Tuning of LQR controller for an experimental inverted pendulum system based on The Bees Algorithm

Stabilizing of an inverted pendulum (IP) system is a main problem for researchers working on control theory. Balancing of an inverted pendulum system is one of the major benchmark problems in the control system community. This paper presents optimal tuning of linear quadratic regulator (LQR) controller with The Bees Algorithm (BA) for a linear inverted pendulum. In this paper, a metaheuristic approach which is a nature-inspired search method that mimics the foraging behavior of honey bees is used for design of LQR controller to obtain optimal performance. In LQR controller design, state (Q) and control (R) weighting matrices are basic parameters of LQR which are tuning by designer using trial and error method in usually. The Bees Algorithm optimizes the weighting matrices of the LQR controller so that it can move the cart to a desired position with the minimum change in pendulum’s angle from vertically upright position during the movement. The tuned LQR controller is benchmarked on the linear inverted pendulum experimental device (IP02) that is manufactured by QUANSER Company. After description of the system and The Bees Algorithm, the paper gives the experimental results obtained from the IP02 system to demonstrating the efficiency of the tuning of the LQR controller. Simulation and experimental results are given graphically to show the success of controller. As a result of the paper, the performance of LQR controller shows the effectiveness of The Bees Algorithm which is a diversity method for provide an efficient solution to conventional trial and error design approach

Discrete-time neural network based state observer with neural network based control formulation for a class of systems with unmatched uncertainties

An observer is a dynamic system that estimates the state variables of another system using noisy measurements, either to estimate unmeasurable states, or to improve the accuracy of the state measurements. The Modified State Observer (MSO) is a technique that uses a standard observer structure modified to include a neural network to estimate system states as well as system uncertainty. It has been used in orbit uncertainty estimation and atmospheric reentry uncertainty estimation problems to correctly estimate unmodeled system dynamics. A form of the MSO has been used to control a nonlinear electrohydraulic system with parameter uncertainty using a simplified linear model. In this paper an extension of the MSO into discrete-time is developed using Lyapunov stability theory. Discrete-time systems are found in all digital hardware implementations, such as that found in a Martian rover, a quadcopter UAV, or digital flight control systems, and have the added benefit of reduced computation time compared to continuous systems. The derived adaptive update law guarantees stability of the error dynamics and boundedness of the neural network weights. To prove the validity of the discrete-time MSO (DMSO) simulation studies are performed using a two wheeled inverted pendulum (TWIP) robot, an unstable nonlinear system with unmatched uncertainties. Using a linear model with parameter uncertainties, the DMSO is shown to correctly estimate the state of the system as well as the system uncertainty, providing state estimates orders of magnitude more accurate, and in periods of time up to 10 times faster than the Discrete Kalman Filter. The DMSO is implemented on an actual TWIP robot to further validate the performance and demonstrate the applicability to discrete-time systems found in many aerospace applications. Additionally, a new form of neural network control is developed to compensate for the unmatched uncertainties that exist in the TWIP system using a state variable as a virtual control input. It is shown that in all cases the neural network based control assists with the controller effectiveness, resulting in the most effective controller, performing on average 53.1% better than LQR control alone --Abstract, page iii

Nonlinear system identification and control using dynamic multi-time scales neural networks

In this thesis, on-line identification algorithm and adaptive control design are proposed for nonlinear singularly perturbed systems which are represented by dynamic neural network model with multi-time scales. A novel on-line identification law for the Neural Network weights and linear part matrices of the model has been developed to minimize the identification errors. Based on the identification results, an adaptive controller is developed to achieve trajectory tracking. The Lyapunov synthesis method is used to conduct stability analysis for both identification algorithm and control design. To further enhance the stability and performance of the control system, an improved . dynamic neural network model is proposed by replacing all the output signals from the plant with the state variables of the neural network. Accordingly, the updating laws are modified with a dead-zone function to prevent parameter drifting. By combining feedback linearization with one of three classical control methods such as direct compensator, sliding mode controller or energy function compensation scheme, three different adaptive controllers have been proposed for trajectory tracking. New Lyapunov function analysis method is applied for the stability analysis of the improved identification algorithm and three control systems. Extensive simulation results are provided to support the effectiveness of the proposed identification algorithms and control systems for both dynamic NN models

Stabilization of the Two Wheels Inverted Pendulum by means Lyapunov approach

[ES] En este trabajo, se presenta un controlador no lineal para estabilizar el sistema Péndulo Invertido Sobre Dos Ruedas. Como primera etapa la estrategia de control, se basa en una linealización parcial por realimentación, para posteriormente proponer una función candidata de Lyapunov en combinación con el principio de invariancia de LaSalle con el fin de obtener el controlador esta- bilizador. El sistema en lazo cerrado obtenido es asintóticamente estable localmente alrededor del punto de equilibrio inestable, con un dominio de atracción calculable.[EN] In this paper, a nonlinear controller is presented for the stabilization of the two wheels inverted pendulum. The control strategy is based on partial feedback linealization, in first stage and then a suitable function Lyapunov in conjunction with LaSalle's invariance principle is formed to obtain a stabilizing feedback controller. 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