برآورد سرعت و تشخیص خطا برای PMSM از طریق حالات شبه کشویی Speed Estimation and Fault Detection for PMSM via Quasi Sliding Modes

Permanent Magnet Synchronous Motors (PMSMs) are widely used in industry, particularly in motion control applications in the low and medium power range (e.g. robotics and machine tool drives) due to their fast dynamical response, high torque to weigh ratio, linear dependence of the torque on one component of the current in a suitable reference frame, simple construction and easy maintenance (Rossi and Tonielli, 1994; Xu and Rahma, 2007; Shyu et al., 2002; Ebrahimi et al., 2009). With advances in digital technology over the last several years, adequate data processing capability is now available on cost-effective DSP-based platforms, enabling the integration of control and fault diagnosis procedure able to increase PMSMs performance, raise their lifetime and lower their high costs. Nevertheless, the cost-effectiveness of any proposed approach for control and fault detection has to be addressed. Indeed, the cost associated with mechanical sensors and expensive hardware required by computational complexity is significant in particular for mass-produced motors in the kW range. Therefore, control and fault diagnosis of motors based on readily available sensors and on algorithms simple enough to be executed using low-cost industrial DSP in real-time appears susceptible of industrial interest due to its cost-effective nature and wide applicability to a large class of motors (Kliman et al., 1997; Aller et al., 2002; Han and Song, 2003). Considering control issues requiring specific attention in electric drive systems, it is well known that electromechanical parameters are subject to significant variations. A nonlinear control strategy widely recognized and successfully applied in recent years is Variable Structure Control (VSC) (Pisano et al., 2008; Utkin et al., 1999; Sabanovic et al., 2002; Chern and Wong, 1995; Hung et al., 1993; Young et al., 1999.; Utkin, 1993; Yan et al., 2000). Indeed, VSC methods provide robustness to matched uncertainties (Utkin, 1992) (Zinober, 1994), and are computational simpler with respect to other robust control approaches, thus well suited for low-cost DSP implementation. VSC schemes are typically affected by chattering of the control signal but, as discussed in (Bartolini et al., 2006; Utkin et al., 1999), this well-known implementation drawback of VSC does not cause difficulties for electric drives since the on-off operation mode is the only admissible one for power converters. For PMSM, the cascade control structure of the Field Oriented Control (FOC) is often usefully applied to achieve fast four quadrant operation, smooth starting and acceleration (Lin, 1997; Lin et al., 1997; Lin and Chiu, 1997; Lin and Lin, 1999; Ghribi and Le-Huy, 1994). FOC is implemented with two current controllers in inner control loops and a speed controller in an outer control loop. The speed controller provides the reference current for one of the two inner current control loops; this reference current corresponds to the required motor torque. As argued in (Utkin et al., 1999), VSC techniques cannot be applied for the outer speed control loop, since the reference input of the inner current control loop should have bounded time derivatives. To overcome this problem, different approaches have been followed, such as, for instance, the ‘direct speed control’ (Utkin et al., 1999) and the ‘second-order sliding-mode technique’ (Pisano et al., 2008). Both techniques, however, share a formulation in the continuous time framework, while the practical implementation on a low-cost DSP of a real motor drive claims for a more appropriate formulation of the problem in a sampled-data systems context. A possible solution is presented in this paper, where a control system based on Discrete-Time VSC (DTVSC) (Chan, 1997; Chen et al., 2001; Corradini and Orlando, 1997; Furuta, 1993; Kaynak and Denker, 1993; Lee and Oh, 1998) is designed. The introduction of DTVSC, in fact, allows to take directly into account the issue of control law digitalization and to ensure robustness with respect to disturbances and model uncertainties. Moreover, decoupling and linearization of the nonlinear PMSM model is not required before the application of the VSC technique. High performance control of PMSM drives also requires the knowledge of the shaft speed (Vas, 1990; Bartolini et al., 2003). The standard backward-difference method to speed estimation, using sampled position measurements provided by a digital incremental encoder, gives high errors in particular at low speed (Khadim et al., 1993; Fujita and Sado, 1992). To overcome the problem of ineffective speed measurement, different results have been given considering the use of nonlinear observers (Misawa and Hedrick, 1989; Rajamani, 1998), in particular based on high-gain, adaptive or sliding mode control (Utkin, 1992; Tornamb`e, 1992; Slotine et al., 1987; Drakunov, 1992). In this paper, a novel observer of the speed variable is presented, and a coupled controller based on quasi sliding modes is proposed. The asymptotic vanishing of both the observation error and the speed tracking error is proved. Summing up, the features of the DTVSC technique combined with the state observer are exploited in this work to design the cascade-based architecture shown in Fig. 1, where it can be identified the external observerspeed control loop and the two internal current control loops (the meaning of the signals and blocks shown in Fig. 1 will be explained throughout this paper). A further feature of the proposed scheme of Fig. 1 is that the observer designed for speed estimation also allows a residual signal to be defined, able to detect fault using Park’s vector currents. Early detection of faults is desirable for online condition assessment, product quality assurance and improved operational efficiency of PMSMs. Indeed, fault detection issues are receiving increasing attention in recent years. Various model-based approaches have been developed (Chen and Patton, 1999), and in particular observer-based techniques constitute a very active research thrust. The comprehensive survey paper (Frank, 1987) provides an overview of observer-based approaches, and a number of results have been established (see e.g. (Shields, 2005; Xu and Zhang, 2004) and the references therein). In particular, sliding mode well-established method for handling disturbances and modeling uncertainties has been employed to develop robust observer for fault detection (Tan and Edwards, 2002; Yan and Edwards, 2007). A noticeable feature of the control approach presented in this paper is that it offers a simple fault diagnosis method that can be implemented at no cost using the readily available electric motor inverter sensor and the DSP control unit. The paper is organized as follows. The motor dynamics is presented in Section 2. In Section 3 some preliminaries are given and details on the considered observer based sliding mode control and fault detection are discussed. Results on numerical tests are reported in Section 4. The paper ends with comments on the performance of the proposed controller.