Pendulums

Input shaping is a technique that seeks to reduce residual vibrations of lightly damped systems through modification of the command input to the system. Although several input shaping techniques have been derived primarily from linear system theory, theoretical results are hard to be traced for their application to nonlinear systems. In most of the reported cases, a fixed shaper is designed based on the linearized version around an operating point of the nonlinear system. In this paper, an adaptive form of the input shaper is proposed for a class of nonlinear lightly damped systems. The adaptive shaper adjusts the magnitude and relative time difference between its impulses according to the instant frequency and damping of the linearized systems. The efficacy of the proposed scheme and its comparison to a fixed shaper is investigated through its application to a pendulum system. The adaptive shaper’s parameters vary according to the pendulum’s angle. The illustrative examples indicat...

An improved version of the immersed boundary (IB) method is developed for simulating flexible filaments in a uniform flow. The proposed IB method is based on an efficient Navier–Stokes solver adopting the fractional step method and a staggered Cartesian grid system. The fluid ...

ABSTRACT This paper presents an evolutionary optimization based LQR controller design for an inverted pendulum system. The objective is to address the challenges of appropriate design parameters selection in LQR controller while providing optimal performance compromise between the system control objectives with respect to pendulum angle and position response. Hence, a Multiobjective differential evolution algorithm is proposed to design an LQR controller with optimal compromise between the conflicting control objectives. The performance of the MODEbased LQR is benchmarked with an existing controller from the system manufacturer (QANSER). The performance shows the effectiveness of the proposed design algorithm, and in addition provides an efficient solution to conventional trial and error design approach.

Abstract The main objective of this paper is to design a state feedback controller for stabilizing and tracking control of self-erecting inverted pendulum employing intelligent method using particle swarm optimization (PSO). This is motivated by the fact that one has to face trial and error approach in conventional feedback control design by pole placement method or linear quadratic regulator (LQR) method via Riccati equation. The simulation results show the effectiveness of the proposed method. The proposed state feedback ...

The paper presents a hybrid system controller, incorporating a neural and an LQG controller. The neural controller has been optimized by genetic algorithms directly on the inverted pendulum system. The failure free optimization process stipulated a relatively small region of the asymptotic stability of the neural controller, which is concentrated around the regulation point. The presented hybrid controller combines benefits of a genetically optimized neural controller and an LQG controller in a single system controller. High quality of the regulation process is achieved through utilization of the neural controller, while stability of the system during transient processes and a wide range of operation are assured through application of the LQG controller. The hybrid controller has been validated by applying it to a simulation model of an inherently unstable system of inverted pendulum.

Scaling laws provide a simple yet meaningful representation of the dominant factors of complex engineering systems, and thus are well suited to guide engineering design. Current methods to obtain useful models of complex engineering systems are typically ad-hoc, tedious, and time consuming. Here we present an algorithm that obtains a scaling law in the form of a power law from

- In this paper, we present two approaches for the control of an inverted pendulum on a cart. First, we use a combination of a neural network and a simple algorithm, where the neural network is responsible for ranking the current states while the algorithm decides the ...

This paper presents a finite element model of the elastica, without dissipation, in a form realizable in the laboratory: a set of rigid links connected by torsion springs. The model is shown to reproduce the linear elastic behavior of beams. The linear beam, and most nonlinear beams are not periodic. (The linear eigenfrequencies are incommensurate.) They do exhibit a basic cyclic behavior, the beam waving back and forth with a measurable period. Extensive exploration of the behavior of a fourlink model reveals windows of periodicity—isolated points in parameter space where the motion is nearly periodic. (The basic phase plane diagrams are asymmetric, and the time evolution of the motion distributes this asymmetry symmetrically in time.) The first such window shows a period twice the basic cycle time, the next, less well observed one, four times the basic cycle time.

In this paper we present a variable structure system representation, in a fuzzy point of view. This approach is shown in a system of two synchronized pendulums in master/slave scheme. The synchronization objective is to match the slave movements to those of the master. A fuzzy model is developed by a Takagi-Sugeno representation of nonlinear systems, from which the difference between the master and slave positions are represented by local linear input-output relations by fuzzy IF-THEN rules. Thus, a variable structure is originated since each fuzzy rules express a structure and an operation condition. The performance of the fuzzy variable structure proposed is illustrated numerically.

Swing-up of a rotating type pendulum from the pendant to the inverted state is known to be one of most difficult control problems, since the system is nonlinear, underactuated, and has uncontrollable states. This paper studies a time optimal swing-up control of the pendulum using bounded input. Time optimal control of a nonlinear system can be formulated by Pontryagin’s Maximum Principle, which is, however, hard to compute practically. In this paper, a new computational approach is presented to attain a numerical solution of the time optimal swing-up problem. Time optimal control problem is described as minimization of the achievable time to attain the terminal state under the bounded input amplitude, although algorithms to solve this problem are known to be complicated. Therefore, in this paper, it is shown how the optimal time swing-up control is formulated as an auxiliary problem in that the minimal input amplitude is searched so that the terminal state satisfies a specification ...

The drawbacks of using FSMC when controlling the position motion on a non linear inverted pendulum system are the chattering problem and the robustness against parameter uncertainty and disturbances. This paper consider about the implementation of Fuzzy Type 2 in combining with SMC (T2FSMC) to enhance the ability of FSMC to overcome both of those problems. To be more optimally damp the oscillation, the range of fuzzy membership is determined based on the minimum ITAE (integral of time absolute error) value while the rule is constructed based on the product between the sliding surfaces and its derivatives. To enhance robustness performance against disturbances and parameter uncertainties, the range of non crisp membership value (footprint uncertainty) of Fuzzy Type 2 is determined by considering the minimum sum of ITAE values at several conditions with different plant parameter. It is proved from the simulation that the proposed method can solve chattering problem more effectively an...

In some practical control problems of essentially continuous systems, the goal is not to tightly track a trajectory in state space, but only some aspects of the state at various points along the trajectory, and possibly only loosely. Here, we show examples in which classical discrete-control approaches can provide simple, low input-, and low output- bandwidth control of such systems. The sensing occurs at discrete state- or time-based events. Based on the state at the event, we set a small set of control parameters. These parameters prescribe features, e.g., amplitudes of open-loop commands that, assuming perfect modeling, force the system to, or toward, goal points in the trajectory. Using this discrete decision continuous actuation (DDCA) control approach, we demonstrate stabilization of two examples: (1) linear “dead-beat” control of a time delayed linearized inverted pendulum and (2) pumping of a hanging pendulum. Advantages of this approach include: It is computationally cheap ...

This paper presents a finite element model of the elastica, without dissipation, in a form realizable in the laboratory: a set of rigid links connected by torsion springs. The model is shown to reproduce the linear elastic behavior of beams. The linear beam, and most nonlinear beams are not periodic. (The linear eigenfrequencies are incommensurate.) They do exhibit a basic cyclic behavior, the beam waving back and forth with a measurable period. Extensive exploration of the behavior of a fourlink model reveals windows of periodicity—isolated points in parameter space where the motion is nearly periodic. (The basic phase plane diagrams are asymmetric, and the time evolution of the motion distributes this asymmetry symmetrically in time.) The first such window shows a period twice the basic cycle time, the next, less well observed one, four times the basic cycle time.

... wgr@aquarium.ia.agh.edu.pl, kko@aquarium.ia.agh.edu.pl, atu@aquarium.ia.agh.edu.pl ... VME bus holding Intel processor and real-time operating system, [11]), • Digital Signal Processor (DSP) based controllers (eg dSpace technology, [12]), • Personal computer (PC) holding a ...

In this paper, we consider the problem of real-time control of an Inverted Pendulum. We design and implement four different control algorithms, namely PID, Pole placement, LQR and Fuzzy Logic. These controllers are applied to the Inverted Pendulum in real-time and their performance is compared on the basis of Pendulum regulation, disturbance rejection and control energy specifications. We also provide a performance comparison based on the ISE index.

ABSTRACT This paper addresses development of body mapping from a human demonstrator to an inverted-pendulum mobile robot for imitation. An inverted-pendulum mobile robot with torso and body links learns a dynamic kicking motion shown by a human. The robot observes the human demonstration with a camera, extracts the human region in each of images, maps the region to its own two links, estimates the link posture trajectories, and starts kicking motion learning based on the trajectory parameters for imitation. The mapping parameter gives an important role for successive imitation. A reasonable and feasible procedure of learning from observation for an inverted-pendulum robot and development of the body mapping is proposed and investigated in this paper.

-This paper describes a robust controller design procedure based on H control theory for translational mechatronic system, trolley with pendulum. The goal is to achieve fast trolley positioning with minimization of pendulum swinging. This system, trolley with pendulum, represents gantry crane. Minimization of the load transfer time and load swing angle in the crane applications are conflicting control demands and thus proper control action is required. However, friction effect is unavoidable in mechanical parts of the system and significantly influences the control system performances. In this paper H theory based crane controller is designed in order to minimize friction effect. H controller has been tested and compared with the pole placement controller on a laboratory gantry crane model. Ǥ In modern industrial system, gantry cranes are widely used for the heavy loads transfer [1] For the anti-sway control of traveling cranes, there are several solutions, i.e., by fuzzy control, o...

This paper presents investigations into the development of hybrid control schemes for sway suppression and rotational angle tracking of a rotary crane system. A lab-scaled rotary crane is considered and the dynamic model of the system is derived using the Euler-lagrange formulation. To study the effectiveness of the controllers, initially a collocated proportional-derivative (PD) controller is developed for control of rotary motion. This is then extended to incorporate a non-collocated PID controller for control of sway angle of the ...

ABSTRACT In this document, a two-wheeled auto-balancing vehicle prototype is described, the upright balancing control of this inverted-pendulum-type vehicle is tackled by a classical control scheme in real time. Even though the system is nonlinear, unstable and under-actuated which implies a difficult control problem, a classical PID strategy together with a dead-zone and an anti windup compensation is used to get acceptable results. The upright balancing is the most fundamental control for the two-wheeled inverted pendulum because no other control is possible without stable upright balancing. This document shows the electromechanical prototype structure and its controller for keeping the upright equilibrium.

We consider the problem of creating oscillations of the Furata pendulum around the open-loop unstable equilibrium. Following a proposed technique, we start with shaping the energy of the unactuated link. An dissipativity-based controller is designed to create oscillations, neglecting possibility of unbounded motion of the directly actuated link. After that, an auxiliary linear feedback action is added to the control law, stabilizing a desired level of the reshaped energy. Parameters of the controller are tuned to approximately keep the originally created oscillations but ensuring bounded motion of both links. The analysis is valid only for oscillations of sufficiently high frequency and is based on higher order averaging technique. Performance of the designed controller is verified using numerical simulations and experiments.