This paper presents an linear quadratic Gaussian (LQG)-based robust control strategy for active n... more This paper presents an linear quadratic Gaussian (LQG)-based robust control strategy for active noise reduction in a 3D enclosure wherein acoustic-structure interaction dynamics is present. The acoustic disturbance is created by the piezo-actuated vibrating boundary surface of the enclosure. The control signal is generated by the speaker which is noncollocated with the sensing microphone mounted inside the enclosure. The dynamic model of the system is obtained using frequency-domain system identification techniques. The state weighting matrix in the LQG cost function is determined analytically in the closed-form which allows the control designer to directly penalize the total acoustic energy of the system. The robustness of the controller is also ensured to guarantee the closed-loop stability against the unmodeled dynamics and parametric uncertainties. Simulation and experiment results are given which demonstrate the effectiveness of the proposed control methodology.
A new methodology for parametric sensitivity based robust optimal control sysnthesys (PS-ROCS), i... more A new methodology for parametric sensitivity based robust optimal control sysnthesys (PS-ROCS), is presented for robust optimal control synthesis using augmented plant dynamics with sensitivity co-system. Robustness of the control system to parametric uncertainties is ensured by minimizing the energy in the states where state vector incorporates states of the sensitivity co-system. The sensitivity dynamics is developed for the first-order parametric sensitivities from the system dynamics. This paper uses the Youla parameterization approach for controller synthesis. The robust optimal design methodology is demonstrated using a linearized model of double slider mechanism. For comparative study, two control designs obtained using the proposed methodology is compared with the H∞-based design. It was observed that the new methodology presents a viable alternative for robust optimal control design. The attractiveness of the proposed approach lies in the fact that no uncertainty estimates ...
This paper presents a semi-active control methodology for controlling the vibration of a pneumati... more This paper presents a semi-active control methodology for controlling the vibration of a pneumatic air spring-valve-accumulator system. Three controllers are presented and compared, along with experimental results. Due to the semi-active nature of this system, each controller uses a skyhook switching algorithm, along with a set-point plus PI tracking algorithm to track a desired reference signal. Some combination of pressure and displacement (or relative displacement) sensor feedback is used in each case. The desired reference control signal is generated by three different methods. The first method uses an optimal LQI (Linear Quadratic Impulse) controller generated from Covariance Control Theory. The second method uses a modified skyhook algorithm, and the third method uses a command directly proportional to the relative displacement. The second two methods use the first method (LQI) to tune the required controller gains off-line.
This paper presents the analytical modeling, system identification, and experimental validation f... more This paper presents the analytical modeling, system identification, and experimental validation for an air spring-valve-accumulator pneumatic system. Such system has wide spread use in vibration isolation applications. The motivation for this work was to provide a plant model and gain a deeper understanding of the physical system to be used in model-based development of a semi-active control methodology for vibration suppression. The work presented here is limited to the modeling aspect of the system.
A dual-mode H∞ robust tracking controller design is presented to regulate the speed of a hydrauli... more A dual-mode H∞ robust tracking controller design is presented to regulate the speed of a hydraulic front wheel drive system on a motor grader. The controller design uses a multiplicative unstructured uncertainty model to account for the un-modeled dynamics of the plant and parametric uncertainties such as variations in fluid temperature and air entrainment. The H∞ design is compared to a classical PI controller design, which is the existing industrial practice. It is shown that the H∞ design provides a higher level of stability robustness and better performance guarantees, which make it a viable candidate for motor grader application.
The design of linear-quadratic-Gaussian (LQG) controllers is addressed for uncertain linear time-... more The design of linear-quadratic-Gaussian (LQG) controllers is addressed for uncertain linear time-invariant systems that are either norm bounded or belong to a given sector. The system matrices are assumed to be affine functions of parameters confined to a convex polytopic region in the parameter space. Methods are developed for designing controllers which satisfy certain norm or sector conditions and are simultaneously optimal in the LQG sense. The resulting controllers provide robust stability as well as optimal performance.
The multidisciplinary design approach has gained increasing popularity in recent years due to its... more The multidisciplinary design approach has gained increasing popularity in recent years due to its ability to deal with conflicting design requirements imposed by discipline-specific objectives. The traditional design process involving multiple disciplines is typically a sequential process where the design objectives are met one at a time in a sequence of designs. However, in doing so, unnecessary limitations are imposed on the design parameters and the final design is far from being optimal. The effectiveness of integrated design methodology has been proven and such designs are being obtained in many applications. However, most of the work in this area has been problem and/or system specific and does not address important manufacturing considerations, such as tolerance allocation, robustness with respect to machining tolerances, etc. The results presented in this paper are intended to contribution towards filling these gaps. In particular, the new approach will help designers avoid a common known pitfall of performance optimization, i.e. the fact that designs that are optimized for performance alone are notoriously sensitive to deviations from the nominal design. Thus, optimizing for performance alone leads to designs that fall below acceptable standards of robustness; they are also expensive to manufacture because the tolerances must be kept very tight to ensure acceptable performance. The approach presented here will allow the user to systematically tradeoff performance versus robustness and tolerancing concerns. A proof-of-concept example that was solved to evaluate this methodology is also presented in this paper. This example provides a convincing demonstration of the fact that small sacrifices in performance can yield huge benefits in the other areas, provided a methodology is available for making these tradeoffs in a systematic way. This especially can be used by designers in various fields such as automotive, aerospace, deployable structures, machine tools (including hexapods), robotic systems, precision machinery, etc.
The problem of exact linearization of nonlinear systems with single input via time scale transfor... more The problem of exact linearization of nonlinear systems with single input via time scale transformation (TST) is considered in this paper. If the distribution G r-1 for a given nonlinear system is involutive but G r is not, then the conditions under which the ...
Heating, Ventilating and Airconditioning (HVAC) control systems play an important role in regulat... more Heating, Ventilating and Airconditioning (HVAC) control systems play an important role in regulating indoor air temperature to provide building occupants a comfortable environment. Design of HVAC control system to provide an optimal balance between comfort and energy usage is a challenging problem. This paper presents a framework for control of building HVAC systems using a methodology based on power shaping paradigm that exploits passivity theory. The controller design uses Brayton-Moser formulation for the system dynamics wherein the mixed potential function is the power function and the power shaping technique is used to synthesize the controller by assigning a desired power function to the closed loop dynamics so as to make the equilibrium point asymptotically stable. The methodology is demonstrated using two example HVAC subsystems-a two-zone building system and a heat exchanger system.
Global asymptotic stability of a class of nonlinear multibody flexible space structures under dis... more Global asymptotic stability of a class of nonlinear multibody flexible space structures under dissipative compensation is established. Two cases are considered. The first case allows unlimited nonlinear motions of the entire system and uses quaternion feedback. The second case assumes that the central body motion is in the linear range although the other bodies can undergo unrestricted nonlinear motion. The stability is proved to be robust to the inherent modeling nonlinearities and uncertainties. Furthermore, for the second case, the stability is also shown to be robust to certain actuator and sensor nonlinearities. The stability proofs use the Lyapunov approach and exploit the inherent passivity of such systems. The results are applicable to a wide class of systems, including flexible space structures with articulated flexible appendages.
Abstract This paper addresses stabilization and control issues in autonomous capture andmanipulat... more Abstract This paper addresses stabilization and control issues in autonomous capture andmanipulation of non-cooperative space objects such as asteroids, space debris, andorbital spacecraft in need of servicing. Such objects are characterized by unknownmass-inertia properties, unknown rotational motion, and irregular shapes, whichmakes it a challenging control problem. The problem is further compounded bythe presence of inherent nonlinearities, signi cant elastic modes with low damping,and parameter uncertainties in the spacecraft. Robust dissipativity-based controllaws are presented and are shown to provide global asymptotic stability in spite ofmodel uncertainties and nonlinearities. It is shown that robust stabilization can beaccomplished via model-independent dissipativity-based controllers using thrustersalone, while stabilization with attitude and position control can be accomplishedusing thrusters and torque actuators. 1 Introduction The proposed NASA asteroid redirect mission has created considerable excitementand interest in the public as well as in the worldwide science and engineering com-munities. A study by the Keck Institute [1] has concluded that it is feasible toautonomously capture and return an entire 7-m diameter, 500,000-kg near-Earthasteroid to a high lunar orbit. An alternate approach, consisting of picking a bouldero of a larger asteroid, is also being studied. Investigations are in progress at NASAand other organizations to conceive and develop alternative approaches and methodsfor capture, manipulation, and transport of asteroids.Another important challenge that is technically similar to asteroid capture isorbital debris mitigation. The near-Earth as well as geostationary orbital debrispopulation is continuously growing and its growth is expected to continue in thefuture due to ongoing space activities. On-orbit satellite explosions and collisions(accidental or intentional) create even larger numbers of debris items. Space debrisposes a serious threat both to human-occupied vehicles and to commercial satellites.Some suggested approaches for orbital debris mitigation would involve docking acapture spacecraft with the debris or making a physical impact. This is a techno-logically challenging task as most debris are non-cooperative and possibly tumblingwith unknown spin, precession, nutation, amplitude changes etc.A third technically similar challenge is autonomous on-orbit capture and servic-ing of defunct or functioning satellites. For example, on-orbit refuelling or repairscan extend a satellite’s life at a fraction of the cost of constructing and launching anew satellite. Also, with the rapid ongoing advancement of micro-component tech-nologies, it may be desirable to replace components of older functioning satelliteswith advanced components and signi cantly increase the capabilities. (For refuellingor refurbishment of functioning satellites, the capture and manipulation should besomewhat simpler since they would likely be cooperative objects).A related problem is asteroid strike threat mitigation, which would involve chang-ing an asteroid’s trajectory to avoid collision with Earth.1
This paper presents an linear quadratic Gaussian (LQG)-based robust control strategy for active n... more This paper presents an linear quadratic Gaussian (LQG)-based robust control strategy for active noise reduction in a 3D enclosure wherein acoustic-structure interaction dynamics is present. The acoustic disturbance is created by the piezo-actuated vibrating boundary surface of the enclosure. The control signal is generated by the speaker which is noncollocated with the sensing microphone mounted inside the enclosure. The dynamic model of the system is obtained using frequency-domain system identification techniques. The state weighting matrix in the LQG cost function is determined analytically in the closed-form which allows the control designer to directly penalize the total acoustic energy of the system. The robustness of the controller is also ensured to guarantee the closed-loop stability against the unmodeled dynamics and parametric uncertainties. Simulation and experiment results are given which demonstrate the effectiveness of the proposed control methodology.
A new methodology for parametric sensitivity based robust optimal control sysnthesys (PS-ROCS), i... more A new methodology for parametric sensitivity based robust optimal control sysnthesys (PS-ROCS), is presented for robust optimal control synthesis using augmented plant dynamics with sensitivity co-system. Robustness of the control system to parametric uncertainties is ensured by minimizing the energy in the states where state vector incorporates states of the sensitivity co-system. The sensitivity dynamics is developed for the first-order parametric sensitivities from the system dynamics. This paper uses the Youla parameterization approach for controller synthesis. The robust optimal design methodology is demonstrated using a linearized model of double slider mechanism. For comparative study, two control designs obtained using the proposed methodology is compared with the H∞-based design. It was observed that the new methodology presents a viable alternative for robust optimal control design. The attractiveness of the proposed approach lies in the fact that no uncertainty estimates ...
This paper presents a semi-active control methodology for controlling the vibration of a pneumati... more This paper presents a semi-active control methodology for controlling the vibration of a pneumatic air spring-valve-accumulator system. Three controllers are presented and compared, along with experimental results. Due to the semi-active nature of this system, each controller uses a skyhook switching algorithm, along with a set-point plus PI tracking algorithm to track a desired reference signal. Some combination of pressure and displacement (or relative displacement) sensor feedback is used in each case. The desired reference control signal is generated by three different methods. The first method uses an optimal LQI (Linear Quadratic Impulse) controller generated from Covariance Control Theory. The second method uses a modified skyhook algorithm, and the third method uses a command directly proportional to the relative displacement. The second two methods use the first method (LQI) to tune the required controller gains off-line.
This paper presents the analytical modeling, system identification, and experimental validation f... more This paper presents the analytical modeling, system identification, and experimental validation for an air spring-valve-accumulator pneumatic system. Such system has wide spread use in vibration isolation applications. The motivation for this work was to provide a plant model and gain a deeper understanding of the physical system to be used in model-based development of a semi-active control methodology for vibration suppression. The work presented here is limited to the modeling aspect of the system.
A dual-mode H∞ robust tracking controller design is presented to regulate the speed of a hydrauli... more A dual-mode H∞ robust tracking controller design is presented to regulate the speed of a hydraulic front wheel drive system on a motor grader. The controller design uses a multiplicative unstructured uncertainty model to account for the un-modeled dynamics of the plant and parametric uncertainties such as variations in fluid temperature and air entrainment. The H∞ design is compared to a classical PI controller design, which is the existing industrial practice. It is shown that the H∞ design provides a higher level of stability robustness and better performance guarantees, which make it a viable candidate for motor grader application.
The design of linear-quadratic-Gaussian (LQG) controllers is addressed for uncertain linear time-... more The design of linear-quadratic-Gaussian (LQG) controllers is addressed for uncertain linear time-invariant systems that are either norm bounded or belong to a given sector. The system matrices are assumed to be affine functions of parameters confined to a convex polytopic region in the parameter space. Methods are developed for designing controllers which satisfy certain norm or sector conditions and are simultaneously optimal in the LQG sense. The resulting controllers provide robust stability as well as optimal performance.
The multidisciplinary design approach has gained increasing popularity in recent years due to its... more The multidisciplinary design approach has gained increasing popularity in recent years due to its ability to deal with conflicting design requirements imposed by discipline-specific objectives. The traditional design process involving multiple disciplines is typically a sequential process where the design objectives are met one at a time in a sequence of designs. However, in doing so, unnecessary limitations are imposed on the design parameters and the final design is far from being optimal. The effectiveness of integrated design methodology has been proven and such designs are being obtained in many applications. However, most of the work in this area has been problem and/or system specific and does not address important manufacturing considerations, such as tolerance allocation, robustness with respect to machining tolerances, etc. The results presented in this paper are intended to contribution towards filling these gaps. In particular, the new approach will help designers avoid a common known pitfall of performance optimization, i.e. the fact that designs that are optimized for performance alone are notoriously sensitive to deviations from the nominal design. Thus, optimizing for performance alone leads to designs that fall below acceptable standards of robustness; they are also expensive to manufacture because the tolerances must be kept very tight to ensure acceptable performance. The approach presented here will allow the user to systematically tradeoff performance versus robustness and tolerancing concerns. A proof-of-concept example that was solved to evaluate this methodology is also presented in this paper. This example provides a convincing demonstration of the fact that small sacrifices in performance can yield huge benefits in the other areas, provided a methodology is available for making these tradeoffs in a systematic way. This especially can be used by designers in various fields such as automotive, aerospace, deployable structures, machine tools (including hexapods), robotic systems, precision machinery, etc.
The problem of exact linearization of nonlinear systems with single input via time scale transfor... more The problem of exact linearization of nonlinear systems with single input via time scale transformation (TST) is considered in this paper. If the distribution G r-1 for a given nonlinear system is involutive but G r is not, then the conditions under which the ...
Heating, Ventilating and Airconditioning (HVAC) control systems play an important role in regulat... more Heating, Ventilating and Airconditioning (HVAC) control systems play an important role in regulating indoor air temperature to provide building occupants a comfortable environment. Design of HVAC control system to provide an optimal balance between comfort and energy usage is a challenging problem. This paper presents a framework for control of building HVAC systems using a methodology based on power shaping paradigm that exploits passivity theory. The controller design uses Brayton-Moser formulation for the system dynamics wherein the mixed potential function is the power function and the power shaping technique is used to synthesize the controller by assigning a desired power function to the closed loop dynamics so as to make the equilibrium point asymptotically stable. The methodology is demonstrated using two example HVAC subsystems-a two-zone building system and a heat exchanger system.
Global asymptotic stability of a class of nonlinear multibody flexible space structures under dis... more Global asymptotic stability of a class of nonlinear multibody flexible space structures under dissipative compensation is established. Two cases are considered. The first case allows unlimited nonlinear motions of the entire system and uses quaternion feedback. The second case assumes that the central body motion is in the linear range although the other bodies can undergo unrestricted nonlinear motion. The stability is proved to be robust to the inherent modeling nonlinearities and uncertainties. Furthermore, for the second case, the stability is also shown to be robust to certain actuator and sensor nonlinearities. The stability proofs use the Lyapunov approach and exploit the inherent passivity of such systems. The results are applicable to a wide class of systems, including flexible space structures with articulated flexible appendages.
Abstract This paper addresses stabilization and control issues in autonomous capture andmanipulat... more Abstract This paper addresses stabilization and control issues in autonomous capture andmanipulation of non-cooperative space objects such as asteroids, space debris, andorbital spacecraft in need of servicing. Such objects are characterized by unknownmass-inertia properties, unknown rotational motion, and irregular shapes, whichmakes it a challenging control problem. The problem is further compounded bythe presence of inherent nonlinearities, signi cant elastic modes with low damping,and parameter uncertainties in the spacecraft. Robust dissipativity-based controllaws are presented and are shown to provide global asymptotic stability in spite ofmodel uncertainties and nonlinearities. It is shown that robust stabilization can beaccomplished via model-independent dissipativity-based controllers using thrustersalone, while stabilization with attitude and position control can be accomplishedusing thrusters and torque actuators. 1 Introduction The proposed NASA asteroid redirect mission has created considerable excitementand interest in the public as well as in the worldwide science and engineering com-munities. A study by the Keck Institute [1] has concluded that it is feasible toautonomously capture and return an entire 7-m diameter, 500,000-kg near-Earthasteroid to a high lunar orbit. An alternate approach, consisting of picking a bouldero of a larger asteroid, is also being studied. Investigations are in progress at NASAand other organizations to conceive and develop alternative approaches and methodsfor capture, manipulation, and transport of asteroids.Another important challenge that is technically similar to asteroid capture isorbital debris mitigation. The near-Earth as well as geostationary orbital debrispopulation is continuously growing and its growth is expected to continue in thefuture due to ongoing space activities. On-orbit satellite explosions and collisions(accidental or intentional) create even larger numbers of debris items. Space debrisposes a serious threat both to human-occupied vehicles and to commercial satellites.Some suggested approaches for orbital debris mitigation would involve docking acapture spacecraft with the debris or making a physical impact. This is a techno-logically challenging task as most debris are non-cooperative and possibly tumblingwith unknown spin, precession, nutation, amplitude changes etc.A third technically similar challenge is autonomous on-orbit capture and servic-ing of defunct or functioning satellites. For example, on-orbit refuelling or repairscan extend a satellite’s life at a fraction of the cost of constructing and launching anew satellite. Also, with the rapid ongoing advancement of micro-component tech-nologies, it may be desirable to replace components of older functioning satelliteswith advanced components and signi cantly increase the capabilities. (For refuellingor refurbishment of functioning satellites, the capture and manipulation should besomewhat simpler since they would likely be cooperative objects).A related problem is asteroid strike threat mitigation, which would involve chang-ing an asteroid’s trajectory to avoid collision with Earth.1
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Papers by Atul Kelkar