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In this paper, we show that Prescribed Performance Control (PPC) is a model-free Control Barrier Function (CBF)-based control approach. Specifically, we establish that a function utilized in the PPC design is a Time-Varying Reciprocal Control Barrier Function (TVRCBF). We demonstrate that PPC satisfies the same gradient condition that is well-known in the CBF literature, ensuring forward invariance. As a result, the control inputs generated by the PPC law belong to the input set characterized by the TVRCBF. Apart from assuming a certain controllability property, no further knowledge on the system dynamics is required. Our theoretical findings improve the understanding of the relationship between PPC and other CBF-based controllers. The theoretical results are validated through numerical simulations., QC 20241004 ; Part of ISBN [9798350382655]

In this paper, we show that Prescribed Performance Control (PPC) is a model-free Control Barrier Function (CBF)-based control approach. Specifically, we establish that a function utilized in the PPC design is a Time-Varying Reciprocal Control Barrier Function (TVRCBF). We demonstrate that PPC satisfies the same gradient condition that is well-known in the CBF literature, ensuring forward invariance. As a result, the control inputs generated by the PPC law belong to the input set characterized by the TVRCBF. Apart from assuming a certain controllability property, no further knowledge on the system dynamics is required. Our theoretical findings improve the understanding of the relationship between PPC and other CBF-based controllers. The theoretical results are validated through numerical simulations., QC 20241004 ; Part of ISBN [9798350382655]

In this paper, we show that Prescribed Performance Control (PPC) is a model-free Control Barrier Function (CBF)-based control approach. Specifically, we establish that a function utilized in the PPC design is a Time-Varying Reciprocal Control Barrier Function (TVRCBF). We demonstrate that PPC satisfies the same gradient condition that is well-known in the CBF literature, ensuring forward invariance. As a result, the control inputs generated by the PPC law belong to the input set characterized by the TVRCBF. Apart from assuming a certain controllability property, no further knowledge on the system dynamics is required. Our theoretical findings improve the understanding of the relationship between PPC and other CBF-based controllers. The theoretical results are validated through numerical simulations., QC 20241004 ; Part of ISBN [9798350382655]

Data-driven feedforward control for tracking of varying and non-resetting point-to-point references requires continuous updating of feedforward parameters instead of task-by-task updating. The aim of this paper is to develop an adaptive feedforward controller for non-resetting point-to-point motion tasks by a data-driven feedforward controller. An approximate optimal instrumental variable (IV) estimator with real-time bootstrapping is employed in a closed-loop setting to update the feedforward parameters. A case study on a wafer-stage and experimental validation on a benchmark motion system show the performance benefit., Team Jan-Willem van Wingerden

Eastern Vidzeme is an important, hitherto neglected, area for the study of logophoricity in the Circum-Baltic languages. This paper shows, on the one hand, that logophoricity in Latvian is not restricted to Latgalian dialects, but is almost fully consistent in the writings of the novelist Andrievs Niedra (1871–1942) originating from Tirza, and on the other hand, that Leivu Estonian, a moribund South Estonian language island in Northeastern Vidzeme between Gulbene and Alūksne, is the only Estonian variety having developed a logophoric pronoun. Given the high diversity of logophoricity in Latvian, it is important to study idiolects with large corpora, and written language deserves more study. Like Finnish dialects and Leivu Estonian, Niedra’s idiolect uses logophoric pronouns even for marking the report addressee in questions. Unlike in the Latgalian tales discussed by Nau (2006), logophoricity can be extended beyond the domain of report to thought. A distinction between allophoric (frame and report speaker are different) and autophoric reports (frame and report speaker are the same) is introduced. It is argued that logophoric pronouns are a non-deictic and non-coreference-based strategy to mark reports, that their function is not primarily reference tracking, and that logophoric pronouns in Latvian are constructionalized rather than grammaticalized., Dynamiska uttryck för tillstånd: resultativkonstruktionernas mångfald

Eastern Vidzeme is an important, hitherto neglected, area for the study of logophoricity in the Circum-Baltic languages. This paper shows, on the one hand, that logophoricity in Latvian is not restricted to Latgalian dialects, but is almost fully consistent in the writings of the novelist Andrievs Niedra (1871–1942) originating from Tirza, and on the other hand, that Leivu Estonian, a moribund South Estonian language island in Northeastern Vidzeme between Gulbene and Alūksne, is the only Estonian variety having developed a logophoric pronoun. Given the high diversity of logophoricity in Latvian, it is important to study idiolects with large corpora, and written language deserves more study. Like Finnish dialects and Leivu Estonian, Niedra’s idiolect uses logophoric pronouns even for marking the report addressee in questions. Unlike in the Latgalian tales discussed by Nau (2006), logophoricity can be extended beyond the domain of report to thought. A distinction between allophoric (frame and report speaker are different) and autophoric reports (frame and report speaker are the same) is introduced. It is argued that logophoric pronouns are a non-deictic and non-coreference-based strategy to mark reports, that their function is not primarily reference tracking, and that logophoric pronouns in Latvian are constructionalized rather than grammaticalized., Dynamiska uttryck för tillstånd: resultativkonstruktionernas mångfald

Eastern Vidzeme is an important, hitherto neglected, area for the study of logophoricity in the Circum-Baltic languages. This paper shows, on the one hand, that logophoricity in Latvian is not restricted to Latgalian dialects, but is almost fully consistent in the writings of the novelist Andrievs Niedra (1871–1942) originating from Tirza, and on the other hand, that Leivu Estonian, a moribund South Estonian language island in Northeastern Vidzeme between Gulbene and Alūksne, is the only Estonian variety having developed a logophoric pronoun. Given the high diversity of logophoricity in Latvian, it is important to study idiolects with large corpora, and written language deserves more study. Like Finnish dialects and Leivu Estonian, Niedra’s idiolect uses logophoric pronouns even for marking the report addressee in questions. Unlike in the Latgalian tales discussed by Nau (2006), logophoricity can be extended beyond the domain of report to thought. A distinction between allophoric (frame and report speaker are different) and autophoric reports (frame and report speaker are the same) is introduced. It is argued that logophoric pronouns are a non-deictic and non-coreference-based strategy to mark reports, that their function is not primarily reference tracking, and that logophoric pronouns in Latvian are constructionalized rather than grammaticalized., Dynamiska uttryck för tillstånd: resultativkonstruktionernas mångfald

For a robot manipulator, an accurate reference tracking capability is one of the most important performance factor. This is especially the case for a robot which is deployed for an industrial use such as welding and laser cutting. Recently, an emerging application of 3D printing also attracts researchers to use robotic manipulators in hope of gaining a higher dimension in the printing process as well as a larger workspace. The conventional method for controlling robot manipulator involves a model based feed-forward controller to eliminate the nonlinearities such as gravity and the coriolis term, combined with a feedback controller to compensate the residual error. This method, however, has a drawback in obtaining a good model of the robot. Furthermore, a robot's physical properties are subject to change over time due to, for instance, degraded gearboxes, etc. Such a problem will require the robot to re-perform a system identification which is often unacceptable due to the time it takes and the possibly dangerous movement the robot must execute. Therefore, this class of controller may not be the best option for such condition. This thesis addresses the aforementioned problem from the point of view of model-free, learning controller which improves the tracking performance safely in an online fashion. The thesis exploits the reinforcement learning (RL) technique which uses the nature of trial and errors to correct the tracking error. Improvement to the control performance is done by feeding an additive compensation signal given by a learned policy function to the robot's nominal controller. Two different compensation methods are proposed in the thesis. Both methods are realized by the so called actor-critic (AC) algorithm in order to cope with the continuous state of a robot arm. The first method compensates the control input of the nominal controller while the second method modifies the reference trajectory. The methods are implemented on a real 6 DoFs 3D printing rob, Delft Center for Systems and Control, Mechanical, Maritime and Materials Engineering

Eastern Vidzeme is an important, hitherto neglected, area for the study of logophoricity in the Circum-Baltic languages. This paper shows, on the one hand, that logophoricity in Latvian is not restricted to Latgalian dialects, but is almost fully consistent in the writings of the novelist Andrievs Niedra (1871–1942) originating from Tirza, and on the other hand, that Leivu Estonian, a moribund South Estonian language island in Northeastern Vidzeme between Gulbene and Alūksne, is the only Estonian variety having developed a logophoric pronoun. Given the high diversity of logophoricity in Latvian, it is important to study idiolects with large corpora, and written language deserves more study. Like Finnish dialects and Leivu Estonian, Niedra’s idiolect uses logophoric pronouns even for marking the report addressee in questions. Unlike in the Latgalian tales discussed by Nau (2006), logophoricity can be extended beyond the domain of report to thought. A distinction between allophoric (frame and report speaker are different) and autophoric reports (frame and report speaker are the same) is introduced. It is argued that logophoric pronouns are a non-deictic and non-coreference-based strategy to mark reports, that their function is not primarily reference tracking, and that logophoric pronouns in Latvian are constructionalized rather than grammaticalized., Dynamiska uttryck för tillstånd: resultativkonstruktionernas mångfald

For a robot manipulator, an accurate reference tracking capability is one of the most important performance factor. This is especially the case for a robot which is deployed for an industrial use such as welding and laser cutting. Recently, an emerging application of 3D printing also attracts researchers to use robotic manipulators in hope of gaining a higher dimension in the printing process as well as a larger workspace. The conventional method for controlling robot manipulator involves a model based feed-forward controller to eliminate the nonlinearities such as gravity and the coriolis term, combined with a feedback controller to compensate the residual error. This method, however, has a drawback in obtaining a good model of the robot. Furthermore, a robot's physical properties are subject to change over time due to, for instance, degraded gearboxes, etc. Such a problem will require the robot to re-perform a system identification which is often unacceptable due to the time it takes and the possibly dangerous movement the robot must execute. Therefore, this class of controller may not be the best option for such condition. This thesis addresses the aforementioned problem from the point of view of model-free, learning controller which improves the tracking performance safely in an online fashion. The thesis exploits the reinforcement learning (RL) technique which uses the nature of trial and errors to correct the tracking error. Improvement to the control performance is done by feeding an additive compensation signal given by a learned policy function to the robot's nominal controller. Two different compensation methods are proposed in the thesis. Both methods are realized by the so called actor-critic (AC) algorithm in order to cope with the continuous state of a robot arm. The first method compensates the control input of the nominal controller while the second method modifies the reference trajectory. The methods are implemented on a real 6 DoFs 3D printing rob, Delft Center for Systems and Control, Mechanical, Maritime and Materials Engineering

Eastern Vidzeme is an important, hitherto neglected, area for the study of logophoricity in the Circum-Baltic languages. This paper shows, on the one hand, that logophoricity in Latvian is not restricted to Latgalian dialects, but is almost fully consistent in the writings of the novelist Andrievs Niedra (1871–1942) originating from Tirza, and on the other hand, that Leivu Estonian, a moribund South Estonian language island in Northeastern Vidzeme between Gulbene and Alūksne, is the only Estonian variety having developed a logophoric pronoun. Given the high diversity of logophoricity in Latvian, it is important to study idiolects with large corpora, and written language deserves more study. Like Finnish dialects and Leivu Estonian, Niedra’s idiolect uses logophoric pronouns even for marking the report addressee in questions. Unlike in the Latgalian tales discussed by Nau (2006), logophoricity can be extended beyond the domain of report to thought. A distinction between allophoric (frame and report speaker are different) and autophoric reports (frame and report speaker are the same) is introduced. It is argued that logophoric pronouns are a non-deictic and non-coreference-based strategy to mark reports, that their function is not primarily reference tracking, and that logophoric pronouns in Latvian are constructionalized rather than grammaticalized., Dynamiska uttryck för tillstånd: resultativkonstruktionernas mångfald

Eastern Vidzeme is an important, hitherto neglected, area for the study of logophoricity in the Circum-Baltic languages. This paper shows, on the one hand, that logophoricity in Latvian is not restricted to Latgalian dialects, but is almost fully consistent in the writings of the novelist Andrievs Niedra (1871–1942) originating from Tirza, and on the other hand, that Leivu Estonian, a moribund South Estonian language island in Northeastern Vidzeme between Gulbene and Alūksne, is the only Estonian variety having developed a logophoric pronoun. Given the high diversity of logophoricity in Latvian, it is important to study idiolects with large corpora, and written language deserves more study. Like Finnish dialects and Leivu Estonian, Niedra’s idiolect uses logophoric pronouns even for marking the report addressee in questions. Unlike in the Latgalian tales discussed by Nau (2006), logophoricity can be extended beyond the domain of report to thought. A distinction between allophoric (frame and report speaker are different) and autophoric reports (frame and report speaker are the same) is introduced. It is argued that logophoric pronouns are a non-deictic and non-coreference-based strategy to mark reports, that their function is not primarily reference tracking, and that logophoric pronouns in Latvian are constructionalized rather than grammaticalized., Dynamiska uttryck för tillstånd: resultativkonstruktionernas mångfald

A common assumption when proving stability of linear MPC algorithms fort racking applications is to assume that the desired setpoint is located farinto the interior of the feasible set. The reason for this is that the terminal state constraint set which is centered around the setpoint must be contained within the feasible set. In many applications this assumption can be severly limiting since the terminal set is relatively large and therefore limits how close the setpoint can be to the boundary of the feasible set. We present simple modifications that can be performed in order to guarantee stability and convergence to setpoints located arbitrarily close to the boundary of the feasible set. The main idea is to introduce a scaling variable which dynamically scales the terminal state constraint set and therefore allowsa setpoint to be located arbitrarily close to the boundary. In addition to this the concept of pseudo setpoints are used to gain the maximum possible region of attraction and to handle infeasible references. Recursive feasibility and convergence to the desired setpoint, or its closest feasible alternative, is proven and a motivating example of controlling an agile fighter aircraftis given.

A common assumption when proving stability of linear MPC algorithms fort racking applications is to assume that the desired setpoint is located farinto the interior of the feasible set. The reason for this is that the terminal state constraint set which is centered around the setpoint must be contained within the feasible set. In many applications this assumption can be severly limiting since the terminal set is relatively large and therefore limits how close the setpoint can be to the boundary of the feasible set. We present simple modifications that can be performed in order to guarantee stability and convergence to setpoints located arbitrarily close to the boundary of the feasible set. The main idea is to introduce a scaling variable which dynamically scales the terminal state constraint set and therefore allowsa setpoint to be located arbitrarily close to the boundary. In addition to this the concept of pseudo setpoints are used to gain the maximum possible region of attraction and to handle infeasible references. Recursive feasibility and convergence to the desired setpoint, or its closest feasible alternative, is proven and a motivating example of controlling an agile fighter aircraftis given.

A common assumption when proving stability of linear MPC algorithms fort racking applications is to assume that the desired setpoint is located farinto the interior of the feasible set. The reason for this is that the terminal state constraint set which is centered around the setpoint must be contained within the feasible set. In many applications this assumption can be severly limiting since the terminal set is relatively large and therefore limits how close the setpoint can be to the boundary of the feasible set. We present simple modifications that can be performed in order to guarantee stability and convergence to setpoints located arbitrarily close to the boundary of the feasible set. The main idea is to introduce a scaling variable which dynamically scales the terminal state constraint set and therefore allowsa setpoint to be located arbitrarily close to the boundary. In addition to this the concept of pseudo setpoints are used to gain the maximum possible region of attraction and to handle infeasible references. Recursive feasibility and convergence to the desired setpoint, or its closest feasible alternative, is proven and a motivating example of controlling an agile fighter aircraftis given.

A common assumption when proving stability of linear MPC algorithms fort racking applications is to assume that the desired setpoint is located farinto the interior of the feasible set. The reason for this is that the terminal state constraint set which is centered around the setpoint must be contained within the feasible set. In many applications this assumption can be severly limiting since the terminal set is relatively large and therefore limits how close the setpoint can be to the boundary of the feasible set. We present simple modifications that can be performed in order to guarantee stability and convergence to setpoints located arbitrarily close to the boundary of the feasible set. The main idea is to introduce a scaling variable which dynamically scales the terminal state constraint set and therefore allowsa setpoint to be located arbitrarily close to the boundary. In addition to this the concept of pseudo setpoints are used to gain the maximum possible region of attraction and to handle infeasible references. Recursive feasibility and convergence to the desired setpoint, or its closest feasible alternative, is proven and a motivating example of controlling an agile fighter aircraftis given.

A common assumption when proving stability of linear MPC algorithms fort racking applications is to assume that the desired setpoint is located farinto the interior of the feasible set. The reason for this is that the terminal state constraint set which is centered around the setpoint must be contained within the feasible set. In many applications this assumption can be severly limiting since the terminal set is relatively large and therefore limits how close the setpoint can be to the boundary of the feasible set. We present simple modifications that can be performed in order to guarantee stability and convergence to setpoints located arbitrarily close to the boundary of the feasible set. The main idea is to introduce a scaling variable which dynamically scales the terminal state constraint set and therefore allowsa setpoint to be located arbitrarily close to the boundary. In addition to this the concept of pseudo setpoints are used to gain the maximum possible region of attraction and to handle infeasible references. Recursive feasibility and convergence to the desired setpoint, or its closest feasible alternative, is proven and a motivating example of controlling an agile fighter aircraftis given.

This paper is focused on reference tracking and disturbance rejection for linear time-invariant time delay systems. The contribution is motivated by the fact that the task of reference tracking and disturbance rejection for non-stepwise those external inputs in the feedback loop is often ignored in the literature. The presented approach is based on algebraic operations in a special ring RMS and on the divisibility condition in the ring. The general idea for a feedback loop with two controllers is introduced. The methodology is clarified and verified by a simulation example in the Matlab/Simulink environment. © 2011 IEEE.

The paper deals with a recently developed algebraic method of control design for retarded linear time delay systems. Tasks of closed loop system stabilization, reference tracking and disturbance rejection are solved on the basis of the solution of the Bézout equation with Youla-Kučera parameterization in the ring of proper and stable RQ-meromorphic functions. The advantage of the method consists in the fact that it provides a finite spectrum assignment of the closed loop. A widely neglected problem is reference tracking of non-stepwise functions as well as rejection of those classes of disturbances. Hence, the aim of this contribution is to outline a possible procedure of solving these two problems. The general results are clarified by some simulation examples.

This paper is focused on reference tracking and disturbance rejection for linear time-invariant time delay systems. The contribution is motivated by the fact that the task of reference tracking and disturbance rejection for non-stepwise those external inputs in the feedback loop is often ignored in the literature. The presented approach is based on algebraic operations in a special ring RMS and on the divisibility condition in the ring. The general idea for a feedback loop with two controllers is introduced. The methodology is clarified and verified by a simulation example in the Matlab/Simulink environment. © 2011 IEEE.

The paper deals with a recently developed algebraic method of control design for retarded linear time delay systems. Tasks of closed loop system stabilization, reference tracking and disturbance rejection are solved on the basis of the solution of the Bézout equation with Youla-Kučera parameterization in the ring of proper and stable RQ-meromorphic functions. The advantage of the method consists in the fact that it provides a finite spectrum assignment of the closed loop. A widely neglected problem is reference tracking of non-stepwise functions as well as rejection of those classes of disturbances. Hence, the aim of this contribution is to outline a possible procedure of solving these two problems. The general results are clarified by some simulation examples.

This paper analyzes the dynamics of reference tracking in switched-mode power converters in terms of both large-signal and small-signal perspectives. Common control schemes, namely, voltage mode, current mode, and V 2-control, are compared for their performance in reference tracking. For small-signal analysis, loop gains and reference-to-output transfer functions are analytically derived and verified by the proposed Matlab-based frequency response simulator. In the case of multiple-loop control like V 2-control, different loop gains are clarified for their application in load transient or reference tracking. Practical circuit-level design considerations are given to current-mode control for achieving fast reference tracking, while end-point prediction (EPP) is used to improve V 2-control, which is inherently slow in reference tracking. The effect of EPP on transfer function is then explained in details. A V 2-controlled buck converter with EPP is fabricated. The measured reference-tracking response shows ten times improvement in tracking speed and verifies the effectiveness of EPP in V2-control. © 2006 IEEE.

This paper analyzes the dynamics of reference tracking in switched-mode power converters in terms of both large-signal and small-signal perspectives. Common control schemes, namely, voltage mode, current mode, and V 2-control, are compared for their performance in reference tracking. For small-signal analysis, loop gains and reference-to-output transfer functions are analytically derived and verified by the proposed Matlab-based frequency response simulator. In the case of multiple-loop control like V 2-control, different loop gains are clarified for their application in load transient or reference tracking. Practical circuit-level design considerations are given to current-mode control for achieving fast reference tracking, while end-point prediction (EPP) is used to improve V 2-control, which is inherently slow in reference tracking. The effect of EPP on transfer function is then explained in details. A V 2-controlled buck converter with EPP is fabricated. The measured reference-tracking response shows ten times improvement in tracking speed and verifies the effectiveness of EPP in V2-control. © 2006 IEEE.

This paper analyzes the dynamics of reference tracking in switched-mode power converters in terms of both large-signal and small-signal perspectives. Common control schemes, namely, voltage mode, current mode, and V 2-control, are compared for their performance in reference tracking. For small-signal analysis, loop gains and reference-to-output transfer functions are analytically derived and verified by the proposed Matlab-based frequency response simulator. In the case of multiple-loop control like V 2-control, different loop gains are clarified for their application in load transient or reference tracking. Practical circuit-level design considerations are given to current-mode control for achieving fast reference tracking, while end-point prediction (EPP) is used to improve V 2-control, which is inherently slow in reference tracking. The effect of EPP on transfer function is then explained in details. A V 2-controlled buck converter with EPP is fabricated. The measured reference-tracking response shows ten times improvement in tracking speed and verifies the effectiveness of EPP in V2-control. © 2006 IEEE.

A constant frequency output-ripple-voltage based CMOS current-mode de-de buck converter, providing fast load transient response and reference-tracking speed, is proposed in this paper. Unlike V-2 control output-ripple-voltage based buck converter, the proposed buck converter can achieve fast and stable load transient response without relying on ESR value of output capacitor. In addition, the proposed converter has faster reference-tracking speed than the V-2 control counterparts by about 25 times.

An integrated DC-DC hysteretic buck converter with ultrafast adaptive output transient response for reference tracking is presented. To achieve the fastest up-tracking speed, the maximum charging current control is introduced to charge up the output voltage with the maximum designed current. For down-tracking, the output is discharged by the load only to save energy. Although the converter works with hysteretic voltage mode control, an adaptive delay compensation scheme is employed to keep the switching frequency constant at 850 kHz to within +/- 2.5\% across the whole operation range. The integrated buck converter was fabricated using a 0.35 mu m CMOS process. With an input voltage of 3 V, the output voltage can be regulated between 0.5 and 2.5 V. With a load resistor of 10 Omega, the up-tracking speed of the maximum reference step (0.5 to 2.5 V) is 12.5 mu s/V. All design features are verified by extensive measurements.

An integrated DC-DC hysteretic buck converter with ultrafast adaptive output transient response for reference tracking is presented. To achieve the fastest up-tracking speed, the maximum charging current control is introduced to charge up the output voltage with the maximum designed current. For down-tracking, the output is discharged by the load only to save energy. Although the converter works with hysteretic voltage mode control, an adaptive delay compensation scheme is employed to keep the switching frequency constant at 850 kHz to within +/- 2.5\% across the whole operation range. The integrated buck converter was fabricated using a 0.35 mu m CMOS process. With an input voltage of 3 V, the output voltage can be regulated between 0.5 and 2.5 V. With a load resistor of 10 Omega, the up-tracking speed of the maximum reference step (0.5 to 2.5 V) is 12.5 mu s/V. All design features are verified by extensive measurements.

A constant frequency output-ripple-voltage based CMOS current-mode de-de buck converter, providing fast load transient response and reference-tracking speed, is proposed in this paper. Unlike V-2 control output-ripple-voltage based buck converter, the proposed buck converter can achieve fast and stable load transient response without relying on ESR value of output capacitor. In addition, the proposed converter has faster reference-tracking speed than the V-2 control counterparts by about 25 times.

A constant frequency output-ripple-voltage based CMOS current-mode de-de buck converter, providing fast load transient response and reference-tracking speed, is proposed in this paper. Unlike V-2 control output-ripple-voltage based buck converter, the proposed buck converter can achieve fast and stable load transient response without relying on ESR value of output capacitor. In addition, the proposed converter has faster reference-tracking speed than the V-2 control counterparts by about 25 times.

An integrated DC-DC hysteretic buck converter with ultrafast adaptive output transient response for reference tracking is presented. To achieve the fastest up-tracking speed, the maximum charging current control is introduced to charge up the output voltage with the maximum designed current. For down-tracking, the output is discharged by the load only to save energy. Although the converter works with hysteretic voltage mode control, an adaptive delay compensation scheme is employed to keep the switching frequency constant at 850 kHz to within +/- 2.5\% across the whole operation range. The integrated buck converter was fabricated using a 0.35 mu m CMOS process. With an input voltage of 3 V, the output voltage can be regulated between 0.5 and 2.5 V. With a load resistor of 10 Omega, the up-tracking speed of the maximum reference step (0.5 to 2.5 V) is 12.5 mu s/V. All design features are verified by extensive measurements.

This paper analyzes the reference tracking behavior of Buck converters using several control schemes including voltage-mode, current-mode and V(2)-control from both large-signal and small-signal domains. Loop gains applicable to reference tracking are highlighted, and reference-to-output transfer functions are derived for the cases when end-point Prediction (EPP) is applied to enhance the response. A novel V(2)-controlled Buck converter with EPP is fabricated. The measured reference tracking response shows 10 times improvement in speed.

A monolithic output-ripple-based buck converter with adaptive output and ultra-fast reference tracking is presented. Fixed-switching-frequency V-2-control is used in steady-state operation; while its speed limitation during reference tracking is eliminated by employing end-point prediction, a novel oscillator with clock-holding function, and the proposed adaptive-output-feedback (AOFB)-scheme. The AOFB-scheme is obtained from a detailed analysis of the dynamics of general output-ripple-based controller during reference tracking. Then, an adaptive feedback voltage which satisfies the switching criterion for optimum switch control in reference tracking is formulated, and is incorporated into the controller design. The resultant single ON/OFF-switching during reference tracking is very close to the optimal solution for fast reference tracking. Moreover, it also leads to the lowest switching loss and minimized conduction loss at the fastest tracking speed, making the converter very suitable for adaptive output applications. Fabricated in a 0.35 mu m CMOS process, the 3-V input prototype chip exhibits stable operation across a wide output range of 0.7-2.4 V. High tracking speed within 10 mu s/V is measured with different output voltages and output voltage steps. Maximum efficiency of 96\% is obtained at 260 mA output current, while maximum output current is 800 mA.

A monolithic output-ripple-based buck converter with adaptive output and ultra-fast reference tracking is presented. Fixed-switching-frequency V-2-control is used in steady-state operation; while its speed limitation during reference tracking is eliminated by employing end-point prediction, a novel oscillator with clock-holding function, and the proposed adaptive-output-feedback (AOFB)-scheme. The AOFB-scheme is obtained from a detailed analysis of the dynamics of general output-ripple-based controller during reference tracking. Then, an adaptive feedback voltage which satisfies the switching criterion for optimum switch control in reference tracking is formulated, and is incorporated into the controller design. The resultant single ON/OFF-switching during reference tracking is very close to the optimal solution for fast reference tracking. Moreover, it also leads to the lowest switching loss and minimized conduction loss at the fastest tracking speed, making the converter very suitable for adaptive output applications. Fabricated in a 0.35 mu m CMOS process, the 3-V input prototype chip exhibits stable operation across a wide output range of 0.7-2.4 V. High tracking speed within 10 mu s/V is measured with different output voltages and output voltage steps. Maximum efficiency of 96\% is obtained at 260 mA output current, while maximum output current is 800 mA.

This paper analyzes the reference tracking behavior of Buck converters using several control schemes including voltage-mode, current-mode and V(2)-control from both large-signal and small-signal domains. Loop gains applicable to reference tracking are highlighted, and reference-to-output transfer functions are derived for the cases when end-point Prediction (EPP) is applied to enhance the response. A novel V(2)-controlled Buck converter with EPP is fabricated. The measured reference tracking response shows 10 times improvement in speed.

This paper analyzes the reference tracking behavior of Buck converters using several control schemes including voltage-mode, current-mode and V(2)-control from both large-signal and small-signal domains. Loop gains applicable to reference tracking are highlighted, and reference-to-output transfer functions are derived for the cases when end-point Prediction (EPP) is applied to enhance the response. A novel V(2)-controlled Buck converter with EPP is fabricated. The measured reference tracking response shows 10 times improvement in speed.

A monolithic output-ripple-based buck converter with adaptive output and ultra-fast reference tracking is presented. Fixed-switching-frequency V-2-control is used in steady-state operation; while its speed limitation during reference tracking is eliminated by employing end-point prediction, a novel oscillator with clock-holding function, and the proposed adaptive-output-feedback (AOFB)-scheme. The AOFB-scheme is obtained from a detailed analysis of the dynamics of general output-ripple-based controller during reference tracking. Then, an adaptive feedback voltage which satisfies the switching criterion for optimum switch control in reference tracking is formulated, and is incorporated into the controller design. The resultant single ON/OFF-switching during reference tracking is very close to the optimal solution for fast reference tracking. Moreover, it also leads to the lowest switching loss and minimized conduction loss at the fastest tracking speed, making the converter very suitable for adaptive output applications. Fabricated in a 0.35 mu m CMOS process, the 3-V input prototype chip exhibits stable operation across a wide output range of 0.7-2.4 V. High tracking speed within 10 mu s/V is measured with different output voltages and output voltage steps. Maximum efficiency of 96\% is obtained at 260 mA output current, while maximum output current is 800 mA.

The end-point prediction (EPP) scheme for voltage-mode buck regulators is proposed. Internal nodal voltages of the regulator controller are predicted and set automatically by the proposed algorithms and circuits. The settling time of the regulator can therefore be significantly reduced for faster dynamic responses, even with dominant-pole compensation. Proven experimentally by a voltage-mode buck regulator implemented in a 0.35-mu m CMOS technology, the reference-tracking speed using the EPP scheme is faster than the conventional buck regulator by about six times.

The end-point prediction (EPP) scheme for voltage-mode buck regulators is proposed. Internal nodal voltages of the regulator controller are predicted and set automatically by the proposed algorithms and circuits. The settling time of the regulator can therefore be significantly reduced for faster dynamic responses, even with dominant-pole compensation. Proven experimentally by a voltage-mode buck regulator implemented in a 0.35-mu m CMOS technology, the reference-tracking speed using the EPP scheme is faster than the conventional buck regulator by about six times.

The end-point prediction (EPP) scheme for voltage-mode buck regulators is proposed. Internal nodal voltages of the regulator controller are predicted and set automatically by the proposed algorithms and circuits. The settling time of the regulator can therefore be significantly reduced for faster dynamic responses, even with dominant-pole compensation. Proven experimentally by a voltage-mode buck regulator implemented in a 0.35-mu m CMOS technology, the reference-tracking speed using the EPP scheme is faster than the conventional buck regulator by about six times.