Forward and backward motion control of wheelchair on two wheels

The challenge in designing wheelchair on two wheels involves the design and implementation of suitable control strategies for a two wheeled wheelchair to perform comparably similar to a normal four wheeled wheelchair. It is important to note that a wheelchair on two wheels is expected not to take much space during mobility as compared to when it is on four wheels. Moreover, disabled people are encouraged and expected to perform most activities that others can do and hence lead an independent life. Thus, wheelchairs on two wheels are needed for disabled persons to perform some of the essential tasks in their living and work environments. In this research a model of the standard wheelchair is developed as a test and verification platform using Visual Nastran software. Novel fuzzy logic control strategies are designed for lifting up the chair transforming a four-wheeled wheelchair to a two-wheeled wheelchair) and maintaining stability and balance while on two wheels. Furthermore, position control for forward and backward mobility of the wheelchair on two wheels is developed using fuzzy logic control. Simulation results of the proposed control strategy are presented and discussed

Second order sliding mode control of underactuated Mechanical systems I: Local stabilization with application to an inverted pendulum

International audienceSecond order sliding mode control synthesis is developed for underactuated mechanical systems, operating under uncertainty conditions. In order to locally stabilize an underactuated system around an unstable equilibrium, an output is specified in such a way that the corresponding zero dynamics is locally asymptotically stable. Then, the desired stability property of the closed-loop system is provided by applying a quasihomogeneous second order sliding mode controller, driving the system to the zero dynamics manifold in finite time. Although the present synthesis exhibits an infinite number of switches on a finite time interval, it does not rely on the generation of first order sliding modes, while providing robustness features similar to those possessed by their standard sliding mode counterparts. A second order sliding mode appears on the zero dynamics manifold which is of co-dimension greater than the control space dimension. Performance issues of the proposed synthesis are illustrated in numerical and experimental studies of a cart-Pendulum system

Control of a Bicycle Using Virtual Holonomic Constraints

The paper studies the problem of making Getz's bicycle model traverse a strictly convex Jordan curve with bounded roll angle and bounded speed. The approach to solving this problem is based on the virtual holonomic constraint (VHC) method. Specifically, a VHC is enforced making the roll angle of the bicycle become a function of the bicycle's position along the curve. It is shown that the VHC can be automatically generated as a periodic solution of a scalar periodic differential equation, which we call virtual constraint generator. Finally, it is shown that if the curve is sufficiently long as compared to the height of the bicycle's centre of mass and its wheel base, then the enforcement of a suitable VHC makes the bicycle traverse the curve with a steady-state speed profile which is periodic and independent of initial conditions. An outcome of this work is a proof that the constrained dynamics of a Lagrangian control system subject to a VHC are generally not Lagrangian.Comment: 18 pages, 8 figure

Bond graph based control and substructuring

A bond graph framework giving a unified treatment of both physical-model based control and hybrid experimental–numerical simulation (also known as real-time dynamic substructuring) is presented. The framework consists of two subsystems, one physical and one numerical, connected by a transfer system representing non-ideal actuators and sensors. Within this context, a two-stage design procedure is proposed: firstly, design and/or analysis of the numerical and physical subsystem interconnection as if the transfer system were not present; and secondly removal of as much as possible of the transfer system dynamics while having regard for the stability margins established in the first stage. The approach allows the use of engineering insight backed up by well-established control theory; a number of possibilities for each stage are given. The approach is illustrated using two laboratory systems: an experimental mass-spring-damper substructured system and swing up and hold control of an inverted pendulum. Experimental results are provided in the latter case

Robust nonlinear controller based on set propagation

Bibliography: leaves 74-[76.]A novel control method, based on interval analysis, that optimises the control surface (or u-surface) for sampled systems with output disturbances is demonstrated on a driven pendulum with actuator constraints. The fitness function to be maximized is the probability of each state of the system being controlled to the setpoint without being perturbed to regions that are more iterations away from the setpoint. The u-surface is designed by finding all the states that could go to the setpoint in an interval and optimising these states. This process is repeated (backwards in time) by optimising states that go to the previously optimised states until no more states that have not been optimised are found. The proposed control method has been applied to the problem of swinging up a driven pendulum from rest to the inverted position with constraints on the torque of the motor. This method is computationally intensive and time constraints limit its current application to systems of low order

On global properties of passivity-based control of an inverted pendulum,”

SUMMARY The paper adresses the problem of stabilization of a speci"c target position of underactuated Lagrangian or Hamiltonian systems. We propose to solve the problem in two steps: "rst to stabilize a set with the target position being a limit point for all trajectories originating in this set and then to switch to a locally stabilizing controller. We illustrate this approach by the well-known example of inverted pendulum on a cart. Particularly, we design a controller which makes the upright position of the pendulum and zero displacement of the cart a limit point for almost all trajectories. We derive a family of static feedbacks such that any solution of the closed loop system except for those originating on some two-dimensional manifold approaches an arbitrarily small neighbourhood of the target position. The proposed technique is based on the passivity properties of the inverted pendulum. A possible extension to a more general class of underactuated mechanical systems is discussed

Analysis and synthesis of SISO H[subscript infinity] controllers

Classical feedback control theories are traditionally concerned with issues like stability and performance, however, they typically fail to address issues such as robustness and plant perturbation. This thesis is concerned with the robust stability and the robust performance of single-input single-output plants. The basic issue under analysis is how to realize the benefits of the usual feedback control structure in the presence of model uncertainty. This is accomplished by seeking feedback controllers providing robust stability and performance by minimizing weighted sensitivity functions of a linear system represented by its transfer function. A characterization of models for plants with unstructured uncertainty is introduced. Specifications and measures of stability and performance for robust controllers and the necessary and sufficient conditions to test the robust stability and the robust performance conditions of a control design are explored. A parametrization of feedback controllers that guarantee closed loop stability for both stable and unstable plants is shown and a systematic procedure for synthesizing robust controllers, known in the literature as HK controllers, is presented. These systematic algorithms are based on the theory of interpolation by analytic functions and the solution to the model matching problem. A case study of the inverted pendulum positioning system is developed to illustrate the concepts of robust analysis and the design algorithms. The controller is compared to a classic state variable feedback solution