Zero Phase Error Tracking Controller Research Articles

Motion profile and control design of fast steering mirror for backscanning step and stare imaging.

Fast steering mirrors (FSMs) have been used for decades to improve the performance of electro-optical imaging systems, such as airborne imaging systems and space-based optical surveillance systems. With the advantage of increasing the accuracy of image motion compensation and the efficiency of scanning imaging, backscanning step-and-stare imaging has become the main approach to realizing wide-area surveillance for airborne imaging systems. According to the operating mode and motion profile of the FSM in the imaging system, a combined optimized profile (COP) is designed to avoid abrupt changes in the velocity and acceleration of the FSM. The angular position sensor based on a four-quadrant detector is used in FSMs to expand the measuring range and cut the cost at the expense of larger measurement noise. Combining a Kalman filter with a disturbance observer and zero-phase error tracking control, a control method is proposed to improve the control precision and bandwidth while suppressing measurement noise. Simulation and experimental results show that the profile designed by COP is smooth enough to meet the special requirements of FSM's backscanning image motion compensation and that the Kalman filter-based FSM control method can significantly improve the control accuracy.

High-performance control of fast tool servos with robust disturbance observer and modified [formula omitted] control

Fast tool servo (FTS) is an effective technique for the generation of complicated surfaces in modern precision manufacture industry. In this paper, a novel three-degree-of-freedom (3-DOF) control scheme is proposed for the FTS to achieve good tracking and disturbance rejection performance. Specifically, the 3-DOF control scheme contains a hysteresis compensation term, a modified H∞ feedback control term, a robust disturbance observer (RDOB) term and a feedforward control term. Firstly, a hysteresis compensator is developed based on the modified Prandtl–Ishlinskii (MPI) model to eliminate the intrinsic hysteresis nonlinearity so as to identify the linear dynamic model of the FTS system. A modified mixed-sensitivity-based H∞ feedback control is then proposed to simultaneously provide an excellent damping and tracking performance with a deliberately designed input weighting function. A RDOB is designed for non-minimum phase (NMP) system based on all-pass factorization of the linear dynamics model and the standard H∞ control framework to compensate uncertain external disturbances as well as unmodeled dynamics while guaranteeing the robust stability of closed-loop system. To remove phase delay and enlarge control bandwidth, a closed-loop-inversion feedforward controller is synthesized by integrating a zero-phase error tracking control (ZPETC) with a finite impulse response (FIR) filter. A series of comparative experiments are conducted on a self-developed flux-biased normal-stressed electromagnetic actuated FTS. The experimental results consistently validate the effectiveness and superiority of the proposed scheme in terms of outstanding tracking performance and disturbance rejection.

Fractional order zero phase error tracking control of a novel decoupled 2-DOF compliant micro-positioning stage

This study focuses on a piezo-actuated two-degrees-of-freedom (2-DOF) decoupled compliant micro-positioning stage driven by a novel compound bridge-type amplification mechanism embedded with Scott-Russell mechanism. According to the system identification, the transfer functions of two working directions are obtained. Both of the measured dynamic cross couplings between them are also lower than −40 dB, demonstrating that the single-input-single-output control strategy can be adopted reasonably. Based on the identified frequency response, a fractional order proportional-integral (FOPI) controller is designed for the 2-DOF compliant micro-positioning stage. Compared with the integer order proportional-integral (IOPI) controller using same parameters, the amplitude error of the FOPI controller is 2% lower than that of IOPI controller. Additionally, a fractional order zero phase error controller (FOZPETC) is designed by obtaining the inverse of the fractional order closed-loop system in a large frequency range. And the gain of the corrected control system is 1 in a wide frequency band to eliminate the phase error in the close-loop control system. Finally, using the compound control strategy of FOZPETC+FOPI, a series of trajectory tracking tests are carried out on the proposed novel 2-DOF compliant micro-positioning stage. All the experimental results prove that the designed controller can achieve good positioning and tracking performance of the micro-positioning stage, and confirm the effectiveness of the compound control strategy of FOZPETC+FOPI.

Tracking Control of an Electro-Hydraulic Actuator System using LQR Controller

Electro-Hydraulic actuator (EHA) is a one type of application used in industry and building high performance of motion control process. Apparently, dealing with EHA behaviour is quite difficult and make the controlling process complicated. Designing Linear Quadratic Regulator (LQR) controller as a feedback controller require in selecting the weighting parameter Q and R. The result shows that the higher value of Q offers fast response and high stability by referring the placement of close-loop poles. However, the higher value of Q gives a higher error that can make position performance of hydraulic actuator become worst. In order to overcome this problem, the feedforward controller is developed by implementing the zero-phase error tracking control (ZPETC). It shows that both feedforward and feedback controller offers good tracking position performance in reducing gain and phase error.

Simplified Realization of Zero Phase Error Tracking

Abstract Zero phase error tracking (ZPET) control has gained popularity as a simple yet effective feedforward control method for tracking time varying desired trajectories by the plant output of a continuous time transfer function of relative order greater than or equal to two. In this paper, we will note that the sampling zeros of the zero-order hold equivalent of chain of integrators, 1/sn, are configured for natural realization of zero phase error tracking. This property is exploited to realize a simplified realization of zero phase error tracking control for chain of integrators. The property can also be utilized for general transfer functions when the sampling period for digital control is small. The effectiveness of the proposed approach for general transfer functions is demonstrated by simulations.

Repetitive Control Meets Continuous Zero Phase Error Tracking Controller for Precise Tracking of B-Spline Trajectories

In this paper, a novel repetitive control scheme is presented and discussed, based on the so-called B-spline filters. These dynamic filters are able to generate a B-spline trajectory if they are fed with the sequence of control points defining the curve. Therefore, they are ideal tools for generating online reference signals with the prescribed level of smoothness for driving dynamic systems, possibly together with a feedforward compensator. In particular, a continuous zero phase error tracking controller (ZPETC) can be used for tracking control of nonminimum phase systems but because of its open-loop nature it cannot guarantee the robustness with respect to modeling errors and exogenous disturbances. For this reason, ZPETC and trajectory generator have been embedded in a repetitive control scheme that allows to nullify interpolation errors even in nonideal conditions, provided that the desired reference trajectory and the disturbances are periodic. This paper is based on the results presented in the conference paper [L. Biagiotti, F. Califano, and C. Melchiorri, “Repetitive control of non-minimum phase systems along b-spline trajectories,” in Proc. IEEE 55th Conf. Decis. Control , 2016, pp. 5496–5501.], where asymptotic stability of the overall control scheme has been proved mathematically, but extends such results with an experimental validation based on a nonminimum phase system. Different models of the same physical system have been identified and used in the implementation of this model-based control scheme, allowing a real evaluation of the relationship between control system performance and model accuracy.

Research on periodic disturbance suppression method in printer paper folding mechanism based on disturbance observer algorithm

The quality of the final prints in electronic-shaft paper-folding machinesseriously influenced by the mechanical periodic disturbance. This paper takes the periodic shock-disturbance and sinusoidal disturbance in the electronic-shaft paper-folding machineas as the research objects. Disturbance observer is designed based on Propotional Integral Diffrential (PID) control algorithm. Firstly this paper establishes a model of the system with MTALAB system identification tools in the process of establishing the control system. Secondly,the paper inverses this established model. In order to approximate the mode and guarantee the stability of the inversed model, zero-phase error-tracking controller (ZPETC) has been designed to remove the instable zero-point of the original model. Finally, the paper constructs the disturbance observer of the established reversed model based on PID control algorithm. The simulation on experimental platform shows that the resistivity of paper-folding machine to the external disturbance has been improved impressively and the proposed PID algorithm disturbance observer has been proved can be used in periodic disturbance suppression in the electronic-shaft paper-folding machine.

Pulse-Width-Modulation with Zero Phase Error Tracking Controller System for Electrocardiogram Feature Extraction and Tracking from Virtual Patient

Pulse-Width-Modulation with Zero Phase Error Tracking Controller System for Electrocardiogram Feature Extraction and Tracking from Virtual Patient

Contour Error Control Based on Optimal Discrete Controller

An optimal discrete controller is presented in this paper for contour error control using the standard linear quadratic (LQ) method, upon which the offset loss function and the control loss function were considered to attain a relatively good compromise. The weight coefficient for the control loss and the optimal discrete sampling period are garnered, then a zero phase error tracking controller (ZPETC) is designed with the disturbance observer (DOB) to improve the anti-interference capability and the robustness of the system. The proposed methods are capable of enhancing the stability and rapidity of the discrete controller and reducing the contour error of the system. The results may be valuable for various trajectory tracking control applications.

Sine phase compensation combining an amplitude phase controller and a discrete feed-forward compensator for electro-hydraulic shaking tables

This article presents a novel control strategy on an electro-hydraulic shaking table under the acceleration control combining an amplitude phase controller and a zero phase error tracking controller with a discrete feed-forward compensator. Because of the electro-hydraulic system’s nonlinearity, phase delay and amplitude attenuation exist in the acceleration response signal inevitably when the electro-hydraulic shaking table system is excited by a sine vibration signal. Moreover, the phase delay of the electro-hydraulic shaking table is composed of phase deviation and actuator delay. For improving the acceleration tracking accuracy, an amplitude phase controller is employed to compensate the phase deviation and amplitude attenuation by introducing weights to adjust the reference signal. Meanwhile, the discrete feed-forward compensator is applied to compensate the actuator delay. As an offline compensator, the zero phase error tracking controller is employed to compensate the phase delay of the response signal and improve the convergence speed of the proposed controller. Overall, the proposed control strategy combines the merits of these three controllers with better tracking performance demonstrated by simulation and experimental results.

Dual‐mode LQR‐feedforward optimal control for non‐minimum phase boost converter

A digital dual-mode linear quadratic regulator (LQR) with feedforward optimal controller is presented, which allows voltage control of a boost converter for wide-load-range condition, whether in continuous conduction mode (CCM) or in discontinuous conduction mode (DCM). Based on the conventional LQR method, the proposed controller is designed and makes the following two improvements. First, in order to eliminate the phase error caused by right-half-phase zero emerged in non-minimum phase boost converter, a feedforward controller is implemented by zero phase error tracking control technique because the inverse of non-minimum phase system is unstable. Second, since the models of DC-DC converter in CCM or DCM are different, the proposed control strategy allows boost converter to autonomously operate in CCM or DCM controller by utilising a mode detector. The proposed mode detector greatly enhances the control performance in both operating modes. Finally, the proposed controller has been implemented for voltage control of a boost converter. The simulation and experimental results show the proposed controller offers better performance in both transient response and frequency response than the conventional LQR controller.

零位相誤差追従コントローラを用いた外乱オブザーバ併用型Predictive Functional Control制御系の追従性能改善

零位相誤差追従コントローラを用いた外乱オブザーバ併用型Predictive Functional Control制御系の追従性能改善

Dynamic tracking performance of servo mechanisms based on compound controller

This article provides systematic analysis and controller design methods for dynamic tracking performance of servo mechanisms associated with practical systems. Discrete general composite nonlinear feedback, as a fundamental controller, will be proposed to yield a good transient performance. Particularly, in the servo systems, there also exist unmodeled disturbances which may lead to tracking errors. A novel repetitive control scheme based on disturbance observer configuration is incorporated into the controller to counteract this unexpected effect. Furthermore, to deal with any periodic signal of variable frequency, a fractional-order repetitive control scheme based on disturbance observer strategy is proposed. The stability of the overall closed-loop system is guaranteed via frequency domain analysis. Three controllers, that is, the proportional–derivative controller with zero-phase error tracking controller scheme and the conventional disturbance observer, the integral backstepping controller, and the compound discrete general composite nonlinear feedback controller with fractional-order repetitive control scheme based on disturbance observer are compared. To demonstrate the dynamic tracking performance of the proposed control strategy, comparative experiments are conducted.

Optimal Design and Hybrid Control for the Electro-Hydraulic Dual-Shaking Table System

This paper is to develop an optimal electro-hydraulic dual-shaking table system with high waveform replication precision. The parameters of hydraulic cylinders, servo valves, hydraulic supply power and gravity balance system are designed and optimized in detail. To improve synchronization and tracking control precision, a hybrid control strategy is proposed. The cross-coupled control using a novel based on sliding mode control based on adaptive reaching law (ASMC), which can adaptively tune the parameters of sliding mode control (SMC), is proposed to reduce the synchronization error. To improve the tracking performance, the observer-based inverse control scheme combining the feed-forward inverse model controller and disturbance observer is proposed. The system model is identified applying the recursive least squares (RLS) algorithm and then the feed-forward inverse controller is designed based on zero phase error tracking controller (ZPETC) technique. To compensate disturbance and model errors, disturbance observer is used cooperating with the designed inverse controller. The combination of the novel ASMC cross-coupled controller and proposed observer-based inverse controller can improve the control precision noticeably. The dual-shaking table experiment system is built and various experiments are performed. The experimental results indicate that the developed system with the proposed hybrid control strategy is feasible and efficient and can reduce the tracking errors to 25% and synchronization error to 16% compared with traditional control schemes.

Adaptive Position Controller Design of Electro-hydraulic Actuator Using Approximate Model Inversion

An electro-hydraulic actuator (EHA) is widely used in industrial motion systems and the increasing bandwidth of EHA position control is important issue. The model-inverse feedforward controller is known to extend the bandwidth of system. When the system has non-minimum phase (NMP) zeros, direct model inversion makes system unstable. To overcome this problem, an approximate model-inverse method is used. A representative approximate model inversion method is zero phase error tracking control (ZPETC). However, if zeros locate right half plane of z-plane, the approximate inverse model amplifies the high-frequency response. In this paper, to solve the problem of ZPETC, an adaptive model-inverse control is proposed. The adaptive algorithm updates feedforward term in real-time. The effectiveness of the proposed adaptive model-inverse position control strategy is verified by comparison with typical proportional-integral (PI) control and feedforward control by experiments. As a result, the proposed adaptive controller extends the bandwidth of EHA position control.

Composite Motion Design Procedure for Vibration Assisted Small-Hole EDM Using One Voice Coil Motor

To address the problem of debris accumulation in small-hole electrical discharge machine (EDM) and simplify the design of the spindle head, the paper proposes a novel composite motion design procedure integrated high frequency vibration and large stroke feed using one voice coil motor (VCM). Particularly, for the purposes of high servo accuracy and high frequency response of the composite motion, an improved zero-phase-error tracking controller (ZPETC) algorithm decoupled with the feedback controller is developed for the process control, in which the feedback parameter adjustment is very simple to reduce the computation complexity. At last, the proposed procedure is validated by the experimental study of the established VCM positioning table; the results verify the efficiency of the proposed method.

Predictive Functional Control of a Table Drive System Using Disturbance Observer and Preview Feedforward Controller

This paper addresses a two-degree-of-freedom control system design for positioning de-vices such as table drive systems based on the predictive functional control (PFC). The aim of the paper is to improve the tracking performance of the previously developed disturbance observer-based predictive functional control (DOB-PFC) system. To this end, we derive a transfer function representation of the PFC controller. On the basis of the representation, we apply the zero phase error tracking controller (ZPETC) as a feedforward preview controller. Experiments using a real table drive system are conducted to compare the proposed control system with DOB-PFC. The experimental results show that the tracking error is greatly reduced compared to DOB-PFC.

A Control Strategy of a Two Degrees-of-Freedom Heavy Duty Parallel Manipulator

The motion accuracy of a heavy duty parallel manipulator is usually low due to time lag and the difficulty to real-time measure the position of the end-effector. In this paper, a dynamic modeling of this system with consideration of the link flexible deformation is proposed, and a double-feedforward control is presented. The link deformation is considered in the kinematic model. Taking link deformation into account, the dynamic model is derived for real-time application, and the inverse dynamic compensator is designed. The zero phase error tracking controller (ZPETC) is introduced as the second compensator. The system stability is investigated by simulations. The control method is compared with the kinematic-based control without consideration of link deformation. The results show that the maximum contouring error reduces from 7.5mm to 10μm. Thus, the tracking performance is improved when using the method proposed in this paper.

Robust repetitive control design and its application on linear servo systems

A robust design method of the discrete-time plug-in repetitive control system is proposed. By modifying the stabilizing compensator, the robustness of the repetitive control system can be well ensured together with the zero-following error performance. The design method is simple and straightforward. Meanwhile, a novel robustness criterion for the discrete-time repetitive control system is introduced, and theoretical analysis is taken to compare the robustness of the proposed controller with the widely used zero phase error tracking controller (ZPETC). The proposed repetitive controller is implemented in a linear servo system. Simulation is performed to verify the theoretical analysis, and the experimental results show the effectiveness of the proposed controller.

A new approach to contour error control in high speed machining

High speed machining technology attempts to maximize productivity through the use of high spindle speeds and axis traverse rates. The technology is dependent upon the development of suitable mechanical hardware, electrical drives and associated control software to ensure that all components are used to maximum advantage. The role of the control software is particularly demanding since one needs to maximize traverse rates while providing the necessary accuracy, and indeed providing a margin of safety to deal with unexpected changes in process, or system parameters. There have been relatively few improvements in commercial CAD or CAM systems that would help machine tool users to take maximum advantage of high speed machining; rather the majority of the approaches have been undertaken at the machine tool controller level. This paper uses circular interpolation and corner tracking to compare several such control techniques, (Cross Coupled Control (CCC), Zero Phase Error Tracking Control (ZPETC), and Realtime Frequency Modulated Interpolation (FMI)), each of which have been proposed in the literature order to improve machining accuracy. None of these approaches are found to be universally successful when used alone and the authors, in this paper, examine the use of these systems in combination. Particular attention is focused upon an extension of a simplified version of cross coupled control together with Frequency Modulated Interpolation. It is shown that the combined system performs extremely well, and is easily actuated at high frequencies with conventional hardware. A custom built high speed x-y table is used to confirm system performance with multiple constraints present.