Design of RBF-Udwadia Controller for Mechanical Systems Considering Non-holonomic Reference Trajectory

This paper presents a control design technique which enables approximate reference trajectory tracking for a class of underactuated mechanical systems. The control law comprises two terms. The first involves feedback of the trajectory tracking error in the actuated coordinates. Building on the concept of vibrational control, the second term imposes high-frequency periodic inputs that are modulated by the tracking error in the unactuated coordinates. Under appropriate conditions on the system structure and the commanded trajectory, and with sufficient separation between the time scales of the vibrational forcing and the commanded trajectory, the approach provides convergence in both the actuated and unactuated coordinates. The procedure is first described for a two degree-of-freedom (DOF) system with one input. Generalizing to higher-dimensional, underactuated systems, the approach is then applied to a 4DOF system with two inputs. A final example involves control of a rigid plate that is flapping in a uniform flow, a 3DOF system with one input. More general applications include biomimetic locomotion systems, such as underwater vehicles with articulating fins and flapping wing micro-air vehicles.

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Control of Uncertain Nonlinear Multibody Mechanical Systems

Journal of Applied Mechanics ◽

10.1115/1.4025399 ◽

2013 ◽

Vol 81 (4) ◽

Cited By ~ 33

Author(s):

Firdaus E. Udwadia ◽

Thanapat Wanichanon

Keyword(s):

Closed Form ◽

Error Bounds ◽

Equations Of Motion ◽

Mechanical Systems ◽

Real Life ◽

Reference Trajectory ◽

Control Force ◽

Control Laws ◽

Nominal System ◽

The Face

Descriptions of real-life complex multibody mechanical systems are usually uncertain. Two sources of uncertainty are considered in this paper: uncertainties in the knowledge of the physical system and uncertainties in the “given” forces applied to the system. Both types of uncertainty are assumed to be time varying and unknown, yet bounded. In the face of such uncertainties, what is available in hand is therefore just the so-called “nominal system,” which is our best assessment and description of the actual real-life situation. A closed-form equation of motion for a general dynamical system that contains a control force is developed. When applied to a real-life uncertain multibody system, it causes the system to track a desired reference trajectory that is prespecified for the nominal system to follow. Thus, the real-life system's motion is required to coincide within prespecified error bounds and mimic the motion desired of the nominal system. Uncertainty is handled by a controller based on a generalization of the concept of a sliding surface, which permits the use of a large class of control laws that can be adapted to specific real-life practical limitations on the control force. A set of closed-form equations of motion is obtained for nonlinear, nonautonomous, uncertain, multibody systems that can track a desired reference trajectory that the nominal system is required to follow within prespecified error bounds and thereby satisfy the constraints placed on the nominal system. An example of a simple mechanical system demonstrates the efficacy and ease of implementation of the control methodology.

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A Dynamic Motion Tracking Control Approach for a Quadrotor Aerial Mechanical System

Shock and Vibration ◽

10.1155/2020/6635011 ◽

2020 ◽

Vol 2020 ◽

pp. 1-17

Author(s):

Hugo Yañez-Badillo ◽

Francisco Beltran-Carbajal ◽

Ruben Tapia-Olvera ◽

Antonio Valderrabano-Gonzalez ◽

Antonio Favela-Contreras ◽

...

Keyword(s):

Trajectory Tracking ◽

Tracking Control ◽

Motion Tracking ◽

Control Method ◽

Mechanical Systems ◽

Time Estimation ◽

Nonlinear Dynamic System ◽

Reference Trajectory ◽

Trajectory Tracking Control ◽

Control Approach

This paper deals with the reference trajectory tracking problem and simultaneous active disturbance suppression on a class of controlled aerial mechanical systems by processing measurable output signals. A novel dynamic control method for desired motion reference trajectory tracking for quadrotor helicopters is introduced. Measurements of position output signals for efficient and robust tracking of motion profiles specified for the unmanned aerial vehicle are only required. Thus, differentiation of signals and real-time estimation of disturbances affecting the multi-input multioutput, underactuated nonlinear dynamic system are unnecessary. The presented active control approach can be directly extended for a class of vibrating mechanical systems. Analytical, experimental, and numerical results are presented to prove the satisfactory performance of the proposed trajectory tracking control approach for considerably perturbed operating scenarios.

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Comparison of Methods for Tracking Control of Nonlinear Uncertain Multi-Body Mechanical Systems

Volume 4: Dynamics, Control and Uncertainty, Parts A and B ◽

10.1115/imece2012-88821 ◽

2012 ◽

Author(s):

F. E. Udwadia ◽

T. Wanichanon

Keyword(s):

Tracking Control ◽

Mechanical Systems ◽

Real Life ◽

Reference Trajectory ◽

Sliding Surface ◽

Nominal System ◽

Damping Control ◽

Multi Body ◽

Tracking Signal ◽

Damping Controller

This paper presents a comparison of several alternative approaches to obtaining tracking control of a nonlinear uncertain system. A real-life multi-body system is in general highly nonlinear and is intrinsically error-prone due to uncertainties in the modeling system. The uncertainty which is time-varying, unknown but bounded, is therefore assumed in this paper, whereby it may arise from two general sources: uncertainty in the knowledge of the physical system and/or uncertainty in the ‘given force’ applied to the system. In this paper, the use of a new, generalized nonlinear controller is illustrated incorporating two control laws—generalized sliding surface control and generalized damping control. The generalized damping control law also provides two control approaches, one with an uncertainty bound and one without the bound on uncertainty. This leads to three sets of closed-form controllers that can guarantee, regardless of the uncertainty, a tracking signal of a desired reference trajectory of the nominal system, which we refer to as our best assessment of the actual real-life situation. A comparison of the use of the proposed three control designs is demonstrated using an example of a control problem in multi-body dynamics. Both the generalized sliding surface controller and the generalized bound damping controller require knowledge of the bound on uncertainty in order to guarantee a tracking signal of a desired reference trajectory within a desired error bound. In contrast, when using the generalized no-bound damping controller, tracking of the nominal system trajectory can be obtained regardless of the knowledge of the uncertainty’s bound. However, the tracking results from the generalized no-bound damping controller are the least optimal when compared with those obtained from the other two controllers. With simplicity and accuracy obtained, all three control approaches can be implemented for a wide range of complex multi-body mechanical systems.

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