Neural Networks Application for the Data of LQG Regulator for the Flexible Joint Robot

Abstract: This paper studied the problems of trajectory tracking and vibration suppression of the end for single-linked flexible arm. The dynamic model of the flexible manipulator is established by the Lagrange method and assumed mode method, and then, we decomposed the model into a double time scale model, which is fast and slow based on singular perturbation theory. We design the controller for the two models separately. As to the slow time scale model, we created a controller with adaptive robust sliding mode, and for the fast one, we designed a controller based on Linear- Quadratic Form (which is LQR). By improving particle swarm optimization, the weight matrix Q in the LQR was optimized independently. Combining the control rate of the fast and the slow, tracked the flexible arm’s trajectory and suppressed its terminal vibration at the same time. The simulating results show that the proposed method greatly improves the trajectory tracking accuracy of flexible manipulator, and reduces the end vibration effectively. Background: Since flexible robotic arms generate free vibration during operation due to the special characteristics of the material, vibration suppression and control are the primary problems in this field. objective: The research objective of this paper is to design an improved controller for a single link flexible robotic arm system that utilises a new control method to achieve more accurate tracking accuracy and less end vibration during the movement of the robotic arm. Objective: The research objective of this paper is to design an improved controller for a single-link flexible robotic arm system that utilizes a new control method to achieve more accurate tracking accuracy and less end vibration during the movement of the robotic arm. Methods: An adaptive robust sliding mode controller is designed for the slow time scale model, a linear quadratic (LQR) controller is designed for the fast time scale model, and the weight matrix Q in the LQR is autonomously optimised by an improved particle swarm algorithm, which combines the control rates of the two to control the trajectory tracking of the flexible robotic arm while suppressing the end vibration. Results: Experimental and comparative studies show that the method proposed in this paper substantially improves the trajectory tracking accuracy of the flexible robotic arm and reduces the end vibration to a large extent with obvious advantages, which verifies the reasonableness of the improved controller. Conclusion: The method proposed in this paper has more prominent advantages in trajectory tracking of flexible robotic arms, which is reflected in its smaller trajectory tracking error and relatively shorter time to track the target curve. At the same time, the search speed and convergence accuracy of the optimal value are improved to make the end vibration smaller, which largely reduces the end vibration of the flexible robotic arm and reduces the mechanical fatigue damage of the flexible robotic arm, which is of great significance for the research and development in this field.

Conventional robot manipulators have singularities in their workspaces and constrained spatial movements. Flexible and soft robots provide a unique solution to overcome this limitation. Flexible robot arms have biologically inspired characteristics as flexible limbs and redundant degrees of freedom. From these special characteristics, flexible manipulators are able to develop abilities such as bend, stretch and adjusting stiffness to traverse a complex maze. Many researchers are working to improve capabilities of flexible arms by improving the number of degrees of freedoms and their methodologies. The proposed flexible robot arm is composed of multiple sections and each section contains three similar segments and a base segment. These segments act as the backbone of the basic structure and each section can be controlled by changing the length of three control wires. These control wires pass through each segment and are held in place by springs. This design provides each segment with 2 DOF. The proposed system single section can be bent 90° with respective to its centre axis. Kinematics of the flexible robot is derived with respect to the base segment.

This paper presents the design of a Linear Quadratic Gaussian (LQG) regulator for the frequency control of a multi-area power system in a restructured competitive electricity market environment. A general model of the LQG regulator has been developed for multi-area system (with hydro and thermal generators) having Poolco and bilateral transactions. To account for the modeling uncertainties and non-measurable states, a Kalman filter has been designed to estimate the state variables. The controller uses these estimates, optimizes a given performance index, and reschedules the generators’ outputs according to their bids for the frequency regulation. The functioning of the proposed LQG regulator has been demonstrated on a four area test system and the results have been compared with those obtained by using an optimal PID controller.

The purpose of this study is to control simultaneously, motion and vibration of flexible 2-link robot arms. For this purpose, we had used modeling method called an 'extended reduced-order physical model (extended model)' to make a model of one-link flexible robot arm. The model of the flexible 2-link robot arms is made of a combination of the model of each link that is regarded as one link flexible robot arm. To connect each link, the constraint addition method is used. This is creating method of an equation of motion in multi-body systems. It is verified that the results of the simulation are effective for control of flexible 2-link robot arms.

The purpose of this work is designing a Linear Quadratic Gaussian (LQG) regulator and a Linear Quadratic Integral (LQI) controller for a fixed-wing aircraft. The LQG regulator design is created in two steps. First, an Unscented Kalman Filter (UKF) is selected as an observer for system dynamics to procreate an overall best estimate of system states. Second, an optimal feedback gain is calculated via the Linear Quadratic Regulator (LQR) approach. An LQI controller is designed for robust tracking of referenced outputs which are airspeed, sideslip, pitch angle and roll angle. The proposed LQG/LQI scheme is implemented in the MATLAB, Simulink environment. The simulation results show that the implemented system regulates and controls the system successfully in a noisy environment.

A linear quadratic Gaussian (LQG) strategy controls a two-link flexible robot manipulator tracking a two-dimensional square trajectory 12.6 m/spl times/12.6 m. Slew angles together with a Gaussian white process and white or non-white measurement noise are fed into a LQG regulator (Kalman filter). A FLC strategy incorporates two fuzzy controllers substituted for the LQR state-space dynamics equations. Trajectories were obtained for the LQG strategy with Gaussian white and non-white measurement noise. The trajectory obtained for white measurement noise closely approaches a perfect square while those obtained for non-white measurement noise deviate. The trajectory obtained with the FLC strategy is similar to that for LQG with white measurement noise. Fuzzy control is found to provide robustness in operation and can be constructed with less mathematical complexity than LQG. The deviation in trajectories for LQG with non-white measurement noise suggests sub-optimal control and possible instability. This study has demonstrated the extent of deviation in tracking with an LQG strategy for non-white measurement noise and the FLC strategy as a viable option for precise and robust tracking control of a two-link flexible robot manipulator.

In the paper a linear quadratic Gaussian (LQG) dynamic regulator is applied with an extended Kalman filter (EKF), a LQG with fuzzy logic adaptive EKF (FLAEKF), LQG with an EKF and a FLAEKF combined with time delays in the feedback loop for modeling non-minimum phase (NMP) response for control of the end effector with non-collocated sensor and in the feed-forward loop for corrective control of a two-link flexible robot in the tracking of square trajectory task. The system is compared in simulations with a fuzzy logic system (FLS) vibration suppression control system. Results show that FLS adaptive vibration suppression yields higher tracking precision than FLAEKF, EKF or corrective time delays. It is also more effective while maintaining tracking accuracy and reasonable time efficiency than the classical PID controller or advanced adaptive controllers. Recursive nonparametric identification procedure for nonlinear friction in the joints of flexible robot is introduced. Its asymptotic properties are investigated.

Structural flexibility in robotic systems has been emerging as an issue of increasing concern, for it is only realistic to include the vibration of such a system in the design of control to secure a certain degree of accuracy. The demands for high speed and low cost are driving the research for control of lightweight flexible robots. In this paper, we first formulate a mathematical model for flexible robot arms. This model describes a one-dimensional vibrating robot arm with a moving base. In general, a Cartesian robot consists of components which are flexible robot arms. There have been many investigations of the subject. Amongst them we list a few, such as works of Cannon and Schmitz [1] in 1984 and more recent work of Z.H. Luo, etc. [6,7,8]. Many of these works approach the subject from the design points of view. They have specific “goal items” to be controlled and designed controls accordingly. Our approach is more theoretical and general. First, we take a fourth order partial differential equation, the beam equation, to model the dynamics of the Cartesian flexible robot arm with several boundary conditions. Then, we consider a corresponding state-space control system in which the parameter matrix has its entries differential operators. In this setting we are able to determine the spectrum of the parameter matrix (see Section 2), and subsequently show that the system is both controllable and observable (see Section 3). In this infinite dimensional control analysis, one needs a heavy dose of functional analysis and operator theory in order to investigate the controllability and observability. This work has laid down a foundation for the design of a real-time closed loop feedback control for a flexible Cartesian robot. It is becoming more urgent that the traditional design of robot arms dependent on only the kinematics needs a makeover to include the dynamics of the system into the control. Our work fits nicely in this thrust of research which is becoming the focus of the research of dynamical robotics. The results of this article are taken from [4]. Further work is presently being pursued.

The development of models and approaches for controlling the spreading dynamics of epileptic seizures is an essential step towards new therapies for people with pharmacologically resistant epilepsy. Beyond resective neurosurgery, in which epileptogenic zones (EZs) are the target of surgery, closed-loop control based on intracranial electrical stimulation, applied at the very early stage of seizure evolution, has been the main alternative, e.g. the RNS system from NeuroPace (Mountain View, CA). In this approach the electrical stimulation is delivered to target brain areas after detection of seizure initiation in the EZ. Here, we examined, on model simulations, some of the closed-loop control aspects of the problem. Seizure dynamics and spread are typically modeled with highly nonlinear dynamics on complex brain networks. Despite the nonlinearity and complexity, currently available optimal feedback control approaches are mostly based on linear approximations. Alternative machine learning control approaches might require amounts of data beyond what is commonly available in the intended application. We thus examined how standard linear feedback control approaches perform when applied to nonlinear models of neural dynamics of seizure generation and spread. In particular, we considered patient-specific epileptor network models for seizure onset and spread. The models incorporate network connectivity derived from (diffusion MRI) white-matter tractography, have been shown to capture the qualitative dynamics of epileptic seizures and can be fit to patient data. For control, we considered simple linear quadratic Gaussian (LQG) regulators. The LQG control was based on a discrete-time state-space model derived from the linearization of the patient-specific epileptor network model around a stable fixed point in the regime of preictal dynamics. We show in simulations that LQG regulators acting on the EZ node during the initial seizure period tend to be unstable. The LQG solution for the control law in this case leads to global feedback to the EZ-node actuator. However, if the LQG solution is constrained to depend on only local feedback originating from the EZ node itself, the controller is stable. In this case, we demonstrate that localized LQG can easily terminate the seizure at the early stage and prevent spread. In the context of optimal feedback control based on linear approximations, our results point to the need for investigating in more detail feedback localization and additional relevant control targets beyond epileptogenic zones.

This paper discusses the open loop control problem of a flexible joint robot that is oriented in the vertical plane. This orientation of the robot arm introduces gravity constraints and imposes undesirable nonlinear behavior. Friction is also added at the joints to increase the accuracy of the model. Including these dynamics to the robot arm amplifies the open loop control problem. Differential flatness is used to propose a feed-forward control that compensates for these nonlinearities and is able to smoothly steer the robot from rest to rest positions. The proposed control is achieved without solving any differential equations which makes the approach computationally attractive. Simulations show the effectiveness of the open loop control design on a single link flexible joint robot arm.

This paper “describes” the investigation of the stability of a single Degree of Freedom (DOF) flexible robotic arm by the diagrams shown below. The derived model is based on Euler- Lagrange approach. Exploration of a flexible robotic arm with using state-of-the-art controllers is essential for intelligent applications. These robot arms have joints that work independently of each other in order to create a smooth connection between joints. They still ensures the natural properties like a real human arm. The use of polarity assignment method “helps” the system to achieve desired output signals which has not been thoroughtly studied before for this system. The author can also compare the effectiveness of control methods for this system to find the most effective method for control strategies. In particular, ANN ( artificial neural network) is the most modern technique currently applied to this system to investigate the security and stability of the system through this program. This is new and it has never been used before for a system of this type. Neural networks strategy has been implemented in this paper as an application of artificial intelligence. It has successfully performed a mission in re-simulating functions of another control method: Polarity assignment method. Simulation results are done by Matlab.

A linear model of a one-link flexible robot arm is only an approximation to the real system, whose parameters are subject to change due to working conditions. The paper presents a simple experiment to demonstrate the necessity of robust control to industrial robots. Two control techniques, linear quadratic Gaussian (LQG) and loop shaping, are used to design controllers for our laboratory flexible robot arm. The LQG controller yields an optimal closed-loop performance for the nominal system, but when plant parameters are perturbed, the performance significantly degrades. On the other hand, under the same perturbations, a loop shaping controller can robustly maintain the system stability and result in an acceptable performance. The agreement between simulation results and experimental results provides an initial step to our laboratory setup which is presently planned for the introduction of a robust control class.

This paper discusses the practical implementation of a flatness based control for a flexible joint robot arm. Using differential flatness theory, reference trajectories are generated for a flexible joint robot and then a tracking controller is implemented. The vibrations experienced by the robot arm are sufficiently damped and nonminimum phase behaviour is eliminated. The control shows fast transcient response as desired for flexible robots. Experimental results proves the effectiveness of the flatness based control approach.

Magnetic bearings provide an energy-saving and resource-sparing possibility for supporting rotors running at high speed. This paper studies the potential of reducing the energy demand of magnetic levitation systems. Practical investigations show that this is obtainable by combining an optimal state estimator with an optimal state space controller. This configuration is known as Linear Quadratic Gaussian (LQG) regulator. In a sequential way, all the steps required for implementing this control strategy are depicted, starting with describing and modelling of the system which is a fully magnetically levitated blower in this case. Subsequently, the realization of the system state estimator is delineated. Both hints for carrying out the discretization of the continuous time model and a simple approach for choosing the variance matrices of the estimator are given. Special attention is paid to the design of the state feedback controller. The influence of the weighting matrix elements on the controller performance is investigated as well as an integrative extension of the regulator which ensures good reference response behaviour. Finally, measurements concerning the energy consumption of the levitation system are presented. The results show that both in static and dynamic case the implementation of the LQG regulator yields reduced control energy effort, compared to a system controlled by a conventional PID controller. It is noteworthy that, simultaneously to the enhancement of energy efficiency, implementing the LQG controller improves the dynamic properties of the levitation system, e.g. transient time and overshoot.

An active vibration control system is proposed for suppressing amplitude vibration of flexible 3D robot arm. This system integrates control algorithms, intelligent materials and software technologies. The mathematical model of physical system is based upon the geometry and properties of an experimental set‐up consisting of a Flex3D robot with a flexible joints and flexible arm. The tip of the arm is loaded by eccentric mass. The vibrations of the plate are measured by the application of a grid of strain sensors and pair of coupled gyroscope‐accelerometer. Two kinds of actuators are used. The first is a grid of PZT elements which form a local segments of compensators. Second is a standard BLDC motor located in the join. For the considered system the linear and non‐linear (Neural Network of Runge‐Kutta type models) of discrete‐time model identification for real‐time active vibration control have been applied. The mathematical model obtained by this method identification is then employed for the two class of controllers: linear pole placement controller for local segments compensators and non‐linear reduced model reference for servo‐controller. Virtual simulations are included and discussed.