04-02-2013, 09:37 AM
New Current Control Loop with Resonant Controllers by using the Causal Ordering Graph - Application to Machine Tools
1New Current Control.pdf (Size: 486.58 KB / Downloads: 28)
Abstract:
Most machine tool applications operate with industrial computer numerical controllers (CNC). This kind of
controllers is settled for three cascaded closed loops: current, speed and position loop, from the internal to the external
loop respectively. More precisely, the current control loop is considered with IP controllers. In this paper, in order to
enhance the precision of such system, we propose to design a new current control loop with resonant controllers.
Nowadays, actuators of machine tools applications are made with linear drives, mainly with permanent magnet linear
synchronous motors (PMLSM). We present the Causal Ordering Graph (COG) representation of a PMLSM model,
which includes harmonics of Back Electromotive Force (EMF) that are classically neglected. After that, by using the
inversion principle of the COG, we propose to design resonant controllers for the current control loop. To confirm the
effectiveness of resonant controllers, we show experimental results.
Introduction
Linear drives offer very high performances: high
traverse speeds, very high acceleration due to their low
inertia, high reliability due to a small number of
components, reduced bulk, which facilitates the
construction of compact machines, especially in the
machine tools framework [1]. The linear motor used is
essentially an iron core, single side, flat permanent
magnet linear synchronous motor [2]. The industrial
computer numerical controllers (CNC) used to control
such linear drives are made with three cascaded closed
loops: an IP controller for the current control loop, an IP
controller for the speed control loop and finally a P
controller for the position control loop, Fig.1 [3].
Model of PMLSM
In this section, we present the model of a PMLSM with a
non-sinusoidal back EMF. To adapt the proposed control
structure, this model is established in Concordia’s
reference frame, Fig.2. As is classically the case in
machine tool applications, the linear motors are starconnected
with an inaccessible neutral wire: only two
currents are really independent. Thus, Concordia’s
reference frame, a so-called diphase stationary reference
frame, is more appropriate to represent such system.
The Causal Ordering Graph
The Causal Ordering Graph is built up with several
graphical processors attached to different objects located
in the studied process. As seen in the previous section,
the evolution of these objects is characterized by a
transformation relation between influencing quantities
and influenced quantities. This relation is induced by the
principle of causality governing the energetic relation of
an object or group of objects. In short, the output of a
processor only depends on present or past values of the
inputs. Such a formulation expresses the causality in
integral form and many significant electrical and
mechanical examples illustrate this concept. Since the
flux in a self is an integral function of the voltage, by
analogy, the kinetic moment of a rigid mass is the
integral function of the applied efforts. The electricity
quantity in a capacitor is an integral function of the
current; by analogy, the endpoints position of a spring is
the integral of the velocity variation between the
endpoints (Hooke’s law) [7].
Resonant controller
Given our model of back-EMF, composed of harmonics
(Table 1), we have decided to compensate two
harmonics of back-EMF: the fundamental and the 5th
harmonic. Thus, the resonant controllers have identical
structures with two resonant frequencies. In this way, the
tracking of the reference currents and the rejection of
disturbances from non-sinusoidal back-EMF can be
simultaneously realised. As explained previously, the
resonant controllers are placed inside the Rc3 processor.
Experimental results
The proposed approach has been experimentally verified
on a laboratory test system equipped with a Rexroth
LSP120C linear motor, Fig.10. Table 2 lists the
specifications of the test system. The control scheme
depicted in Fig.6 has been implemented in a dSPACE
DS1005 real-time digital control card to drive the
PMLSM through an IGBT inverter. We have used a
Heidenhain exposed linear encoder with a grating period
of 20μm, which is a high precision incremental encoder,
to detect the mover position.
Conclusion
This paper presents a novel approach to improve the
thrust control performance of a PMLSM with nonsinusoidal
back-EMF. First, a model of PMLSM with
non-sinusoidal back-EMF has been presented with the
Causal Ordering Graph representation. Then, by
applying the inversion principle of the COG, we have
deduced the controller synthesis. Next, a multifrequency
resonant controller has been proposed to
ensure the tracking of the desired current waveforms. It
has allowed us to compensate for the non-sinusoidal
back-EMF. Finally, experimental results are shown from
a laboratory test system and verify the effectiveness of
the suggested approach.