On vibration rejection of nonminimum-phase long-distance laser pointing system with compensatory disturbance observer

Abstract

This paper focuses on the vibration rejection problem for the nonminimum-phase long-distance laser pointing system on the moving platform. Due to the unstable approximate inverse of nonminimum-phase property, the disturbance-observer based control (DOBC) methods inevitably sacrifice numerous vibration rejection capabilities to stabilize the system. In this paper, a compensatory disturbance-observer-based control (CDOBC) method is proposed to ensure a much stronger vibration rejection performance. In this method, the stable nominal plant replaces the unstable approximate inverse. Limited by stability constraints, the primary filter still sacrifices performances to provide basic vibration rejection capabilities. In the premise of a stable primary filter, the proposed compensatory filter naturally and effectively satisfies its stability constraint. Thus, the novel compensatory filter has sufficient flexibility to make up for the sacrificed vibration rejection capabilities of the primary filter without breaking the system’s stability. The CDOBC method has quite enough capability to reject the vibrations of the nonminimum-phase long-distance laser pointing system, which is impossible for the DOBC methods. Furthermore, the analytical system’s stability and tuning laws for the proposed method are presented. The simulations and experiments demonstrated the effectiveness of the proposed method despite various vibrations.

Introduction

The long-distance laser pointing (LDLP) system is promising in various fields, such as quantum communication, adaptive optics, and long-distance laser communication [1], [2], [3], [4]. In the quantum communication system and long-distance laser communication system, laser light is the carrier of the quantum beacon and message. Thus, the laser in the LDLP system is required to pointing to the target with enough precision. However, the LDLP system suffers from external vibrations, which can be caused by airflow and ground shaking. To satisfy different application scenarios, the LDLP systems are even mounted on moving platforms, such as vehicles, ships, and satellites, where the vibrations are ineluctable nonnegligible [5], [6]. The high-accuracy inertially stabilized laser is crucial to reject the disturbances of the LDLP system, which is the fundamental component of the high-efficiency quantum communication and long-distance laser communication [7], [8].

In recent years, vibration rejection of the LDLP system on moving platforms is becoming a very popular research field. In the actual environments, the vibrations introduced by moving platforms are mostly located at low and mid frequencies, which can significantly affect the pointing errors of the LDLP system [8], [9], [10]. In the LDLP system, the image detectors such as charge-coupled device (CCD) are used as a position sensors. With the CCD, the position closed loop (PCL) is built to control the LDLP system to point at a far-away target. However, the CCD requires sufficient integration time to obtain a clear image with a high signal-to-noise ratio [8], [11]. Thus, the CCD’s sampling rate is limited, which restricts the bandwidth and vibration rejection performance of the PCL according to the Nyquist Sampling Theorem [12].

Some new measuring appliances and control methods have been introduced into the LDLP system. The inertial sensors, such as the micro-electro-mechanical system (MEMS) accelerometers and the fiber optical gyroscopes (FOGs) with low weights, small sizes, and high sampling rates , are beneficial to build the high-bandwidth closed loops [13], [14]. The higher bandwidth is instrumental in rejecting more vibrations over a wider frequency range. Besides, the inertial sensors are able to directly measure the acceleration and velocity of the LDLP system in the inertial space. Thus, the MEMS accelerometers and the FOGs are introduced into the system to establish the acceleration closed loop (ACL) and the velocity closed loop (VCL). Based on these, the multi-loop feedback control (MFC) system was proposed [15], [16], which was composed of the PCL, VCL, and ACL. In the MFC system, the bandwidth of the inner loop is obviously higher than that of the outer loop. The vibration rejection capability of the MFC system is the product of each loop. Thus, MFC is considered as the fundamental in LDLP control system that could provide good vibration rejection capacity [6].

For the LDLP system on the moving platform, the basic MFC system is insufficient to reject vibrations, which has no specialized controllers to reject disturbances. Thus, the disturbance feedforward methods based on measurements are recommended to reject the external vibrations in theory [17], [18]. However, it requires extra costs for disturbance sensors to measure the vibrations. In some extreme environments, it is even impossible to measure the vibrations directly. Therefore, the disturbance-observer-based control (DOBC) methods were introduced to estimate disturbances and those estimated statements are used to reject vibrations. The DOBC method without extra sensors was presented by Ohnishi [19], [20], which had been applied to assistive exoskeletons, motion control, servo track writing, and engine servo systems [21], [22], [23], [24]. To remove the impact of mismatched uncertainty with the DOBC method, the systematic disturbance compensation gain design method and sliding-mode control method were introduced [25], [26]. Based on the DOBC method, the repetitive controller and reduced-order observer were presented to deal with the slow dynamics system [27], [28]. The extended state observer, equivalent-input-disturbance approach, and robust state estimation could also estimate the disturbances [29], [30], [31], [32].

However, the current methods are difficult to reject vibrations of the LDLP system. To stabilize the laser in inertial space, the inertial sensors are essential for the LDLP system to obtain high-bandwidth closed loops. In the inertial closed loops, critical stable zeros compose the nonminimum-phase (NMP) property of the LDLP system. The NMP property hinds in the vibration rejection performances of the LDLP system. The standard extended state observer could be problematic for the system with the NMP property [33], and robust state estimation method sacrificed its nominal performance to estimate the disturbances [32]. Although some new DOBC methods have been proposed to reject vibrations of the LDLP system, they ignored the NMP property, which could make the system unstable. In [34], to avoid the NMP property, the DOBC method was introduced in the PCL without critical stable zeros. However, the PCL’s vibration suppression was only effective in the low frequency domain due to its bandwidth limitation. The DOBC method was also utilized in the ACL [35]. However, the NMP property limited the system’s stability of the DOBC method. To stabilize the system, the DOBC method sacrificed the vibration rejection capabilities in the low-frequency band according to [35]. To reject more vibrations, a straightforward approach was presented by introducing the DOBC structure into the both PCL and ACL [36]. However, the approach was a reuse of the same DOBC methods. Consequently, all those methods mentioned before have little help for directly dealing with the NMP property in LDLP systems.

Motivated by the above discussion, this paper proposes a compensatory disturbance-observer-based control (CDOBC) method to reject vibrations of the LDLP system with NMP property. In this method, the stable nominal plant replaces the unstable approximate inverse. Because of the NMP property, the primary filter of the CDOBC method is limited by the system’s stability. Thus, it still has to sacrifice its capabilities to stabilize the system. However, in the premise of a stable primary filter, the compensatory filter of the CDOBC method has no stability constraints. Thus, the design of compensatory filter has enough flexibility to make up for the sacrifices of the primary filter. Even though NMP property still exists in the inertial closed loop, the dual-filter CDOBC method has the unabridged disturbance estimation capabilities and vibration rejection capabilities. Therefore, the proposed CDOBC method can deal with the NMP property of the LDLP system, which can reject much more vibrations than the DOBC methods. The advantages of the proposed method are summarized as follows:

$•$ The capability of handling the NMP property in inertial closed loops.

$•$ The capability to compensate for the sacrificed vibration rejection capabilities of primary filter.

$•$ The CDOBC method is independent of precise disturbance models.

$•$ The capability to reject external vibrations and modeling uncertainties.

$•$ The vibration rejection capability of the proposed method does not influence the nominal performance.

The rest of this paper is organized as follows. In Section 2, the structure of the CDOBC method is proposed. In Section 3, the stability constraints are discussed. In Section 4, the analytical tuning laws of the dual filters are presented. Based on the tuning laws, the stability constraints of the CDOBC method are further analyzed. In Section 5, simulations and experiments to validate the CDOBC method are described. Finally, concluding remarks are presented in Section 6.