Ryan James Caverly

Dynamic Modeling and Passivity-Based Control of a Single Degree of Freedom Cable-Actuated System

In this paper, a lumped-mass dynamic model of a single degree of freedom cable-actuated system is derived, and passivity-based control is considered. The dynamic model developed takes into consideration the changing cable stiffness and mass as the cable is wrapped around a winch. In addition, the change in the winch inertia as the cable is wrapped around the winch is modeled. It is assumed that the mass of the payload is much greater than the mass of the cables and the equivalent mass of the winches, which allows for an approximation where the rigid dynamics can be decoupled from the elastic dynamics of the system. This approximation enables the definition of a modified input torque and modified output rate, allowing the establishment of passive input-output mappings. Passivity-based controllers are investigated, shown to render the closed-loop system input-output stable, and tested in simulation.

Dynamic Modeling and Noncollocated Control of a Flexible Planar Cable-Driven Manipulator

This paper investigates the dynamic modeling and passivity-based control of a planar cable-actuated system. This system is modeled using a lumped-mass method that explicitly considers the change in cable stiffness and winch inertia that occurs when the cables are wound around their respective winches. In order to simplify the modeling process, each cable is modeled individually and then constrained to the other cables. Exploiting the fact that the payload is much more massive than the cables allows the definition of a modified output called the μ -tip rate. Coupling the μ-tip rate with a modified input realizes the definition of a passive input-output map. The two degrees of freedom of the system are controlled by four winches. This overactuation is simplified by employing a set of load-sharing parameters that effectively reduce four inputs to two. The performance and robustness of the controllers are evaluated in the simulation.

Conic-sector-based controller synthesis: Theory and experiments

The Passivity Theorem is a popular input-output stability analysis tool. However, passivity violations, which are often due to sensor and actuator dynamics, may cause instabilities, necessitating the adoption of alternative stability results. This paper presents experimental results employing controllers that ensure stability via the Conic Sector Theorem. A new conic sector controller synthesis method mimicking an ℋ2-optimal controller is presented and compared to an existing conic sector controller synthesis method, and an ℋ2 controller itself. The conic controllers are found to yield increased robustness and improved performance in the presence of passivity violations.

Robust controller design using the Large Gain Theorem: The full-state feedback case

This paper presents full-state feedback controller synthesis methods that are robust to inverse additive uncertainty via the Large Gain Theorem. In particular, the controller synthesis methods can account for unstable uncertainties. Controllers are designed to either maximize robustness or maximize performance while satisfying a linear matrix inequality (LMI) that enforces a sufficient condition on the minimum gain of the closed-loop system. The Large Gain Theorem is used to prove the robust input-output stability of the system subject to inverse additive uncertainty. A numerical example is provided to illustrate the proposed controller design methods.

Flexible kiteplane modeling and control with an unsteady aerodynamic model

This paper considers dynamic modeling and control of a flexible kiteplane used for wind-energy harvesting. Each component of the kiteplane is modeled separately and is then constrained to the other components using the null-space method. The flexible wings are modeled as thin plates with bending and torsional stiffness. An unsteady aerodynamic model is included to increase the fidelity of the simulation under transient conditions. A proportional-integral-derivative (PID) attitude control law is implemented that uses the direction cosine matrix (DCM) directly and proportional-integral (PI) control is used to track a desired tether reel-in rate. Numerical simulation of the closed-loop system demonstrate the kiteplanes ability to harvest wind energy.

Saturated control of flexible-joint manipulators using a Hammerstein strictly positive real compensator

In this paper the control of flexible-joint manipulators while explicitly avoiding actuator saturation is considered. The controllers investigated are composed of a bounded proportional control term and a Hammerstein strictly positive real angular rate control term. This control structure ensures that the total torque demanded of each actuator is bounded by a value that is less than the maximum torque that each actuator is able to provide, thereby disallowing actuator saturation. The proposed controllers are shown to render the closed-loop system asymptotically stable, even in the presence of modeling uncertainties. The performance of the controllers is demonstrated experimentally and in simulation.

Regional pole and zero placement with static output feedback via the Modified Minimum Gain Lemma

This paper presents static output feedback controller synthesis methods that place closed-loop poles, blocking zeros, and transmission zeros within regions of the complex plane. In particular, closed-loop poles are placed within linear matrix inequality (LMI) regions of the complex plane, while closed-loop blocking and transmission zeros are placed in the open left-half plane (OLHP), and are thus minimum phase. An LMI formulation of the Modified Minimum Gain Lemma is used to ensure that the closed-loop system is minimum phase by forcing a nonzero minimum gain constraint. Two controller synthesis methods are presented, including Method 1, which places the closed-loop poles in the OLHP, and Method 2, which places closed-loop poles in the OLHP and closed-loop poles within a specified LMI region of the complex plane. Numerical examples are provided for both controller synthesis methods, with comparisons to controllers in the literature.

Maintaining positive cable tensions during operation of a single degree of freedom flexible cable-driven parallel manipulator

This paper investigates the control of a single degree of freedom flexible cable-driven parallel manipulator (CDPM) with a focus on maintaining positive cable tensions. A control architecture that uses a particular saturation prevention function is used to force the control torques to remain within limits that maintain positive cable tensions. The maximum and minimum allowable control torque limits are calculated by solving a linear programming problem on an element-wise inequality involving the equations of motion of the system. It is shown that the controller is input strictly passive and the closed-loop system is input-output stable. Numerical simulation results compare the performance of the proposed controller to that of an existing controller from the literature.

Modelling of Flexible Cable-Driven Parallel Robots Using a Rayleigh-Ritz Approach

This paper investigates the use of the Rayleigh-Ritz method to model single degree-of-freedom flexible cable-driven parallel robots (CDPRs) using a set of time-dependent basis functions to discretize cables of varying length. An energy-based model simplification is proposed to further facilitate reduction in the computational load when performing numerical simulations involving the proposed model. Open-loop system responses are used to compare the effect of the energy-based model simplification. Frequency responses are used to compare the influence of the number of basis functions used and to provide a comparison to a lumped-mass model.

Dynamic Modeling, Trajectory Optimization, and Control of a Flexible Kiteplane

This paper investigates dynamic modeling, trajectory optimization, and control of a flexible kiteplane used for wind energy harvesting. The individual components of the kiteplane, including flexible wings and a rigid fuselage, are modeled separately and then constrained together using the null-space method. The flexible wings of the kiteplane are modeled as flexible plates, and the Rayleigh–Ritz method is used to discretize the partial differential equation that describes the strain energy stored in the wing. The attitude of the kiteplane is described by the direction cosine matrix (DCM) directly and a proportional-integral-derivative control law that makes use of the DCM is implemented for attitude control. An unsteady aerodynamic model based on Theodorsen’s lift model is used in simulation to allow for an accurate model under transient conditions. An optimal trajectory is found using a simplified dynamic model and solving a finite-dimensional constrained optimization problem. Numerical simulations of the optimal trajectories are performed to demonstrate the kiteplane’s energy-harvesting capability.