224 research outputs found
Implementation of the New Control Methods in Simplification of a Multidimensional Control and Optimization of a Control System Parameters.
The main purpose of this text is to present application of the Largest Lyapunov Exponent (LLE) as a criterion for optimization of the new type of simple controller parameters. Investigated controller is the part of numerically simulated control system. The calculation of LLE was done with a new method [2]. Introduction contains reference to previous publications on inverted pendulum control and Lyapunov stability. Application of the new simple formula for LLE estimation in control systems is discussed. In the next part simulated dynamical system is described and new type of simple controller allowing to control multidimensional system is introduced. In the last part results of the simulation are shown along with conclusions to whole dynamics analysis. Comparison of the proposed regulator with the linearquadratic regulator (LQR) was verified and its better effectiveness with respect to LQR was proved
Normal forms for underactuated mechanical systems with symmetry
We introduce cascade normal forms for underactuated mechanical systems that are convenient for control design. These normal forms include three classes of cascade systems, namely, nonlinear systems in strict feedback form, feedforward form, and nontriangular quadratic form (to be defined). In each case, the transformation to cascade systems is provided in closed-form. We apply our results to the Acrobot, the rotating pendulum, and the cart-pole system
Hidden Parameter Markov Decision Processes: A Semiparametric Regression Approach for Discovering Latent Task Parametrizations
Control applications often feature tasks with similar, but not identical,
dynamics. We introduce the Hidden Parameter Markov Decision Process (HiP-MDP),
a framework that parametrizes a family of related dynamical systems with a
low-dimensional set of latent factors, and introduce a semiparametric
regression approach for learning its structure from data. In the control
setting, we show that a learned HiP-MDP rapidly identifies the dynamics of a
new task instance, allowing an agent to flexibly adapt to task variations
Friction compensation in the swing-up control of viscously damped underactuated robotics
A dissertation submitted to the Faculty of Engineering and the Built Environment,
University of the Witwatersrand, Johannesburg, in fulfilment of the requirements
for the degree of Master of Science in Engineering in the Control Research Group
School of Electrical and Information Engineering, Johannesburg, 2017In this research, we observed a torque-related limitation in the swing-up control
of underactuated mechanical systems which had been integrated with viscous
damping in the unactuated joint. The objective of this research project was thus to
develop a practical work-around solution to this limitation.
The nth order underactuated robotic system is represented in this research as a
collection of compounded pendulums with n-1 actuators placed at each joint with
the exception of the first joint. This system is referred to as the PAn-1 robot (Passive
first joint, followed by n-1 Active joints), with the Acrobot (PA1 robot) and the PAA
robot (or PA2 robot) being among the most well-known examples. A number of friction
models exist in literature, which include, and are not exclusive to, the Coulomb
and the Stribeck effect models, but the viscous damping model was selected for
this research since it is more extensively covered in existing literature. The effectiveness
of swing-up control using Lyapunovâs direct method when applied on the
undamped PAn-1 robot has been vigorously demonstrated in existing literature, but
there is no literature that discusses the swing-up control of viscously damped systems.
We show, however, that the application of satisfactory swing-up control using
Lyapunovâs direct method is constrained to underactuated systems that are either
undamped or actively damped (viscous damping integrated into the actuated joints
only). The violation of this constraint results in the derivation of a torque expression
that cannot be solved for (invertibility problem, for systems described by n > 2) or a
torque expression which contains a conditional singularity (singularity problem, for
systems with n = 2). This constraint is formally summarised as the matched damping
condition, and highlights a clear limitation in the Lyapunov-related swing-up control
of underactuated mechanical systems. This condition has significant implications
on the practical realisation of the swing-up control of underactuated mechanical
systems, which justifies the investigation into the possibility of a work-around. We
thus show that the limitation highlighted by the matched damping condition can be
overcome through the implementation of the partial feedback linearisation (PFL)
technique. Two key contributions are generated from this research as a result, which
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include the gain selection criterion (for Traditional Collocated PFL), and the convergence
algorithm (for noncollocated PFL).
The gain selection criterion is an analytical solution that is composed of a set of
inequalities that map out a geometric region of appropriate gains in the swing-up
gain space. Selecting a gain combination within this region will ensure that the
fully-pendent equilibrium point (FPEP) is unstable, which is a necessary condition
for swing-up control when the system is initialised near the FPEP. The convergence
algorithm is an experimental solution that, once executed, will provide information
about the distal pendulumâs angular initial condition that is required to swing-up a
robot with a particular angular initial condition for the proximal pendulum, along
with the minimum gain that is required to execute the swing-up control in this
particular configuration. Significant future contributions on this topic may result
from the inclusion of more complex friction models. Additionally, the degree of
actuation of the system may be reduced through the implementation of energy
storing components, such as torsional springs, at the joint.
In summary, we present two contributions in the form of the gain selection criterion
and the convergence algorithm which accommodate the circumnavigation of the
limitation formalised as the matched damping condition. This condition pertains to the
Lyapunov-related swing-up control of underactuated mechanical systems that have
been integrated with viscous damping in the unactuated joint.CK201
Brachiating power line inspection robot: controller design and implementation
The prevalence of electrical transmission networks has led to an increase in productivity and prosperity. In 2014, estimates showed that the global electric power transmission network consisted of 5.5 million circuit kilometres (Ckm) of high-voltage transmission lines with a combined capacity of 17 million mega-volt ampere. The vastness of the global transmission grid presents a significant problem for infrastructure maintenance. The high maintenance costs, coupled with challenging terrain, provide an opportunity for autonomous inspection robots. The Brachiating Power Line Inspection Robot (BPLIR) with wheels [73] is a transmission line inspection robot. The BPLIR is the focus of this research and this dissertation tackles the problem of state estimation, adaptive trajectory generation and robust control for the BPLIR. A kinematics-based Kalman Filter state estimator was designed and implemented to determine the full system state. Instrumentation used for measurement consisted of 2 Inertial Measurement Units (IMUs). The advantages of utilising IMUs is that they are less susceptible to drift, have no moving parts and are not prone to misalignment errors. The use of IMU's in the design meant that absolute angles (link angles measured with respect to earth) could be estimated, enabling the BPLIR to navigate inclined slopes. Quantitative Feedback Control theory was employed to address the issue of parameter uncertainty during operation. The operating environment of the BPLIR requires it to be robust to environmental factors such as wind disturbance and uncertainty in joint friction over time. The resulting robust control system was able to compensate for uncertain system parameters and reject disturbances in simulation. An online trajectory generator (OTG), inspired by Raibert-style reverse-time symmetry[10], fed into the control system to drive the end effector to the power line by employing brachiation. The OTG produced two trajectories; one of which was reverse time symmetrical and; another which minimised the perpendicular distance between the end gripper and the power line. Linear interpolation between the two trajectories ensured a smooth bump-less trajectory for the BPLIR to follow
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