Feedforward Control Strategies for High-Speed Contouring Machine Tools

d (t) u(t) y(t F((J,q) P(q) ~ I .. ... I I I I I I I I Figure 2: A general architecture of tracking systems using feedforward control I I I I I I I I I I I I I I I I I I I I I ~ Feedforward _ ............. : . Closed LooP--": ; Controller ~ Plant ! In Figure 2, the feedforward controller appears as a pre-filter before the closed-loop system comprising the prevalently adopted is to feed forward a signal representative of the rate of change of the position command. The feedforward signal breaks into the feedback loop as illustrated in Figure 1. In the past decade, a number of researchers have proposed pre-filtering or "shaping" the command signal so as to give more emphasis to frequency components which are not de~t with adequately by the feedback system. The concept leads to a general form of feedforward con-, .. troller (or series compensator) as shown in Figure 2, where (J is a parameter vector. y Figure 1: The arrangement of a conventional feedforward controller Recent feedforw~dcontrol strategies to achieve higher motion-control bandwidths for contouring machine tools are investigated in this paper. Conventionally, a simple feedforward signal based on the derivative of the input is added to the feedback control signal to reduce the system dynamic lag and thereby increase the bandwidth. H accurate parameters of the system are known in advance, a more sophisticated feedforward controller can be designed based on the inverse of the system model. In this paper, several feedforward control strategies are discussed and their performances are compared with a proposed Adaptive Calibrating Controller. Servo-driven contouring machine tools such as laser cutting and milling machines are capable of producing highquality precise parts. However, the productivity of such machines is often limited by the loss of dynamic contouring accuracy as cutting speeds are increased. A variety of sources, including meehanical inaccuracies and machine/controller dynamics, are known to be major factors causing contouring errors. A detailed discussion of these performance limiting factors in highspeed contouring can be found in [Ko et al., 1998a], where they are categorised as dynamic constraints, uncertainties and non-lin.earities. When cutting is performed at low speeds,dynamic constraints such as the system bandwidth do not contribute much to the .contouring error. However, the attainable bandwidth can become the dominant factor when the contouring speed or profile curvature is increased, because of the increased high frequency content of the input to the motion control system. The lagging response of a feedback control system often results in a significaat contomhtg error. A strategy