation, dead-zone, and other nonlinearities is proposed. The proposed scheme consists of two controller modes: a tracking controller mode and a two-layered controller mode. In the tracking controller mode, any stable controller can be used if the controller can trigger the fuzzy compensator around the goal position. The two-layered controller consists of a fuzzy precompensator and a PD controller. The fuzzy precompensator is introduced to improve the performance of the PD controller.
Normally, the fuzzy rules are obtained from an expert. But, it is a time-consuming and difficult task, even for an expert to tune fuzzy rules to obtain a high-precision control. In proposed scheme, for the high-precision control, experimental evolutionary algorithm (EEA) is employed to directly obtain the real values of the consequent parts of the fuzzy rules. Techniques are introduced to incorporate the apriori knowledge into the design process. The same were tested and evaluated with different cases and are found to give superior performance.
Validating controller performance becomes problematic when a controller is not designed using analytic techniques. In such cases it is insufficient to evaluate time domain responses for a few initial conditions. Instead, controller validation should involve global evaluation of its performance over the entire operating region. But this is intractable because a continuous phase space has an uncountably infinite number of states. In this work, a cell-to-cell mapping approach for analyzing the global performance of proposed controller is introduced. It makes the problem of analyzing a continuous state space computationally tractable by partitioning it into a finite number of disjoint, equal-sized cells.
The applicability of the proposed scheme for high-precision control is demonstrated by experiments on the X-Y table, with a positioning error of less than 1㎛ where the maximum velocity and acceleration are 0.25 m/s and 1.7 $m/s^2$, respectively.
