ROBUST TWO‐DEGREE‐OF‐FREEDOM CONTROL OF AN ATOMIC FORCE MICROSCOPE

The performance of an atomic force microscope (AFM) is improved substantially by utilizing modern model‐based control methods in comparison to a standard proportional‐integral (PI) controlled AFM system. We present the design and implementation of a two‐degree‐of‐freedom (2DOF)‐controller to accomplish topography measurements at high scan‐rates with reduced measurement error. An H_∞‐controller operates the AFM system in a closed loop while a model‐based feedforward controller tracks the scanner to the last recorded scan‐line. Experimental results compare the actual performance of the standard PI‐controlled AFM and the 2DOF controlled system. The new controller reduces the control error considerably and enables imaging at higher speeds and at weaker tip‐sample interaction forces.     

Robust nonlinear control of atomic force microscope via immersion and invariance

This paper reports an immersion and invariance (I&I)–based robust nonlinear controller for atomic force microscope (AFM) applications. The AFM dynamics is prone to chaos, which, in practice, leads to performance degradation and inaccurate measurements. Therefore, we design a nonlinear tracking controller that stabilizes the AFM dynamics around a desired periodic orbit. To this end, in the tracking error state space, we define a target invariant manifold, on which the system dynamics fulfills the control objective. First, considering a nominal case with full state measurement and no modeling uncertainty, we design an I&I controller to render the target manifold exponentially attractive. Next, we consider an uncertain AFM dynamics, in which only the displacement of the probe cantilever is measured. In the framework of the I&I method, we recast the robust output feedback control problem as the immersion of the output feedback closed‐loop system into the nominal full state one. For this purpose, we define another target invariant manifold that recovers the performance of the nominal control system. Moreover, to handle large uncertainty/disturbances, we incorporate the method of active disturbance rejection into the I&I output feedback control. Through Lyapunov‐based analysis of the closed‐loop stability and robustness, we show the semiglobal practical stability and convergence of the tracking error dynamics. Finally, we present a set of detailed, comparative software simulations to assess the effectiveness of the control method.     

Reduction of phase error between sinusoidal motions and vibration of a tube scanner during spiral scanning using an AFM

The design of a phase-locked loop (PLL)-based proportional integral (PI) controller for compensating the phase error between motions from the lateral axes of a piezoelectric tube scanner (PTS) during spiral scanning for an atomic force microscope (AFM) is proposed in this paper. Spiral motion of the PTS for scanning of material surfaces or biological samples using an AFM is achieved by applying two sinusoidal signals with a 90 degree phase-shift and of varying amplitudes to the X and Y-axes of the scanner. The phase error between the X and Y-axes positions and scanner’s vibration due to its mechanical properties increase with increasing scanning speeds which reduce the imaging performance of the AFM at high frequencies. In the proposed control scheme, a vibration compensator is used with the X and Y-PTS to damp the vibration of the PTS at its resonant frequency and the phase error between the displacements of the two lateral axes of the scanner is measured by a phase detector and a PI controller is used to reduce the error. Comparisons of experimental results for reference tracking and imaging performance with the AFM PI controller demonstrate the efficiency of the proposed control method.     

Internal model based robust inversion feedforward and feedback 2DOF control for LPV system with disturbance

To reduce the adverse effects on the control performance and disturbance rejection caused by system uncertainty, a novel internal model based robust inversion feedforward and feedback 2DOF control approach was proposed for LPV system with disturbance. The proposed control approach combines the internal model control and robust inversion based 2DOF control, it utilizes internal model based control to reject external disturbance, utilizes robust inversion 2DOF control to enhance the control resolution and guarantee the system control performance. At first, a LMI synthesis approach for LPV system model identification and a disturbance compensator optimization design method which could minimize H_∞ norm of output error caused by disturbance are presented. Then, combined with internal loop for disturbance compensation, a robust inversion feedforward controller is designed by robust inversion approach and the feedback controller which could render the requirements of reference signal tracking performance and robustness satisfied is obtained by the H_∞ mixed sensitivity synthesis approach. Finally, atomic force microscopy (AFM) vertical positioning simulation experiments are conducted and the experiment results showed that the proposed control approach could achieve better output performance and disturbance rejection compared with conventional internal model based control and robust inversion based 2DOF control approach.     

Integrated design of the feedback controller and topography estimator for atomic force microscopy

In atomic force microscopy (AFM) the force between the measurement tip and the sample is controlled in a feedback loop to prevent damage of the tip and sample during imaging, and to convert the measurement of the tip–sample force into an estimate of the sample topography. Dynamical uncertainties of the system limit the achievable control bandwidth and the accuracy of the topography estimation. This paper presents an integrated approach to design a feedback controller and topography estimator, taking into account the dynamical uncertainties of the system. The proposed methodology is experimentally demonstrated on a commercial AFM system, showing a direct trade-off between the control bandwidth and the accuracy of the topography estimation.     

Hysteresis Compensation and Adaptive Controller Design for a Piezoceramic Actuator System in Atomic Force Microscopy

This paper presents an indirect adaptive controller combined with hysteresis compensation to achieve high accuracy positioning control of piezoceramic actuators and illustrates the results with an atomic force microscope (AFM) application. A dynamic model of a piezoceramic actuator system in AFM is derived and analyzed. A feedforward controller based on the Preisach model is proposed to compensate for the nonlinear hysteresis effects. Then an indirect adaptive controller is designed to achieve desired tracking performance as well as deal with the uncompensated nonlinearity from hysteresis and the system parameter variation due to creep. Experimental results indicate that the proposed controller can significantly improve the positioning control accuracy of the piezoceramic actuator as well as achieve high image quality of the AFM system. The maximum scanning error was reduced from 2µm to 0.3µm in comparison with a proportional‐integral‐derivative (PID) controller. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Development Of Cvt Control System And Its Use For Fuel‐Efficient Operation Of Engine

Continuously variable transmission (CVT) provides an automobile with the ability to change the gear ratio continuously, which can then improve not only ride quality such as acceleration performance but also fuel‐efficiency. However, to take advantage of the ability, a control system that can precisely control the gear ratio is required. This paper proposes such a control system for a belt‐driven CVT system. For controller design, first the CVT system is modeled by analytical and experimental approaches. The resultant static and dynamic characteristics provide a nonlinear first‐order model with an uncertain time constant and time delay. The nonlinear steady‐state gain is adjusted to one by a gain‐scheduled pre‐compensator. Thereby the plant model becomes a linear first‐order lag system with a dead time. The next step is controller design using the plant model. To guarantee stability and control performance against the parameter variation and time delay, the μ‐synthesis, a robust control method, is employed for feedback control. In addition, a feedforward controller is incorporated into the feedback control system to obtain better output response. The feedforward controller is given by a combination of the inverse system of the plant and a reference model that gives desired output response. As a result, the control system becomes a two‐degree‐of‐freedom control system. To evaluate the performance of the control system and its effectiveness on the fuel‐efficiency, computer simulation and driving tests were conducted. The simulation and experiment results prove that the proposed control system can make the gear ratio track a reference output quickly and precisely in the presence of the uncertainties. The results also show that the control system improves fuel‐efficiency by changing the gear ratio so that the engine torque and its revolution speed can satisfy optimum‐efficiency operating condition.     

Effect of Improved Tracking for Atomic Force Microscope on Piezo Nonlinear Behavior

Nanotechnology is an area of modern science which deals with the control of matter at dimensions of 100 nm or less. In recent years, of all the available microscopy techniques, atomic force microscopy (AFM) has proven to be extremely versatile as an investigative tool in this field. However the performance of AFM is significantly limited by the effects of hysteresis, creep, cross‐coupling, and vibration in its scanning unit, the piezoelectric tube scanner (PTS). This article presents the design and experimental implementation of a single‐input single‐output (SISO) model predictive control (MPC) scheme with a vibration compensator which is based on an identified model of the PTS. The proposed controller provides an AFM with the capability to achieve improved tracking and results in compensation of the nonlinear effects. The experimental results, which compare the tracking performances of the proposed controller for different reference signals, highlight the usefulness of the proposed control scheme.     

A Novel Application of Minimax LQG Control Technique for High‐speed Spiral Imaging

Over the last two decades, increasing the scanning speed of an atomic force microscopy (AFM) has been attempted either by applying novel controllers, using alternative scanning methods, or by modifying the hardware setup. This paper demonstrates, the first two approaches to achieve high‐speed AFM image scanning. A robust minimax linear quadratic Gaussian (LQG) controller is designed and spiral scanning is considered as an alternative scanning method rather than conventional raster scanning. The minimax LQG controller is designed based on an uncertain system model which is constructed by measuring the plant variations due to variations in sample mass and also modeling error between the measured and model frequency responses. This controller is also robust against uncertainties introduced as a result of variations of sample mass, spillover dynamics of the scanner at frequencies higher than the first resonance frequency of the scanner, and variation in plant transfer functions due to temperature and humidity. The designed controller is experimentally implemented on an AFM using a dSPACE ds‐1103 real‐time prototyping system and open‐loop and closed‐loop spiral imaging performances are evaluated. The proposed controller provides sufficient damping at the resonant modes to accurately track the sinusoidal reference signal and generate vibration free images. Also, creep, hysteresis, and cross‐coupling effects are significantly reduced. The experimental results show that the proposed scheme outperforms the open‐loop case and some other existing approaches.     

Global tracking of nonlinear systems with simultaneous unknown time‐varying state and input delays

This paper presents the design of a robust control law for a class of nonlinear dynamical systems subjected to parametric uncertainty and simultaneous unknown, variable state and input delays. A novel controller is developed, which consists of a filtered tracking error and the integral of previous values of control input where the limits of integration are dependent on the known bound of the input delay. Lyapunov‐Krasovskii functionals–based stability analysis guarantees a global uniformly ultimately bounded tracking result where sufficient conditions on controller gains and maximum allowable delay are derived. The performance and robustness of the controller are evaluated by simulation on a two‐link robot manipulator for different combinations of time‐varying state and input delays.     

On automating atomic force microscopes: An adaptive control approach

In this paper, modeling and experimental results are given to reveal the structure of atomic force microscope (AFM) dynamics and uncertainties which are strongly impacted by the user's choice of scan and controller parameters. A robust adaptive controller is designed to eliminate the need for the user to manually tune controller gains for different sample cantilever combinations and compensate for uncertainties arising from the user choice of different scan parameters. The performance of the designed adaptive controller is studied in simulation and verified through experiments. A substantial reduction in contact force can be achieved with the adaptive controller in comparison with an integral controller.     

原子力显微镜系统广义预测控制与成像

在原子力显微镜(atomic force microscope,AFM)扫描样品时,控制参数调节困难,依赖于操作经验.本文基于在线动态模型辨识,提出了一种AFM系统广义预测自校正控制与成像方法.首先,利用CARIMA(controlled autoregressive and moving-average)参数模型来描述局部线性化后的AFM系统模型,并通过在线动态模型辨识得到线性化模型的参数;基于该模型,采用基于GPC(generalized predictive control)的优化方法,在线求解类PI(proportional integral)控制器的参数,进而得到一种具有控制参数自动调整功能的AFM成像方法.为了验证本文方法的有效性,进行了仿真与实验测试.结果表明,在AFM扫描速度不同或PI参数选择不恰当的情况下,该方法能够自动地调整控制器参数,从而减小控制误差,提高成像精度.     

Design of a two‐level controller for an active suspension system

The paper focuses on a control design for a vehicle suspension system in which a balance between different performance demands is achieved. The starting point of the control design is a full–car model which contains nonlinear components, i.e. the dynamics of the dampers and springs and nonlinear actuator dynamics. In order to handle the high complexity of the problem this paper proposes the design of a two‐level controller of an active suspension system. The required control force is computed by applying a high‐level controller, which is designed using a linear parameter varying (LPV) method. For the control design the model is augmented with weighting functions specified by the performance demands and the uncertainty assumptions. The actuator generating the necessary control force is modelled as a nonlinear system for which a low‐level force‐tracking controller is designed. To obtain the low‐level controller a backstepping method is proposed. As an alternative solution a feedback linearization method is also presented. The operation of the controller is illustrated through simulation examples. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Simultaneous ℋ︁2/ℋ︁∞ control of uncertain jump systems with functional time‐delays

This paper presents new results pertaining to the control design of a class of linear uncertain systems with Markovian jump parameters. An integral part of the system dynamics is a delayed state in which the time‐delays are mode dependent. The jumping parameters are modelled as a continuous‐time, discrete‐state Markov process and the uncertainties are norm‐bounded. We construct an appropriate Lyapunov–Krasovskii functional and design a simultaneous ℋ︁₂/ℋ︁_∞ controller which minimizes a quadratic ℋ︁₂ performance measure while satisfying a prescribed ℋ︁_∞‐norm bound on the closed‐loop system. It is established that sufficient conditions for the existence of the simultaneous ℋ︁₂/ℋ︁_∞ controller and the associated performance upper bound are cast in the form of linear matrix inequalities. Simulation results are provided and extension to the case where the jumping rates are subject to uncertainties is presented. Copyright © 2007 John Wiley & Sons, Ltd.     

An LMI approach to output‐feedback‐guaranteed cost control for uncertain time‐delay systems

This paper considers the problem of output‐feedback‐guaranteed cost controller design for uncertain time‐delay systems. The uncertainty in the system is assumed to be norm‐bounded and time‐varying. The time‐delay is allowed to enter the state and the measurement equations. A linear quadratic cost function is considered as a performance measure for the closed‐loop system. Necessary and sufficient conditions are provided for the construction of a guaranteed cost controller. These conditions are given in terms of the feasibility of LMIs which depend on a positive definite matrix and a scaling variable. A numerical algorithm is developed to search for a full order dynamic output‐feedback controller which minimizes the cost bound. Copyright © 2000 John Wiley & Sons, Ltd.     

Fixed‐order robust H∞ control and control‐oriented uncertainty set shaping for systems with ellipsoidal parametric uncertainty

In this paper, sufficient conditions for robust output feedback controller design for systems with ellipsoidal parametric uncertainty are given in terms of solutions to a set of linear matrix inequalities. A polynomial method is employed to design a fixed‐order controller that assigns closed‐loop poles within a given region of the complex plane and that satisfies an H_∞ performance specification. The main feature of the proposed method is that it can be extended easily for control‐oriented uncertainty set shaping using a standard input design approach. Consequently, the results can be extended to joint robust control/input design procedure whose controller structure and performance specifications are translated into the requirements on the input signal spectrum used in system identification. This way, model uncertainty set can be tuned for the robust control design procedure. The simulation results show the effectiveness of the proposed method. Copyright © 2010 John Wiley & Sons, Ltd.     

Robust stability,stabilization and ℋ∞ control of time‐delay systems with Markovian jump parameters

In this paper, the problems of stochastic stability and stabilization for a class of uncertain time‐delay systems with Markovian jump parameters are investigated. The jumping parameters are modelled as a continuous‐time, discrete‐state Markov process. The parametric uncertainties are assumed to be real, time‐varying and norm‐bounded that appear in the state, input and delayed‐state matrices. The time‐delay factor is constant and unknown with a known bound. Complete results for both delay‐independent and delay‐dependent stochastic stability criteria for the nominal and uncertain time‐delay jumping systems are developed. The control objective is to design a state feedback controller such that stochastic stability and a prescribed ?_∞‐performance are guaranteed. We establish that the control problem for the time‐delay Markovian jump systems with and without uncertain parameters can be essentially solved in terms of the solutions of a finite set of coupled algebraic Riccati inequalities or linear matrix inequalities. Extension of the developed results to the case of uncertain jumping rates is also provided. Copyright © 2003 John Wiley & Sons, Ltd.     

Quantized output feedback control with multiplicative measurement noises

In this paper, we consider the problem of quantized quadratic performance control for a class of stochastic systems, which are subject to multiplicative noises in the measurement. A dynamic output feedback controller is designed to guarantee a given level of performance. By using the sector bound approach to characterize the quantization error, the existence of a solution for the quantized quadratic performance control problem is found by solving the so‐called guaranteed cost control problem of the associated system with a sector bounded uncertainty. We show that the latter problem can be solved using LMIs. Copyright © 2014 John Wiley & Sons, Ltd.     

Inertia‐free saturated output feedback attitude stabilization for uncertain spacecraft

In this article, the problem of robust output feedback attitude stabilization control for a class of uncertain spacecraft is investigated, which contains external disturbances, model parameter uncertainty, unknown and uncertain inertia, controller's gain perturbations, measurement errors, and input saturation. The aim of this work is to design a dynamic output feedback controller such that the closed‐loop attitude system is stabilized, while the H_∞ norm of the transfer function from the lumped disturbance and measurement error to output is ensured to be less than a pre‐specified disturbance attenuation level, and the actual control input is confined into a certain range simultaneously. Based on the Lyapunov theory, the existence conditions of such controller are derived in terms of linear matrix inequalities. It is worth mentioning that the controller's additive and multiplicative perturbations are accounted for respectively. An illustrative example is given to demonstrate the effectiveness and advantage of the proposed control design method.     

Sliding Mode ∑‐Δ Modulation Control of the Boost Converter

A switched implementation of average dynamic output feedback laws trough a ∑‐Δ‐modulator, widely known in the classic communications and analog signal encoding literature, not only frees the sliding mode control approach from state measurements and the corresponding synthesis of sliding surfaces in the plant's state space, but it also allows to effectively transfer all desired closed loop features of an uniformly bounded, continuous, average output feedback controller design into the more restrictive discrete‐valued (ON‐OFF) control framework of a switched system. The proposed approach is here used for the input‐output sliding mode stabilization of the “boost” DC‐to‐DC converter. This is achieved by means of a well known passivity based controller but any other output feedback design would have served our purposes. This emphasizes the flexibility of the proposed sliding mode control design implementation through ∑‐Δ‐modulators.