Directional control of the motion of a rolling disk by using a rotor fixed in the disk's plane

This work deals with the stabilization and control of a system which is composed of a disk rolling on a plane, and a circular rotor plate fixed in the disk's plane. The disk's motion is controlled by the above-mentioned rotor, a “tillting moment” and a pedalling moment. It is shown here that by applying a kind of inverse dynamics control, the motion of the disk is stabilized about a given angle, while simultaneously controlling its speed and direction in such a manner that the point of contact between the disk and the horizontal plane will be able, during a given time interval [0, t_f], to move from a given point. r_A to a another given point r_B, both of them fixed in the plane.     

Tracking control of a rolling disk

The tracking control of a disk rolling without slipping on the horizontal (X, Y)-plane is considered. The motion of the disk can be controlled via a tilting torque and a pedaling torque. The concept of path controllability of the disk is introduced and then used to calculate control laws such that the disk tracks a given path in the (X, Y)-plane     

Control of the motion of a disk rolling on a plane curve

This work deals with the control of the motion of a disk rolling without slipping on a curve located in the horizontal plane. The disk’s motion is driven by a pedalling torque and by using two overhead rotors. In addition, the case where the disk rolls on a plane curve with its plane vertical to the (X,Y)-plane, is discussed.     

Modelling and control of the motion of a riderless bicycle rolling on a moving plane

This work deals with the modelling and control of a riderless bicycle rolling on a moving plane. It is assumed here that the bicycle is controlled by a pedalling torque, a directional torque and by a rotor mounted on the crossbar that generates a tilting torque.In particular, a kinematic model of the bicycle’s motion is derived by using its dynamic model. Then, using this kinematic model, the expressions for the applied torques are obtained.     

Stabilization of collective motion on a sphere

We provide a Lyapunov-based design of decentralized control laws that stabilize relative equilibria in a model of self-propelled particles that travel on the surface of a sphere. Such control laws have applications in planetary-scale mobile sensing networks in air, sea, and space. Relative equilibria of the closed-loop model include formations in which all of the particles travel around a common circular trajectory. Particle interaction can be time-invariant or time-varying and directed or undirected. The algorithm for time-invariant and undirected particle interaction uses a gradient-like control induced from the associated Laplacian matrix. The algorithm for time-varying and directed interaction replaces average quantities in the control law with dynamic consensus variables. An augmented Laplacian algorithm is also proposed to stabilize symmetric circular formations.     

Stabilization of oscillations by a nonnegative feedback control

The feedback stabilization of m-dimensional nonlinear systems is studied in this note. The Jacobian is assumed to possess 2q purely imaginary eigenvalues and m-2q eigenvalues with negative real parts. The feedback control law is assumed to be nonnegative and given by the square of a linear function. The direct and indirect control systems are investigated. In both cases stabilizability is proved and explicit formulas for the feedback functions are obtained. Lyapunov's direct method is employed     

Robust roll motion control of a vehicle using integrated control strategy

This paper presents an electrically actuated roll motion control of a vehicle using simulation and experimental analysis. The controller is designed with an H_∞ control scheme based on the 3 DOF vehicle model considering parameter variations, which affect the roll dynamics. To investigate the feasibility of the active roll control system, its performance is evaluated by simulation in a full vehicle model under various conditions. The Hil setup with the electrically actuated roll control system was devised and its performance was investigated through experimental works. Finally, to enhance the performance in a transient region, an integrated control strategy is presented.     

Stabilization of desired motion of a quadrotor helicopter

In this paper, a problem of constructing a control law for a quadrotor helicopter—a fourrotor helicopter is considered. The classical design of this vehicle contains a four-way frame, at which nodes electric motors with propellers rigidly mounted on their axles. An approach to solving the problem is proposed, based on application of the method of two-level control, according to which the required control is constructed in the form of the sum of a desired control and an additional feedback stabilizing the zero solution of the system of equations in deviations from the desired motion. The complete controllability of the nonstationary linear system in deviations is strictly proved. For constructing a stabilizing feedback, a known solution of the problem on linear controller with quadratic cost function is used. The proposed approach makes it possible to develop a general numerical method for constructing a control that provides a stable motion of the quadrotor helicopter along arbitrary smooth three-dimensional trajectories.     

Synchronization of the four identical unbalanced rotors in a vibrating system of plane motion

A new mechanism is proposed to implement the synchronization of the four unbalanced rotors in a vibrating system, which consists of a main rigid frame (MRF) and two accessorial rigid frames (ARF). An analytical approach is developed to study the coupling dynamic characteristics of the four unbalanced rotors, which converts the problem of synchronization of the four unbalanced rotors into the existence and the stability of zero solutions for the non-dimensional differential equations of the angular velocity ...     

Optimal motion control for a system of two bodies on a straight line

The optimal control problem for motions of a system of two rigid bodies on an inclined straight line in a plane that are periodic in velocity is solved. The external body (frame) moves on a plane under the action of a force from the inner body in the course of its motions relative to the frame under dry friction between the frame and plane. The acceleration of the inner body relative to the outer one is the control whose absolute value is bounded. An optimal control that maximizes the average velocity of the system motion for a given period is found. It is shown that optimal relative acceleration of the inner body has three intervals of constancy on this period, and the outer body is in the state of rest on a part of the period (in the case of horizontal straight line, it is in a state of rest on half a period), and during the rest of the period, it moves in the desired direction and never performs a reversion. It is established that, for the found control law and under an additional constraint on the amplitude of oscillations of the inner body, it is possible to make the motion velocity of the system arbitrarily large under arbitrarily large accelerations of the inner body and an under arbitrarily large frequency of its oscillations simultaneously.     

Stabilization of nonlinear systems with state and control constraints using Lyapunov-based predictive control

This work considers the problem of stabilization of nonlinear systems subject to state and control constraints, for cases where the state constraints need to be enforced at all times (hard constraints) and where they can be relaxed for some time (soft constraints). We propose a Lyapunov-based predictive control design that guarantees stabilization and state and input constraint satisfaction for all times from an explicitly characterized set of initial conditions. An auxiliary Lyapunov-based analytical bounded control design is used to characterize the stability region of the predictive controller and also provide a feasible initial guess to the optimization problem in the predictive controller formulation. For the case when the state constraints are soft, we propose a switched predictive control strategy that reduces the time during which state constraints are violated, driving the states into the state and input constraints feasibility region of the Lyapunov-based predictive controller. We demonstrate the application of the Lyapunov-based predictive controller designs through a chemical process example.     

Partial feedback linearization control of a three-dimensional overhead crane

Based on partial feedback linearization, an improved nonlinear controller is analyzed and designed for the three-dimensional motion of an overhead crane. Three control inputs composed of bridge moving, trolley travelling, and cargo hoisting forces are used to drive five state variables consisting of bridge motion, trolley movement, cargo hoisting displacement, and two cargo swing angles. The control scheme is constituted by linearly combining two components that are separately obtained from the nonlinear feedback of actuated and un-actuated states. To verify the quality of the control process, both numerical simulation and experimental study are carried out. The proposed controller asymptotically stabilizes all system states.     

Stabilization of a class of nonlinear systems by a smooth feedback control

We consider the stabilizability problem for systems of the form in the neighborhood of an equilibrium point of f(x). First, by means of center manifold theory, a lower order system is introduced. If this system is stabilizable, then so is the original system. Results on the stabilization of the low order system are presented. No resort is taken to Liapunov theory. The relation between stabilizability and controllability is discussed.     

Stabilization of a memristor-based chaotic system by intermittent control and fuzzy processing

This paper further investigates the problem of intermittent control of a memristor-based Chua’s oscillator and presents the oscillator as the T-S fuzzy model system. Based on Lyapunov stability theory, we design an intermittent controller to guarantee the stability of the chaotic system. Simulation results are presented to verify the effectiveness of the method.     

Modelling and motion control of a mechatronic system using BGM with intelligent controllers

In this research paper, a mechatronics system such as a pan tilt platform (PTP) has been considered for motion control under intelligent controllers. A proportional-derivative (PD) controller is considered for comparison of results obtained from fuzzy and hybrid controllers. The trajectory following performance of the mechatronics system is found against these controllers. The results of simulations show that hybrid fuzzy controller reduce the tracking error effectively in lesser settling time. The intelligent controllers require knowledge base of error and derivative of error to compensate the PTP dynamics. The intelligent controllers have similar trends as the PD controllers and compensated both electrical and mechanical dynamics. The PD controller requires position measurement. The intelligent controllers have knowledge base consisting of position and velocity data. Thus intelligent controllers have position measurement along with knowledge base for position control system. The best results were achieved with hybrid fuzzy controllers. They meet the desired specifications.     

Stabilization of unstable and unintuitive plants by fuzzy control

A heuristically derived stabilization strategy for an unstable and unintuitive plant by fuzzy control is described. It is shown that the often used classical fuzzy controller, which is both static and time invariant, is incapable of stabilizing such types of plants. However, a simple modification to the classical fuzzy controller architecture that separates the measurement and control phases, together with a hierarchical control strategy, enable the unstable and unintuitive plant to be stabilized. The fuzzy control strategy, as well as the new fuzzy controller architecture, are based on the consideration of "what a human subject would do when dealing with a physical plant which is both unstable and unintuitive". The stabilization strategy is then generalized to other mathematically similar systems. While the rules for the stabilization of the plant are heuristically defined, the membership functions associated with the rules are tuned by a simulated annealing procedure.     

Maneuvering control of a rolling four-links robot

This work deals with the maneuvering control of the planar motion of a rolling four-links robot as described in Figure 1. The system is composed of four links, two identical wheels, and a mass m_O attached to the joint O. The problem that is addressed is to develop control laws for the rolling four-links robot such that the mass m_O performs prescribed maneuvers in the vertical (X, Z)-plane.     

Position error reduction in magnetic disk drives using a head gimbal assembly with radial head motion capability

Reducing the head positioning error is important to achieve higher track density in hard disk drives. In this paper, it is shown that the head off-track due to disk vibration can be reduced by using a head gimbal assembly capable of moving not only vertically to disk surface but also radially across the track. We find the optimal geometric relationship to minimize the head off-track due to disk vibration. The relationship is obtained based on precise mathematical modeling of head off-track mechanism due to disk vibration. Some examples of head gimbal assembly (HGA) with radial head motion capability, which satisfy such optimal relationship, are also proposed. It is experimentally found that the proposed optimal HGA can reduce non-repeatable run-out (NRRO) position error signal (PES) significantly. Since it reduces NRRO PES during servo track writing as well, the written-in portion of repeatable run-out PES can be also significantly reduced.     

Stabilization of distributed parameter systems by piecewisepolynomial control

In this paper we consider the stabilization of continuous-time distributed parameter systems by piecewise polynomial controls. We obtain necessary and sufficient conditions for stabilization by piecewise polynomial controls     

The switching algorithm for the control of overhead crane

This paper presents the fuzzy logic based method to control the trolley cranes. The information, including the position of trolley, load swing and the differences between the present and previous signals, are applied to derive the proper power to drive the trolley. An easy but effective switching algorithm is investigated to improve the control of trolley and suppress the load swing in this paper. This also helps to enhance the control power of the crane to depart from the deadzone. Finally, several experiments through the scaled trolley crane demonstrate the effectiveness of the scheme.This work was supported by the National Science Council of the Republic of China under Grant NSC-91-2213-E-231-007.