Robust stabilization of the wave equation against small delays

In this paper we consider a system which can be modeled by (undamped) wave equation in a bounded domain. We assume that the system is fixed at one end and is controlled by a boundary controller at the other end. We also considered two damped versions of this system, both parameterized by a nonnegative damping constant. We study two problems for these models, namely the stabilization by means of a boundary controller, and the stability robustness of the closed-loop system against small time delays in the feedback loop. We propose a class of finite dimensional dynamic boundary controllers to solve these problems. One basic feature of these controllers is that the corresponding controller transfer functions are required to be strictly positive real functions. We show that these controllers stabilize both damped and undamped models and solve the stability robustness problem for the damped models. It is also shown that while strict positive realness of the controller transfer functions is important for closed-loop stability, the strict properness is important for the stability robustness against small time delays in the feedback loop

Stabilization and disturbance rejection for the wave equation

We consider a system described by the one dimensional linear wave equation in a bounded domain with appropriate boundary conditions. To stabilize the system, we propose a dynamic boundary controller applied at the free end of the system. We also consider the case where the output of the controller is corrupted by a disturbance and show that it may be possible to attenuate the effect of the disturbance at the output if we choose the controller transfer function appropriately

Orientation and control of a flexible spacecraft: Planar motion

We consider a flexible spacecraft modeled as a rigid body which rotates in an inertial frame; a light flexible beam is clamped to the rigid body at one end and free at the other end. We assume that the flexible spacecraft performs only planar motions. We pose two control problems; namely, the orientation and the stabilization of the system. It is shown that suitable boundary controls applied to the free end of the beam and suitable control torques applied to the rigid body solve the problems posed above

Extending The Lossy Spring-Loaded Inverted Pendulum Model with a Slider-Crank Mechanism

Spring Loaded Inverted Pendulum (SLIP) model has a long history in describing running behavior in animals and humans as well as has been used as a design basis for robots capable of dynamic locomotion. Anchoring the SLIP for lossy physical systems resulted in newer models which are extended versions of original SLIP with viscous damping in the leg. However, such lossy models require an additional mechanism for pumping energy to the system to control the locomotion and to reach a limit-cycle. Some studies solved this problem by adding an actively controllable torque actuation at the hip joint and this actuation has been successively used in many robotic platforms, such as the popular RHex robot. However, hip torque actuation produces forces on the COM dominantly at forward direction with respect to ground, making height control challenging especially at slow speeds. The situation becomes more severe when the horizontal speed of the robot reaches zero, i.e. steady hoping without moving in horizontal direction, and the system reaches to singularity in which vertical degrees of freedom is completely lost. To this end, we propose an extension of the lossy SLIP model with a slider-crank mechanism, SLIP- SCM, that can generate a stable limit-cycle when the body is constrained to vertical direction. We propose an approximate analytical solution to the nonlinear system dynamics of SLIP- SCM model to characterize its behavior during the locomotion. Finally, we perform a fixed-point stability analysis on SLIP-SCM model using our approximate analytical solution and show that proposed model exhibits stable behavior in our range of interest.Comment: To appear in The 17th International Conference on Advanced Robotic

Communication scheme by using synchronized chaotic systems

A method to synchronize systems with chaotic behavior, in a master-slave configuration adapted to communication systems, is discussed. This work is motivated by the need for secure communication. In this method, the synchronization and message transmission phases are separated, and while the synchronization is achieved in the synchronization phases, the message is only sent in the message transmission phases

Discrete-time LQ optimal repetitive control

LQ optimal repetitive control is developed in single-input single-output discrete-time signal/system framework. For a given plant and a stabilizing controller, the LQ optimal repetitive control system can be obtained by the addition of a plug-in unit to the existing control system. The overall behaviour (stochastic behaviour, stability robustness etc.) of the new system can be improved by the appropriate choice/tuning of the design parameters

LQ optimal design at finitely many frequencies

The notion of Linear Quadratic (LQ) optimality at a single frequency is developed in single-input single-output (SISO) linear time-invariant (LTI) system/quasi-stationary signal framework and the optimality condition is given. LQ optimal design at finitely many frequencies is then shown to be reducible to an interpolation problem

RC realization of Chua's circuit family

In this brief, we consider a Wien bridge-based resistance-capacitance (RC) chaotic oscillator. We show that this circuit realizes the well-known Chua's oscillator under some conditions. We also show that this circuit is linearly conjugate, hence equivalent, to a large class of three-dimensional (3-D) systems when the parameters are appropriately chosen. We also present some experimental results

Stability of a Compass Gait Walking Model with Series Elastic Ankle Actuation

Passive dynamic walkers exhibit stable human-like walking on inclined planes. The simplest model of this behavior is the well known passive compass gait (PCG) model, which consists of a point mass at the hip and two stick legs. Due to their passive nature, these systems rely on a sloped ground to recover energy lost to ground collisions. A variety of methods have been proposed to eliminate this requirement by using different actuation methods. In this study, we propose a simple model to investigate how series elastic actuation at the ankle can be used to achieve stable walking on level ground. The structure we propose is designed to behave in a similar fashion to how humans utilize toe push-off prior to leg liftoff, and is intended to be used for controlling the ankle joint in a lower-body robotic orthosis. We present the derivation of the hybrid equations of motion for this model, resulting in a numerically computed return map for a single stride. We then numerically identify fixed points of this system and investigate their stability. We show that asymptotically stable walking on flat ground is possible with this model and identify the dependence of limit cycles and their stability on system parameters

Stability and control of planar compass gait walking with series-elastic ankle actuation

Passive dynamic walking models are capable of capturing basic properties of walking behaviours and can generate stable human-like walking without any actuation on inclined surfaces. The passive compass gait model is among the simplest of such models, consisting of a planar point mass and two stick legs. A number of different actuation methods have been proposed both for this model and its more complex extensions to eliminate the need for a sloped ground, balancing collision losses using gravitational potential energy. In this study, we introduce and investigate an extended model with series-elastic actuation at the ankle towards a similar goal, realizing stable walking on level ground. Our model seeks to capture the basic structure of how humans utilize toe push-off prior to leg liftoff, and is intended to eventually be used for controlling the ankle joint in a lower-body robotic orthosis. We derive hybrid equations of motion for this model, and show numerically through Poincare analysis that it can achieve asymptotically stable walking on level ground for certain choices of system parameters. We then study the bifurcation regimes of period doubling with this model, leading up to chaotic walking patterns. Finally, we show that feedback control on the initial extension of the series ankle spring can be used to improve and extend system stability