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     

Track-following control of a dual-stage hard disk drive using a neuro-control system

This paper describes the track-following control of a dual-stage hard disk drive system using neural-networks. A neural-network approach to on-line learning control, and a real-time implementation for a dual-stage hard disk drive, are presented. The use of the dual-stage actuator in hard disk drive systems has become a means of achieving increased servo actuator bandwidth. The dual-stage actuator presented here uses a voice-coil motor (VCM) as a coarse actuator, and a piezoelectric actuator (PZT) as a fine actuator. The control system consists of a series combination of both a plant with a feedback loop and a neural-network with a feedforward loop. The neural-network functions as the reference input filter, and it organizes a new reference signal to the closed-loop circuit. Numerical and experimental results for the track-following control system of the dual-stage hard disk drive show the validity of the proposed neuro-control system.     

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 the planar vertical take-off and landing using nonlinear feedback control

This article presents a new control strategy for the well-known problem of the planar vertical take-off and landing. The total thrust is computed using a nonlinear feedback compensation so that the altitude reaches the desired altitude. The horizontal position x is then controlled by choosing the orientation angle as a smooth saturation function of x and . A proof of convergence is presented using a Lyapunov approach. The proposed control strategy is successfully tested in numerical simulations.     

A unified symplectic pseudospectral method for motion planning and tracking control of 3D underactuated overhead cranes

In this paper, a unified symplectic pseudospectral method for motion planning and tracking control of 3D underactuated overhead cranes is proposed. A feasible reference trajectory taking constraints into consideration is first generated offline by the symplectic pseudospectral optimal control method. Then, a trajectory tracking model predictive controller also based on the symplectic pseudospectral method is developed to track the reference trajectory. At each sampling instant, the trajectory tracking controller works by solving an open‐loop optimal control problem where linearized system dynamics is used instead to improve the computational efficiency. Since the symplectic pseudospectral optimal control method is the core algorithm for both offline trajectory planning and online trajectory tracking, constraints on state variables and control inputs can be easily imposed and hence theoretically guaranteed in solutions. By selecting proper weighted matrices on tracking error and control, the developed controller could achieve control objectives in both accurate trolley positioning and fast suppressing of residual swing angles. Simulations for 3D overhead crane systems in the presence of perturbations in initial conditions, an abrupt variation of system parameter, and various external disturbances demonstrate that the developed controller is robust and of excellent control performance.     

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.     

Velocity control of a cylindrical rolling robot by shape changing

A rolling robot is developed that possesses an elliptically shaped outer surface with the ability to change shape as it rolls, resulting in a gravity-powered torque imbalance that accelerates or brakes the robot’s motion. Angular position and velocity are measured onboard and used as feedback control to trigger and define shape change actuation. Goal of the control is to direct the robot to follow a given step angular velocity profile. An equation of motion for the rolling robot is derived and solved numerically, and simulations are compared to velocity data from roll trials of the actual robot. Results show that when the robot is given a set of advantageous initial conditions, it is able to accelerate from rest, maintain constant average velocity, and brake its motion in order to follow a desired velocity profile with significant accuracy.     

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.     

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.     

双轮共轴移动式倒立摆动力学建模与状态反馈控制

应用第一类拉格朗日方法对系统进行力学分析,建立了以电机转矩为输入且轮在轴向无滑移的非完整约束下系统的数学模型.双轮共轴移动式倒立摆的运动控制目标是移动式倒立摆在二维平面内按指定的方向和速度运动,同时保持摆杆平衡.利用状态反馈,构造闭环系统的状态方程,通过极点配置求得控制量.仿真结果验证了系统状态方程的正确性和控制方法的合理性.     

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.