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## PDE boundary control for flexible articulated aircraft wings,” presented at the AIAA

Venue: | Guidance Navigat. Contr. Conf |

Citations: | 4 - 2 self |

### Citations

865 |
Nonlinear and Adaptive Control Design
- Krstić, Kokotović
- 1995
(Show Context)
Citation Context ...d stabilizer. The procedure is called backstepping because it involves a Volterra operator with a lower triangular structure similar to backstepping transformation for ordinary differential equations =-=[29]-=-, [30], and allows the controller acting at the boundary to compensate for the undesired (unmatched) dynamics. 3) With the integral of wing twist as the output, and shear force at the wing tip as the ... |

357 |
An Introduction to Infinite-Dimensional Linear Systems Theory
- Curtain, Zwart
- 1995
(Show Context)
Citation Context ...sts of methods that convert the PDEs into ordinary differential equations using approximation methods such as those of Galerkin or Rayleigh-Ritz [9], [22], or using operator theoretic tools [4], [5], =-=[11]-=-, [27], [33], [34]. The second set of methods leaves the PDEs intact, and uses a “model-following” approach as described in a recent book by Krstic and Smyshlyaev [30]. A finite-state approximation to... |

224 | On contraction analysis for nonlinear systems
- Lohmiller, Slotine
- 1998
(Show Context)
Citation Context ...effectors [3], [46] or passive energy sinks for flutter [25]. There is a substantial amount of literature on boundary control theory of partial differential equations (PDEs) (see [8], [9], [12], [30]–=-=[32]-=-, [47] for material pertinent to this paper and references cited therein). There are two sets of methods for boundary control of PDEs. The first set consists of methods that convert the PDEs into ordi... |

156 |
Output regulation of nonlinear systems”,
- Byrnes, Isidori
- 1990
(Show Context)
Citation Context ... methods that convert the PDEs into ordinary differential equations using approximation methods such as those of Galerkin or Rayleigh-Ritz [9], [22], or using operator theoretic tools [4], [5], [11], =-=[27]-=-, [33], [34]. The second set of methods leaves the PDEs intact, and uses a “model-following” approach as described in a recent book by Krstic and Smyshlyaev [30]. A finite-state approximation to a PDE... |

118 |
Controllability and stabilizability theory for linear partial di¤erential equations: recent progress and open questions
- Russell
- 1978
(Show Context)
Citation Context ...ors [3], [46] or passive energy sinks for flutter [25]. There is a substantial amount of literature on boundary control theory of partial differential equations (PDEs) (see [8], [9], [12], [30]–[32], =-=[47]-=- for material pertinent to this paper and references cited therein). There are two sets of methods for boundary control of PDEs. The first set consists of methods that convert the PDEs into ordinary d... |

112 |
Feedback Control of Flexible System,"
- Balas
- 1978
(Show Context)
Citation Context ...ions of the approximation [8]. Stability analysis that is based on a finite-state approximation is vulnerable to spillover instabilities which arise due to inadequate accounting of the residual modes =-=[2]-=-, [37]. On the other hand, keeping PDEs intact makes the control law design more intuitive. A PDE-based approach has been used for maneuvering robotic arms [30], [44], controlling the Navier–Stokes mo... |

88 | The First Takeoff of a Biologically Inspired At-Scale Robotic Insect.
- Wood
- 2008
(Show Context)
Citation Context ...t motion, unmanned aerial vehicles. I. INTRODUCTION THERE is a considerable interest in developing robotic air-craft, which is inspired by birds and bats [10], [16], [20], [43] and insects [13]–[15], =-=[60]-=-. While insect wings can be modeled as simple rigid wings, both wing flexibility and wing articulation are believed to play a key role in flight performance and agility for bird and bat flight [43], [... |

71 |
Boundary Control of PDEs: A Course on Backstepping Designs,
- Krstic, Smyshlyaev
- 2008
(Show Context)
Citation Context ...ased effectors [3], [46] or passive energy sinks for flutter [25]. There is a substantial amount of literature on boundary control theory of partial differential equations (PDEs) (see [8], [9], [12], =-=[30]-=-–[32], [47] for material pertinent to this paper and references cited therein). There are two sets of methods for boundary control of PDEs. The first set consists of methods that convert the PDEs into... |

64 | Sastry,“Flapping flight for biomimetic robotic insects: part I-system modeling,”,
- Deng, Schenato, et al.
- 2006
(Show Context)
Citation Context ...ntrol, robot motion, unmanned aerial vehicles. I. INTRODUCTION THERE is a considerable interest in developing robotic air-craft, which is inspired by birds and bats [10], [16], [20], [43] and insects =-=[13]-=-–[15], [60]. While insect wings can be modeled as simple rigid wings, both wing flexibility and wing articulation are believed to play a key role in flight performance and agility for bird and bat fli... |

59 | Realization theory in Hilbert space
- Salamon
- 1989
(Show Context)
Citation Context ...ces a yawing moment on the aircraft. Remark 1: The well-posedness of the closed-loop systems considered here can be shown by proving that the input–output map of the system exists and is bounded [7], =-=[48]-=-. For the twisting dynamics actuated by root control, this is achieved by designing the control to map the system onto well-posed and exponentially stable dynamics. For twisting dynamics actuated at t... |

50 |
Introduction to Structural Dynamics and Aeroelasticity,
- Hodges, Pierce
- 2002
(Show Context)
Citation Context ... for boundary control of PDEs. The first set consists of methods that convert the PDEs into ordinary differential equations using approximation methods such as those of Galerkin or Rayleigh-Ritz [9], =-=[22]-=-, or using operator theoretic tools [4], [5], [11], [27], [33], [34]. The second set of methods leaves the PDEs intact, and uses a “model-following” approach as described in a recent book by Krstic an... |

28 |
Nonlinear Inversion Flight Control for a Supermaneuverable Aircraft,”
- Snell, Enns, et al.
- 1992
(Show Context)
Citation Context ...for bending and twist can be designed separately, which simplifies the design process considerably in practice. Time-scale separation is used quite routinely to design flight control laws [24], [45], =-=[53]-=-, [59]. We introduce one of the main results of this paper—the new perturbation-observer-based method to design a bending controller. In particular, we design a root-based bending controller [δR in (3... |

22 |
Flight Characteristics of Shaping the Membrane Wing of a Micro Air Vehicle,”
- Abdulrahim, Garcia, et al.
- 2005
(Show Context)
Citation Context ... Robotic bat testbed, where the control laws proposed in this paper can be tested [10], [16]. only improves aircraft performance and stability passively, but can also be actuated actively for control =-=[1]-=-, [39], [55]. Fig. 1 shows a robotic bat testbed, which was developed at the University of Illinois at Urbana-Champaign (UIUC) by the authors of [10] and [16]. Each wing is actuated at the root, and d... |

22 |
P.: Finite-dimensional control of parabolic PDE systems using approximate inertial manifolds
- Christofides, Daoutidis
- 1997
(Show Context)
Citation Context ...sing flap-based effectors [3], [46] or passive energy sinks for flutter [25]. There is a substantial amount of literature on boundary control theory of partial differential equations (PDEs) (see [8], =-=[9]-=-, [12], [30]–[32], [47] for material pertinent to this paper and references cited therein). There are two sets of methods for boundary control of PDEs. The first set consists of methods that convert t... |

22 |
State-space representation of aerodynamic characteristics of an aircraft at high angles of attack
- Goman, Khrabrov
- 1994
(Show Context)
Citation Context ...aircraft acceleration and added mass effect, and gravity. An aerodynamic model to calculate Fb , which is based on an ODE approximation for the time-varying flow dynamics on the wing, can be found in =-=[18]-=-. Then, the PDE model of the structural dynamics of the right wing is given by [ m̃ −m̃xec −m̃xec Ip ] [ ξtt θtt ] + [ ηEIbξtyyyy + EIbξyyyy −ηGJ̃θtyy −GJ̃θyy ] = [ Fb(ξy , θ,u, u̇B ) −xacFb(ξy , θ,u,... |

22 |
Recent progress in flapping wing aerodynamics and aeroelasticity [J]. Prog Aerospace Sci
- Shyy
- 2010
(Show Context)
Citation Context ...and bat flight, was introduced by Paranjape and coauthors [39], [40]. The concept lends itself readily to aeroelastic tailoring, which is seen as an asset in the development of agile MAVs [26], [39], =-=[50]-=-, [55]. Wing flexibility not Manuscript received May 20, 2012; revised September 30, 2012; accepted January 12, 2013. Date of publication February 11, 2013; date of current version June 3, 2013. This ... |

20 | A closed-form feedback controller for stabilization of the linearized 2D Navier–Stokes Poiseuille flow,
- Vazquez, Krstic
- 2007
(Show Context)
Citation Context ...7]. On the other hand, keeping PDEs intact makes the control law design more intuitive. A PDE-based approach has been used for maneuvering robotic arms [30], [44], controlling the Navier–Stokes model =-=[58]-=-, and suppressing vibrations in a flexible beam [21]. A gain-scheduling-based approach for nonlinear PDEs has been presented in [52], while Krstic and Smyshlyaev [31] derived an adaptive controller fo... |

19 |
Robust control of hyperbolic PDE systems
- Christodes, Daoutidis
- 1998
(Show Context)
Citation Context ...ted using flap-based effectors [3], [46] or passive energy sinks for flutter [25]. There is a substantial amount of literature on boundary control theory of partial differential equations (PDEs) (see =-=[8]-=-, [9], [12], [30]–[32], [47] for material pertinent to this paper and references cited therein). There are two sets of methods for boundary control of PDEs. The first set consists of methods that conv... |

18 |
Direct Strain Feedback Control of Flexible Robot Arms: New Theoretical and Experimental Results,”
- Luo
- 1993
(Show Context)
Citation Context ...ds that convert the PDEs into ordinary differential equations using approximation methods such as those of Galerkin or Rayleigh-Ritz [9], [22], or using operator theoretic tools [4], [5], [11], [27], =-=[33]-=-, [34]. The second set of methods leaves the PDEs intact, and uses a “model-following” approach as described in a recent book by Krstic and Smyshlyaev [30]. A finite-state approximation to a PDE may w... |

17 |
On the Problem of Observation Spillover in Self-Adjoint Distributed-Parameter Systems,"
- Meirovitch, Baruh
- 1983
(Show Context)
Citation Context ...of the approximation [8]. Stability analysis that is based on a finite-state approximation is vulnerable to spillover instabilities which arise due to inadequate accounting of the residual modes [2], =-=[37]-=-. On the other hand, keeping PDEs intact makes the control law design more intuitive. A PDE-based approach has been used for maneuvering robotic arms [30], [44], controlling the Navier–Stokes model [5... |

16 |
Adaptive control theory: guaranteed robustness with fast adaptation
- Hovakimyan, Cao
- 2010
(Show Context)
Citation Context ... The unmatched nonlinearity can be tackled using backstepping, or a more direct approach such as in [23, Ch. 3, pp. 140–174]. Fig. 7 compares the performance of two controllers. The first is based on =-=[23]-=- and designed using a finite-state approximation of the beam, and the other is based on the perturbation observer and trajectory planning approach in Section V. The beam is assumed to be loaded unifor... |

15 |
Dynamic Inversion for Nonaffine-In-Control Systems Via Time-scale Separation Part I
- 8Hovakimyan, Lavretsky, et al.
- 2007
(Show Context)
Citation Context ...ontrol laws for bending and twist can be designed separately, which simplifies the design process considerably in practice. Time-scale separation is used quite routinely to design flight control laws =-=[24]-=-, [45], [53], [59]. We introduce one of the main results of this paper—the new perturbation-observer-based method to design a bending controller. In particular, we design a root-based bending controll... |

14 | Robust nonlinear flight control of a high performance aircraft.
- Wang, Stengel
- 2005
(Show Context)
Citation Context ...nding and twist can be designed separately, which simplifies the design process considerably in practice. Time-scale separation is used quite routinely to design flight control laws [24], [45], [53], =-=[59]-=-. We introduce one of the main results of this paper—the new perturbation-observer-based method to design a bending controller. In particular, we design a root-based bending controller [δR in (3)] usi... |

13 |
Robust Adaptive StateFeedback Tracking for Nonlinear Systems,”
- Marino, Tomei
- 1998
(Show Context)
Citation Context ...̂(t) to ensure that the error e(t) remains bounded with as small a bound as possible. The projection operator, which is denoted by Proj(·, ·), is used commonly in the adaptive control literature [6], =-=[35]-=- for parameter estimation. Theorem 3: Let x(t) = [e(t), ė(t)]T . Suppose that there exist positive constants B1 and B2 such that |M | < B1 and |Ṁ | < B2 . Then, the following adaptive law ˙̂ M(t) = ... |

11 |
Output regulation for linear distributed parameter systems,”
- Byrnes, Lauko, et al.
- 2000
(Show Context)
Citation Context ...consists of methods that convert the PDEs into ordinary differential equations using approximation methods such as those of Galerkin or Rayleigh-Ritz [9], [22], or using operator theoretic tools [4], =-=[5]-=-, [11], [27], [33], [34]. The second set of methods leaves the PDEs intact, and uses a “model-following” approach as described in a recent book by Krstic and Smyshlyaev [30]. A finite-state approximat... |

11 |
Well-posedness of boundary control systems.
- Cheng, A
- 2003
(Show Context)
Citation Context ...produces a yawing moment on the aircraft. Remark 1: The well-posedness of the closed-loop systems considered here can be shown by proving that the input–output map of the system exists and is bounded =-=[7]-=-, [48]. For the twisting dynamics actuated by root control, this is achieved by designing the control to map the system onto well-posed and exponentially stable dynamics. For twisting dynamics actuate... |

11 | Transfer functions of distributed parameter systems:
- Curtain, Morris
- 2009
(Show Context)
Citation Context ...flap-based effectors [3], [46] or passive energy sinks for flutter [25]. There is a substantial amount of literature on boundary control theory of partial differential equations (PDEs) (see [8], [9], =-=[12]-=-, [30]–[32], [47] for material pertinent to this paper and references cited therein). There are two sets of methods for boundary control of PDEs. The first set consists of methods that convert the PDE... |

11 |
2008 Aeromechanics of membrane wings with implications for animal flight
- Song, Tian, et al.
- 2003
(Show Context)
Citation Context ...]. While insect wings can be modeled as simple rigid wings, both wing flexibility and wing articulation are believed to play a key role in flight performance and agility for bird and bat flight [43], =-=[54]-=-. A new concept to control microaerial vehicles (MAVs), which uses wing articulation and is inspired by bird and bat flight, was introduced by Paranjape and coauthors [39], [40]. The concept lends its... |

10 |
A sufficiently smooth projection operator
- Cai, Queiroz, et al.
- 2006
(Show Context)
Citation Context ...for M̂(t) to ensure that the error e(t) remains bounded with as small a bound as possible. The projection operator, which is denoted by Proj(·, ·), is used commonly in the adaptive control literature =-=[6]-=-, [35] for parameter estimation. Theorem 3: Let x(t) = [e(t), ė(t)]T . Suppose that there exist positive constants B1 and B2 such that |M | < B1 and |Ṁ | < B2 . Then, the following adaptive law ˙̂ M... |

9 |
Optimal boundary control with critical penalization for a PDE model of fluid-solid interactions,
- Bucci, Lasiecka
- 2010
(Show Context)
Citation Context ... set consists of methods that convert the PDEs into ordinary differential equations using approximation methods such as those of Galerkin or Rayleigh-Ritz [9], [22], or using operator theoretic tools =-=[4]-=-, [5], [11], [27], [33], [34]. The second set of methods leaves the PDEs intact, and uses a “model-following” approach as described in a recent book by Krstic and Smyshlyaev [30]. A finite-state appro... |

9 |
Exponential Stabilization of a Transversely Vibrating Beam via Boundary Control,”
- Fard
- 2001
(Show Context)
Citation Context ...d in [52], while Krstic and Smyshlyaev [31] derived an adaptive controller for parabolic PDEs. There are several PDE and ODE controller designs in the literature to stabilize and control beam bending =-=[17]-=-, [21], [28], [33], [34], [52], [56], although the literature mostly concerns bending that is encountered in loaded cables, structural beams, or robotic arms. Flexible wings of robotic aircraft are un... |

8 |
Neurobiologically inspired control of engineered flapping flight,”
- Chung, Dorothy, et al.
- 2009
(Show Context)
Citation Context ...nonlinear control systems, robot control, robot motion, unmanned aerial vehicles. I. INTRODUCTION THERE is a considerable interest in developing robotic air-craft, which is inspired by birds and bats =-=[10]-=-, [16], [20], [43] and insects [13]–[15], [60]. While insect wings can be modeled as simple rigid wings, both wing flexibility and wing articulation are believed to play a key role in flight performan... |

8 |
Adaptive nonlinear boundary control of a flexible link robot arm,”
- Queiroz, Donepudi, et al.
- 1999
(Show Context)
Citation Context ...e accounting of the residual modes [2], [37]. On the other hand, keeping PDEs intact makes the control law design more intuitive. A PDE-based approach has been used for maneuvering robotic arms [30], =-=[44]-=-, controlling the Navier–Stokes model [58], and suppressing vibrations in a flexible beam [21]. A gain-scheduling-based approach for nonlinear PDEs has been presented in [52], while Krstic and Smyshly... |

8 |
Explicit integral operator feedback for local stabilization of nonlinear thermal convection loop PDEs
- VAZQUEZ, KRSTIC
- 2006
(Show Context)
Citation Context ...explained in this paper can still be employed for such wings. The two-time-scale approach is rigorously applicable to coupled infinite-dimensional systems, as illustrated for thermalfluid dynamics in =-=[57]-=-, and for flexible structure dynamics in [51]. Moreover, although the coupled dynamics overlap over an infinitely wide frequency range, the slower subsystem has only a tiny fraction of its energy in t... |

7 | Flapping Flight for Biomimetic Robotic Insects - Deng, Schenato, et al. - 2006 |

6 | Flutter Suppression Using Micro-Trailing Edge Effectors
- Bieniawski, Kroo
- 2003
(Show Context)
Citation Context ...hat aeroelastic instabilities such as wing divergence and flutter 1552-3098/$31.00 © 2013 IEEE 626 IEEE TRANSACTIONS ON ROBOTICS, VOL. 29, NO. 3, JUNE 2013 can be mitigated using flap-based effectors =-=[3]-=-, [46] or passive energy sinks for flutter [25]. There is a substantial amount of literature on boundary control theory of partial differential equations (PDEs) (see [8], [9], [12], [30]–[32], [47] fo... |

6 | Robustadaptive boundary control of a flexible marine riser with vesseld ynamics
- He, SS, et al.
- 2011
(Show Context)
Citation Context ... control law design more intuitive. A PDE-based approach has been used for maneuvering robotic arms [30], [44], controlling the Navier–Stokes model [58], and suppressing vibrations in a flexible beam =-=[21]-=-. A gain-scheduling-based approach for nonlinear PDEs has been presented in [52], while Krstic and Smyshlyaev [31] derived an adaptive controller for parabolic PDEs. There are several PDE and ODE cont... |

6 |
Control of a tipforce destabilized shear beam by observer-based boundary feedback
- Krstic, Guo, et al.
- 2008
(Show Context)
Citation Context ...hile Krstic and Smyshlyaev [31] derived an adaptive controller for parabolic PDEs. There are several PDE and ODE controller designs in the literature to stabilize and control beam bending [17], [21], =-=[28]-=-, [33], [34], [52], [56], although the literature mostly concerns bending that is encountered in loaded cables, structural beams, or robotic arms. Flexible wings of robotic aircraft are unique because... |

6 |
Flight mechanics of a tailless articulated wing aircraft
- Paranjape, Chung, et al.
- 2011
(Show Context)
Citation Context ... Remark 7: Wings with smaller aspect ratios would have to be modeled as plates rather than beams. Although several MAV wings do have aspect ratios smaller than 3 (such as the one built by the authors =-=[40]-=-), their structure consists of a skin wrapped around or on a more traditional beam-like structure. The control design explained in this paper can still be employed for such wings. The two-time-scale a... |

6 |
Flexible-link robot arm control by a feedback linearization/singular perturbation method
- Vandegriff, Lewis, et al.
- 1994
(Show Context)
Citation Context ...ev [31] derived an adaptive controller for parabolic PDEs. There are several PDE and ODE controller designs in the literature to stabilize and control beam bending [17], [21], [28], [33], [34], [52], =-=[56]-=-, although the literature mostly concerns bending that is encountered in loaded cables, structural beams, or robotic arms. Flexible wings of robotic aircraft are unique because they experience a close... |

5 |
Dynamics and performance of taillessmicro aerial vehicle with flexible articulated wings,”AIAA
- Paranjape, Chung, et al.
- 2012
(Show Context)
Citation Context ...or bird and bat flight [43], [54]. A new concept to control microaerial vehicles (MAVs), which uses wing articulation and is inspired by bird and bat flight, was introduced by Paranjape and coauthors =-=[39]-=-, [40]. The concept lends itself readily to aeroelastic tailoring, which is seen as an asset in the development of agile MAVs [26], [39], [50], [55]. Wing flexibility not Manuscript received May 20, 2... |

4 |
A fundamental study of wing actuation for a 6-in-wingspan flapping microaerial vehicle
- Hamamoto, Ohta, et al.
- 2010
(Show Context)
Citation Context ...ntrol systems, robot control, robot motion, unmanned aerial vehicles. I. INTRODUCTION THERE is a considerable interest in developing robotic air-craft, which is inspired by birds and bats [10], [16], =-=[20]-=-, [43] and insects [13]–[15], [60]. While insect wings can be modeled as simple rigid wings, both wing flexibility and wing articulation are believed to play a key role in flight performance and agili... |

4 | Adaptive Control of PDEs - Krstic, Smyshlyaev - 2010 |

4 |
Aircraft spin recovery, with and without thrust vectoring, using nonlinear dynamic inversion
- Raghavendra, Sahai, et al.
- 2005
(Show Context)
Citation Context ... laws for bending and twist can be designed separately, which simplifies the design process considerably in practice. Time-scale separation is used quite routinely to design flight control laws [24], =-=[45]-=-, [53], [59]. We introduce one of the main results of this paper—the new perturbation-observer-based method to design a bending controller. In particular, we design a root-based bending controller [δR... |

3 |
Modeling interactions between flexible flapping-wing (a) Wind tunnel (b) Mounted on a pendulum
- Doman, Tang, et al.
(Show Context)
Citation Context ..., robot motion, unmanned aerial vehicles. I. INTRODUCTION THERE is a considerable interest in developing robotic air-craft, which is inspired by birds and bats [10], [16], [20], [43] and insects [13]–=-=[15]-=-, [60]. While insect wings can be modeled as simple rigid wings, both wing flexibility and wing articulation are believed to play a key role in flight performance and agility for bird and bat flight [... |

3 |
Targeted energy transfer between a model flexible wing and nonlinear energy sink
- Hubbard, McFarland, et al.
- 2010
(Show Context)
Citation Context ...ergence and flutter 1552-3098/$31.00 © 2013 IEEE 626 IEEE TRANSACTIONS ON ROBOTICS, VOL. 29, NO. 3, JUNE 2013 can be mitigated using flap-based effectors [3], [46] or passive energy sinks for flutter =-=[25]-=-. There is a substantial amount of literature on boundary control theory of partial differential equations (PDEs) (see [8], [9], [12], [30]–[32], [47] for material pertinent to this paper and referenc... |

3 |
Further theoretical results on direct strain feedback control of flexible robot arms
- Luo, Guo
- 1995
(Show Context)
Citation Context ...t convert the PDEs into ordinary differential equations using approximation methods such as those of Galerkin or Rayleigh-Ritz [9], [22], or using operator theoretic tools [4], [5], [11], [27], [33], =-=[34]-=-. The second set of methods leaves the PDEs intact, and uses a “model-following” approach as described in a recent book by Krstic and Smyshlyaev [30]. A finite-state approximation to a PDE may wrongly... |

3 |
Gain scheduling-inspired boundary control for nonlinear partial differential equations
- Siranosian, Krstic, et al.
- 2011
(Show Context)
Citation Context ...vering robotic arms [30], [44], controlling the Navier–Stokes model [58], and suppressing vibrations in a flexible beam [21]. A gain-scheduling-based approach for nonlinear PDEs has been presented in =-=[52]-=-, while Krstic and Smyshlyaev [31] derived an adaptive controller for parabolic PDEs. There are several PDE and ODE controller designs in the literature to stabilize and control beam bending [17], [21... |

2 |
Towards bio-inspired robotic aircraft: Control experiments on flapping and gliding
- Dorothy, Paranjape, et al.
- 2012
(Show Context)
Citation Context ...ear control systems, robot control, robot motion, unmanned aerial vehicles. I. INTRODUCTION THERE is a considerable interest in developing robotic air-craft, which is inspired by birds and bats [10], =-=[16]-=-, [20], [43] and insects [13]–[15], [60]. While insect wings can be modeled as simple rigid wings, both wing flexibility and wing articulation are believed to play a key role in flight performance and... |

2 |
PDE boundary control for Euler-Bernoulli beam using a two stage perturbation observer
- Paranjape, Guan, et al.
- 2012
(Show Context)
Citation Context ...cking error and rapid convergence to the reference signal after the impulsive perturbation. Additional experimental results, including those for root control of beam bending, can be found in [19] and =-=[42]-=-. VIII. CONCLUSION This paper has introduced a boundary control formulation for a class of PDEs whose output consists of a spatial integral of the state variable. Although the primary focus of this pa... |

2 |
Output tracking control of a parallel-flow heat exchange process,” Syst
- Sano
- 2011
(Show Context)
Citation Context ...es y2 I ′′n (y) + yI ′n (y) − (y2 + n2 )In (y) = 0. are tight bounds on the tracking error. A similar approach, which is based on backstepping, but for constant reference signals, has been derived in =-=[49]-=-. Step 3 (Trajectory planning for wing twist): We design a trajectory planning-based algorithm (see [30], Ch. 12). We define a new state vr , where the superscript “r” denotes the reference value. The... |

2 |
Parameterizing stability derivatives and flight dynamics with wing deformation,” presented at the AIAA
- Tran, Lind
(Show Context)
Citation Context ...t flight, was introduced by Paranjape and coauthors [39], [40]. The concept lends itself readily to aeroelastic tailoring, which is seen as an asset in the development of agile MAVs [26], [39], [50], =-=[55]-=-. Wing flexibility not Manuscript received May 20, 2012; revised September 30, 2012; accepted January 12, 2013. Date of publication February 11, 2013; date of current version June 3, 2013. This paper ... |

1 | Design and control strategy of a flexible, hyper-redundant robotic arm using electroactive dielectric polymers
- Guan
- 2012
(Show Context)
Citation Context ...erturbation. control input u(t) = ξyyy (t, L) = Ftip/EIb results in u(t) = 4× 10−3 L3 W 1.5 =⇒ W = 39.67L(u(t))2/3 . (73) The control law u(t) is obtained from an equation, which is analogous to (64) =-=[19]-=- u(t) = 5 η2(t) L − 18Rh(t) L3 , Rh(t) = R(t)− ξ̂p(t, L) η̈2(t) + ( p + 60 L4 ) (bb η̇2(t) + abη2(t)) = 180 L6 ( bbṘh(t) + abRh(t) ) . (74) The gain was set to p = 500 for the experiments. Fig. 9 sho... |

1 |
Flexible-wing-based micro air vehicles,” presented at the AIAA Aerospace Sci. Meeting Exhibit
- Ifju, Jenkins, et al.
(Show Context)
Citation Context ...red by bird and bat flight, was introduced by Paranjape and coauthors [39], [40]. The concept lends itself readily to aeroelastic tailoring, which is seen as an asset in the development of agile MAVs =-=[26]-=-, [39], [50], [55]. Wing flexibility not Manuscript received May 20, 2012; revised September 30, 2012; accepted January 12, 2013. Date of publication February 11, 2013; date of current version June 3,... |

1 |
Dynamics and control of robotic aircraft with articulated wings
- Paranjape
- 2011
(Show Context)
Citation Context ...CRAFT 637 Fig. 7. Comparison of controllers derived from finite-state approximations of the open loop and the homogeneous component, respectively, with a controller obtained using trajectory planning =-=[41]-=-. (a) Traditional ODE control. (b) PDE perturbation observer with trajectory planning. states, can be recast into the form ẋ = Ax + Bū + f(x), y = Cx (70) where ū(t) equals the highest derivative o... |

1 | Novel dihedral-based control of flapping-wing aircraft with application to perching
- Paranjape, Kim, et al.
(Show Context)
Citation Context ...systems, robot control, robot motion, unmanned aerial vehicles. I. INTRODUCTION THERE is a considerable interest in developing robotic air-craft, which is inspired by birds and bats [10], [16], [20], =-=[43]-=- and insects [13]–[15], [60]. While insect wings can be modeled as simple rigid wings, both wing flexibility and wing articulation are believed to play a key role in flight performance and agility for... |

1 |
Integrated aerodynamic-structural-control wing design
- Rais-Rohani, Haftka, et al.
- 1992
(Show Context)
Citation Context ...eroelastic instabilities such as wing divergence and flutter 1552-3098/$31.00 © 2013 IEEE 626 IEEE TRANSACTIONS ON ROBOTICS, VOL. 29, NO. 3, JUNE 2013 can be mitigated using flap-based effectors [3], =-=[46]-=- or passive energy sinks for flutter [25]. There is a substantial amount of literature on boundary control theory of partial differential equations (PDEs) (see [8], [9], [12], [30]–[32], [47] for mate... |

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Motion planning and tracking for tip displacement and deflection angle for flexible beams
- Siranosian, Krstic, et al.
- 2009
(Show Context)
Citation Context ... for such wings. The two-time-scale approach is rigorously applicable to coupled infinite-dimensional systems, as illustrated for thermalfluid dynamics in [57], and for flexible structure dynamics in =-=[51]-=-. Moreover, although the coupled dynamics overlap over an infinitely wide frequency range, the slower subsystem has only a tiny fraction of its energy in the (semi-infinite) frequency range, where it ... |