Robust control and data‐driven tuning of a hybrid integrator‐gain system with applications to wafer scanners

A hybrid integrator‐gain system is discussed that aims for improved low‐frequency disturbance rejection, while, at the same time, does not deteriorate overshoot and settling times when compared with a linear integrator. The hybrid integrator has similar phase advantages as the well‐known Clegg integrator but without inducing the discontinuous behavior resulting from resetting system state values. Optimal tuning of the controller parameters of the hybrid integrator is strongly influenced by machine‐specific properties and therefore favors a data‐driven optimization approach. However, as a time‐domain optimization algorithm can easily lead to nonrobust solutions in the sense of large peaking of the closed‐loop frequency response functions, frequency‐domain robustness constraints will be imposed. By means of an adaptive weighting filter design, the parameter updates are penalized upon violation of said robustness constraints. Posed in an unconstrained problem formulation, this is subsequently solved by applying a Gauss‐Newton–based parameter update scheme. Closed‐loop stability of the linear time‐invariant plant and controller in feedback connection with a hybrid integrator‐gain system element follows from a circle‐criterion‐like analysis, which is based on evaluating (measured) frequency response data. Measurement results obtained from an industrial wafer scanner demonstrate the effectiveness of the approach.     

Transfer function‐matched capacitor‐current sensing and its circuit implementation for high‐frequency power converters

It would effectively achieve a fast load transient response in switching‐mode power converters when introducing capacitor current into the feedback control loop. In these schemes, an accurate and rapid sensing of capacitor current is crucial in the control circuit design. On this issue, a paralleled nonintrusive sensing scheme for capacitor current is proposed in this paper, which is implemented by matching the transfer functions of the sensing circuit and the sensed capacitor branch. With the proposed transfer function matching approach, 4 possible circuit topologies are derived in theory, and on this basis, a parameter design flow chart is given for 2 of candidate topologies. With the application of the proposed capacitor‐current sensing circuit to a constant‐frequency hysteresis controlled Buck converter, a fast and accurate sensing of capacitor current is achieved in experiment, as well as a fast load transient response.     

Analytical multi‐parametric stability boundaries of DC‐DC buck converters under V1 control concept

Two main methods for controlling switching converters exist in the literature. The direct one is the voltage mode control, which suffers from some disadvantages such as slow response to load variations and an input voltage‐dependent total loop gain. The current mode control can overcome these problems but at the expense of extra cost and more complex control design. V¹ concept is a new promising control technique for designing voltage mode control of buck‐type converters with an optimal response similar to current mode control. In this paper, the dynamics and the stability of buck converters under V¹ control are studied. In particular, subharmonic oscillation limits in the parameter space are addressed. First, a closed‐loop state‐space model is derived and then used to formulate an analytical matrix‐form expression for predicting the stability limit of the system. Using this expression, multi‐parametric stability boundaries are obtained. It is shown that the equivalent series inductance of the output capacitor can narrow the stability region. It is also demonstrated that the integral action in the feedback loop of a V¹‐controlled buck converter has a negligible effect on the subharmonic oscillation boundary. The theoretical analysis is validated through numerical simulation of the circuit‐level switched model of the system. Copyright © 2017 John Wiley & Sons, Ltd.     

A convex optimization approach to adaptive stabilization of discrete‐time LTI systems with polytopic uncertainties

This paper suggests a simple convex optimization approach to state‐feedback adaptive stabilization problem for a class of discrete‐time LTI systems subject to polytopic uncertainties. The proposed method relies on estimating the uncertain parameters by solving an online optimization at each time step, such as a linear or quadratic programming, and then, on tuning the control law with that information, which can be conceptually viewed as a kind of gain‐scheduling or indirect adaptive control. Specifically, an admissible domain of stabilizing state‐feedback gain matrices is designed offline by means of linear matrix inequality problems, and based on the online estimation of the uncertain parameters, the state‐feedback gain matrix is calculated over the set of stabilizing feedback gains. The proposed stabilization algorithm guarantees the asymptotic stability of the overall closed‐loop control system. An example is given to show the effectiveness of the proposed approach. Copyright © 2014 John Wiley & Sons, Ltd.     

A small‐gain approach for adaptive output‐feedback NN control of switched pure‐feedback nonlinear systems

This paper investigates the problem of adaptive output‐feedback neural network (NN) control for a class of switched pure‐feedback uncertain nonlinear systems. A switched observer is first constructed to estimate the unmeasurable states. Next, with the help of an NN to approximate the unknown nonlinear terms, a switched small‐gain technique‐based adaptive output‐feedback NN control scheme is developed by exploiting the backstepping recursive design scheme, input‐to‐state stability analysis, the common Lyapunov function method, and the average dwell time (ADT) method. In the recursive design, the difficulty of constructing an overall Lyapunov function for the switched closed‐loop system is dealt with by decomposing the switched closed‐loop system into two interconnected switched systems and constructing two Lyapunov functions for two interconnected switched systems, respectively. The proposed controllers for individual subsystems guarantee that all signals in the closed‐loop system are semiglobally, uniformly, and ultimately bounded under a class of switching signals with ADT, and finally, two examples illustrate the effectiveness of theoretical results, which include a switched RLC circuit system.     

Multiple‐model adaptive robust dynamic surface control with estimator resetting

A multiple‐model adaptive robust dynamic surface control with estimator resetting is investigated for a class of semi‐strict feedback nonlinear systems in this paper. The transient performance is mainly considered. The multiple models are composed of fixed models, one adaptive model, and one identification model that can be obtained when the persistent exciting condition is satisfied. The transient performance of the final tracking system can be improved significantly by designing proper switching mechanism during the parameter tuning procedure. The semi‐globally uniformly ultimately bounded stability of the closed‐loop system can be easily achieved because of the framework of adaptive robust dynamic surface control. Numerical examples are provided to demonstrate the effectiveness of the proposed multiple‐model controller. Copyright © 2014 John Wiley & Sons, Ltd.     

Limit‐cycle stable control of current‐mode dc‐dc converter with zero‐perturbation dynamical compensation

Regarding the non‐limit‐cycle instabilities, which commonly exist in the feedback‐controlled switching power converters, a new zero‐perturbation dynamical compensation method is proposed based on a simplified self‐stable dynamical compensation condition in this paper. With a current‐mode Buck converter as the subject of investigation, the corresponding self‐stable perturbation control equation is given. At the same time, the system stability boundary is obtained based on the investigation of the system eigenvalues, and hence, the working range of control parameters is determined. Finally, the presented simulation and experiment results reveal that the new zero‐perturbation dynamical compensation controller is easily realized with an analog circuit and it will not sacrifice the working range of the original reference current compared with the traditional slope compensation. Copyright © 2013 John Wiley & Sons, Ltd.     

Adaptive homo‐backstepping tracking control for strict‐feedback systems in presence of unknown dead‐zones

An adaptive homo‐backstepping control for nonlinear strict‐feedback systems subjected to unknown actuator dead‐zone and disturbance is investigated. A sliding‐mode‐based integral filter is constructed and used to approximate the desired feedback control in the backstepping‐like recursive design technique. Subsequently, the problem of “explosion of complexity” is solved by obviating the analytic derivatives deduction for virtual control in the conventional backstepping technology. The actuator dead‐zone dynamic is modeled as the combination of a line and a disturbance‐like term, which makes the controller design simpler. The interconnected control module and filter module in the resulting closed‐loop system satisfy the input‐to‐state practically stability‐modularity condition, provided that the small‐gain theorem is exploited to ensure the stability of closed‐loop system. The proposed approach cannot only mitigate the effect of dead‐zone but also solve the problem of explosion of complexity in the previous literature. Numerical simulations performed on a manipulator with a brushed DC motor are introduced to illustrate the effectiveness of underlying control scheme.     

Synthesis‐oriented double‐loop feedback model

This paper presents a new feedback model that focuses on the synthesis rather than the analysis of feedback amplifiers. First, a single‐loop synthesis‐oriented feedback model is developed that enables the full synthesis of such amplifiers in a hierarchical and systematic way. This model is subsequently extended to a double‐loop synthesis model, so that also feedback amplifiers with a characteristic input or output impedance—employing two feedback loops—can be synthesized through the same systematic approach. That these new models are suitable for synthesis lies in the fact that they map directly to the circuit level, such that the intended, asymptotic behavior as well as the various individual contributors to the deviation from this intended behavior, like finite loop gain, non‐ideal input and output impedances of the forward gain block, direct feed‐through and attenuations outside the feedback loop(s), are clearly distinguished and can be assigned to the responsible sections of the network. For this purpose, the double‐loop synthesis model makes the transfers of the two feedback networks explicitly visible, so that it gives immediate insight in how to design these networks to get the required signal transfer and characteristic impedance. Copyright © 2017 John Wiley & Sons, Ltd.     

Dynamics of PFC power converters subject to time‐delayed feedback control

Power factor correction converters are power electronics circuits used as AC‐DC power supplies. These systems are well known to exhibit nonlinear phenomena such as subharmonic oscillations and chaotic regimes. These undesirable behaviors increase the THD and therefore can jeopardize enormously the system performances. In this paper, time delay feedback control is applied to stabilize a two‐stage power factor correction AC‐DC converter when it exhibits these instabilities under traditional controllers. This control technique introduces many advantages to the most and widely used average current mode control through widening the stability domain of the system. By appropriately selecting the time delay feedback gain and the time delay period, the undesirable subharmonic components are eliminated, whereas the desired ones remain unchanged. A harmonic balance approach is used for studying the dynamics of the system under the new control scheme and to obtain the stabilization domain. Copyright © 2010 John Wiley & Sons, Ltd.     

Optimal switching Lyapunov‐based control of power electronic converters

This paper presents new ideas and insights towards a novel optimal control approach for power electronic converters. The so‐called stabilizing or Lyapunov‐based control paradigm is adopted, which is well known in the area of energy‐based control of power electronic converters, in which the control law takes a nonlinear state‐feedback form parameterized by a positive scalar λ . The first contribution is the extension to an optimal Lyapunov‐based control paradigm involving the specification of the optimal value for the parameter λ in a typical optimal control setting. The second contribution is the extension to more flexible optimal switching‐gain control laws, where the optimal switching surfaces are parameterized by a number of positive scalars λ _j . Systematic derivation of gradient information to apply gradient‐descent algorithms is provided. The proposed techniques are numerically evaluated using the exact switched model of a DC–DC boost converter. Copyright © 2016 John Wiley & Sons, Ltd.     

Fast‐transient DC‐DC converter using a high‐performance error amplifier with a rapid output‐voltage control technique

This letter presents a method for improving the transient response of DC‐DC converters. The proposed technique replaces the conventional error amplifier with a combination of two different amplifiers to achieve a high loop gain and high slew rate. In addition, a rapid output‐voltage control circuit is employed to further reduce the recovery time. The proposed technique was applied to a four‐phase buck converter, and the chip was implemented using a 0.18‐μm CMOS process. The switching frequency of each phase was set at 2 MHz. Using a supply voltage of 2.7–5.5 V and an output voltage of 0.6–1.5 V, the regulator provided up to 2‐A load current with maximum measured recovery time of only 6.2 and 6.5 μs for increasing and decreasing load current, respectively. Copyright © 2017 John Wiley & Sons, Ltd.     

Parameter‐dependent Riccati equation–based output feedback adaptive control

A parameter‐dependent Riccati equation approach is proposed to design and analyze the stability properties of an output feedback adaptive control law design. The adaptive controller is intended to augment an existing fixed‐gain observer‐based output feedback control law. Although the formulation is in the setting of model reference adaptive control, the realization of the adaptive controller does not require implementing the reference model. In this regard, the increased complexity of implementing the adaptive controller, above that of a fixed‐gain control law, is less than that of other methods. The error signals are shown to be uniformly ultimately bounded, and an estimate for the ultimate bound is provided. The issue of sensor noise is addressed by introducing an error filter. The control design process and the theoretical results are illustrated using a model for wing rock dynamics.     

FPGA‐based implementation for improved control scheme of grid‐connected PV system with 3‐phase 3‐level NPC‐VSI

The large scale penetration of renewable energy resources has boosted the need of using improved control technique and modular power electronic converter structures for efficient and reliable operation of grid‐connected systems. This study investigates the performance of a grid‐connected 3‐phase 3‐level neutral‐point clamped voltage source inverter for renewable energy integration by using improved current control technique. For medium or high‐voltage grid interfacing, the multilevel inverter structure is generally used to reduce the voltage stress across the switching device as well as the harmonic distortion. The neutral‐point clamped voltage source inverter is controlled by using decoupling technique along with the proper grid synchronization via moving average filter–based phase‐locked loop. The moving average filter–based phase‐locked loop is used to reduce the delay in grid angle estimation under balanced as well as distorted grid conditions. A Lyapunov‐based approach for analysing the stability of the system has also been discussed. In this study, the hardware‐in‐loop (HIL) simulation of the control algorithm and the grid synchronization technique is realized using Virtex‐6 FPGA ML605 evaluation kit. The performance of the system is analyzed by conducting a time‐domain simulation in the Matlab/Simulink platform and its performance is examined in the HIL environment. The simulation and the hardware cosimulation results are presented to validate the effectiveness of the proposed control scheme.     

Sampled‐data poles,zeros, and modeling for current‐mode control

Exact and approximate sampled‐data models in closed forms are derived for switching DC–DC converters under peak/valley current‐mode control. The corresponding sampled‐data poles and zeros in closed forms are also derived. The location and stability conditions of the poles and zeros, boundary conditions of subharmonic instability, and nulling of the audio‐susceptibility are also derived. It is proved that the stable operating range of the source voltage is linearly proportional to the ramp slope. The sampled‐data models agree with previous experiment results and accurately predict the subharmonic instability. The different view from the sampled‐data model about the number and stability (minimum phase) of pole and zero does not necessarily invalidate the traditional continuous‐time averaged model. However, this different view gives better prediction about converter dynamics and is useful for the analog or digital controller design for DC–DC converters. Copyright © 2011 John Wiley & Sons, Ltd.     

Two‐loop power‐flow control of grid‐connected microgrid based on equivalent‐input‐disturbance approach

This study employed the equivalent‐input‐disturbance (EID) approach to devise a two‐loop power‐flow control system that controls the output current of an inverter so as to regulate the flow of active and reactive power between a distributed generation unit and a utility grid. It actively eliminates disturbances that degrade the power quality of a microgrid. The pq theory and an all‐pass filter are employed to generate an instantaneous reference current for the control system based on the prescribed active and reactive power of a utility grid terminal. The inner loop consists of a disturbance compensator and a state observer. The disturbance compensator uses information acquired from the state observer to estimate disturbances, such as drops and harmonics in the grid voltage, and compensates for them by incorporating the equivalent input disturbance into the control law. The outer loop consists of a resonance‐based internal model and a state‐feedback controller, which enables the output current of inverter to track the instantaneous reference current. The small‐gain theorem ensures the stability of the system. The system improves the power quality and guarantees that the flow of active and reactive power from the grid and inverter has low harmonic distortion. Simulations demonstrated the effectiveness of the system. © 2014 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.     

Minimum switching control for adaptive tracking

The switching adaptive control method has been used for quite a few years to solve the adaptive stabilization and model reference adaptive control problems. However, a serious problem with the switching control method is that the number of ‘candidate’ controllers can potentially be very large, especially for multi‐input–multi‐output systems. In this paper, we consider a class of minimum‐phase multi‐input–multi‐output plants with some mild compactness assumptions. Given any polynomial reference input, we provide a switching control law which guarantees exponentially stability of the closed‐loop system with exponential tracking performance. The main contribution of the paper is that we give the minimum number of candidate controllers required for switching. In particular, the number is equal to 2 for single‐input–single‐output plants (one for each sign of the high‐frequency gain), and is equal to 2^m for m‐input–m‐output plants. That is, the number is independent of the degree and the relative degree of the plant. Copyright © 2006 John Wiley & Sons, Ltd.     

Observer‐based nonlinear feedback decentralized neural adaptive dynamic surface control for large‐scale nonlinear systems

This paper presents a nonlinear gain feedback technique for observer‐based decentralized neural adaptive dynamic surface control of a class of large‐scale nonlinear systems with immeasurable states and uncertain interconnections among subsystems. Neural networks are used in the observer design to estimate the immeasurable states and thus facilitate the control design. Besides avoiding the complexity problem in traditional backstepping, the new nonlinear feedback gain method endows an automatic regulation ability into the pioneering dynamic surface control design and improvement in dynamic performance. Novel Lyapunov function is designed and rigorous stability analysis is given to show that all the closed‐loop signals are kept semiglobally uniformly ultimately bounded, and the output tracking errors can be guaranteed to converge to sufficient area around zero, with the bound values characterized by design parameters in an explicit manner. Simulation and comparative results are shown to verify effectiveness.     

Fractional‐order multivariable composite model reference adaptive control

A novel multivariable composite model reference adaptive control scheme is developed for multivariable fractional‐order systems with arbitrary relative degree. Firstly, by introducing right gain matrix to substitute left gain matrix, the stringent symmetry assumption is no longer required. The design procedures of controller with certain and uncertain high‐frequency gain matrix are then provided, respectively. The (robust) stability of the resulting closed‐loop control system is investigated by indirect Lyapunov method. It is shown that the composite model reference adaptive control can achieve better performance on output tracking than that of model reference adaptive control. Finally, the effectiveness and applicability of the proposed control scheme are demonstrated in 3 numerical examples.     

Dynamic modeling of DC–DC converters with peak current control in double‐stage photovoltaic grid‐connected inverters

In photovoltaic (PV) double‐stage grid‐connected inverters a high‐frequency DC–DC isolation and voltage step‐up stage is commonly used between the panel and the grid‐connected inverter. This paper is focused on the modeling and control design of DC–DC converters with Peak Current mode Control (PCC) and an external control loop of the PV panel voltage, which works following a voltage reference provided by a maximum power point tracking (MPPT) algorithm. In the proposed overall control structure the output voltage of the DC–DC converter is regulated by the grid‐connected inverter. Therefore, the inverter may be considered as a constant voltage load for the development of the small‐signal model of the DC–DC converter, whereas the PV panel is considered as a negative resistance. The sensitivity of the control loops to variations of the power extracted from the PV panel and of its voltage is studied. The theoretical analysis is corroborated by frequency response measurements on a 230 W experimental inverter working from a single PV panel. The inverter is based on a Flyback DC–DC converter operating in discontinuous conduction mode (DCM) followed by a PWM full‐bridge single‐phase inverter. The time response of the whole system (DC–DC + inverter) is also shown to validate the concept. Copyright © 2011 John Wiley & Sons, Ltd.