scholarly journals Robust Full State Feedback Controller Design Using H∞ for Inverted Pendulum System

2018 ◽  
pp. 39-48
Keyword(s):  
State Feedback ◽  
Inverted Pendulum ◽  
Controller Design ◽  
Upright Position ◽  
Feedback Controller ◽  
Pendulum System ◽  
Integral Term ◽  
Inverted Pendulum System ◽  
Full State ◽  
Full State Feedback

This paper presents the design of a full state feedback H∞ controller to an inverted pendulum system. The nonlinear and linearized models of the system are obtained. The main goal of the proposed controller is to maintain the pendulum in the upright position and achieve a desirable tracking for the cart position. To achieve desirable tracking properties an integral term is added. The robustness of the proposed controller is examined when a 20% variation in the parameters of system is considered.

Robust Stabilizing Controller Design for Inverted Pendulum System

2014 ◽  
Vol 71 (1) ◽  
Author(s):  
Hazem I. Ali
Keyword(s):  
Steady State ◽  
Time Domain ◽  
State Feedback ◽  
Inverted Pendulum ◽  
Controller Design ◽  
H Infinity ◽  
Pendulum System ◽  
Stabilizing Controller ◽  
Inverted Pendulum System ◽  
System Uncertainties

In this paper the design of robust stabilizing state feedback controller for inverted pendulum system is presented. The Ant Colony Optimization (ACO) method is used to tune the state feedback gains subject to different proposed cost functions comprise of H-infinity constraints and time domain specifications. The steady state and dynamic characteristics of the proposed controller are investigated by simulations and experiments. The results show the effectiveness of the proposed controller which offers a satisfactory robustness and a desirable time response specifications. Finally, the robustness of the controller is tested in the presence of system uncertainties and disturbance.

scholarly journals H2 Sliding Mode Controller Design for Mobile Inverted Pendulum System

2018 ◽  
pp. 17-29
Keyword(s):  
Mathematical Model ◽  
Inverted Pendulum ◽  
Controller Design ◽  
Sliding Mode ◽  
Upright Position ◽  
Sliding Mode Controller ◽  
Pendulum System ◽  
System Parameters ◽  
Inverted Pendulum System ◽  
The Mathematical Model

The design of an H2 sliding mode controller for a mobile inverted pendulum system is proposed in this paper. This controller is conducted to stabilize the mobile inverted pendulum in the upright position and drive the system to a desired position. Lagrangian approach is used to develop the mathematical model of the system. The H2 controller is combined with the sliding mode control to give a better performance compared to the case of using each of the above controllers alone. The results show that the proposed controller can stabilize the system and drive the output to a given desired input. Furthermore, variations in system parameters and disturbance are considered to illustrate the robustness of the proposed controller.

Three-Stage Feedback Controller Design With Applications to Three Time-Scale Linear Control Systems

2017 ◽  
Vol 139 (10) ◽  
Author(s):  
Verica Radisavljevic-Gajic ◽  
Milos Milanovic ◽  
Garrett Clayton
Keyword(s):  
Time Scale ◽  
State Feedback ◽  
Controller Design ◽  
Feedback Controller ◽  
New Technique ◽  
Feedback Controllers ◽  
Linear Dynamic ◽  
Subsystem Level ◽  
Full State ◽  
Full State Feedback

This paper presents a new technique for design of full-state feedback controllers for linear dynamic systems in three stages. The new technique is based on appropriate partitioning of the linear dynamic system into linear dynamic subsystems. Every controller design stage is done at the subsystem level using only information about the subsystem (reduced-order) matrices. Due to independent design in each stage, different subsystem controllers can be designed to control different subsystems. Partial subsystem level optimality and partial eigenvalue subsystem assignment can be achieved. Using different feedback controllers to control different subsystems of a system has not been present in any other known linear full-state feedback controller design technique. The new technique requires only solutions of reduced-order subsystem level algebraic equations. No additional assumptions were imposed except what is common in linear feedback control theory (the system is controllable (stabilizable)) and theory of three time-scale linear systems (the fastest subsystem state matrix is invertible)). The local full-state feedback controllers are combined to form a global full-state controller for the system under consideration. The presented results are specialized to the three time-scale linear control systems that have natural decomposition into slow, fast, and very fast subsystems, for which numerical ill conditioning is removed and solutions of the design algebraic equations are easily obtained. The proposed three-stage three time-scale feedback controller technique is demonstrated on the eighth-order model of a fuel cell model.

scholarly journals Application of LQR Full-State Feedback Controller for Rotational Inverted Pendulum

2021 ◽  
Vol 2111 (1) ◽  
pp. 012006
Author(s):  
N Setiawan ◽  
G N P Pratama
Keyword(s):  
State Feedback ◽  
Inverted Pendulum ◽  
Equilibrium Points ◽  
Linear Quadratic Regulator ◽  
Feedback Controller ◽  
Control Law ◽  
Linear Quadratic ◽  
State Feedback Controller ◽  
Full State ◽  
Full State Feedback

Abstract The rotational inverted pendulum is an interesting subject for some researchers, especially control engineers. Its nonlinear and underactuated characteristic make it quite challenging to stabilize it. Hence, a proper control law is a must to make it stable. Here, in this paper, we present a control law using LQR (Linear-Quadratic Regulator) to stabilize the rotational inverted pendulum. The experiments are carried out by linearizing the model and simulate the response in MATLAB. The results show that the controller succeeds to stabilize the states of rotational inverted pendulum to their respective equilibrium points. Even more, it provides zero settling errors.

Full State Feedback Control Design for “Delay Scheduling”

2008 ◽  
Author(s):  
Mursel Emre Cavdaroglu ◽  
Nejat Olgac
Keyword(s):  
State Feedback ◽  
Controller Design ◽  
Linear Time ◽  
State Feedback Control ◽  
Control Synthesis ◽  
Delayed Systems ◽  
Pendulum System ◽  
Characteristic Roots ◽  
Full State ◽  
Full State Feedback

A fixed full state feedback controller design approach is proposed for linear time invariant (LTI) systems with time delays. This approach enables the designer to use recently introduced “delay scheduling” procedure, which opens a new direction in control synthesis. “Delay scheduling” strategy suggests prolonging the existing (and unavoidable) delays in order to recover stability or to improve the control performance features. To be able to do this, however, system should have multiple stable operating zones in the domain of the delays. The main contribution of this paper is to develop a procedure for designing such a control law. It starts with a simple usage of LQR for non-delayed systems. This approach, nevertheless, imparts some complexities when delays are introduced. We handle them using a recent paradigm, called the Cluster Treatment of Characteristic Roots (CTCR). For an example to the ensuing design strategy, we use a fully actuated cart-pendulum system. Relevant simulations are carried out to show the viability of the proposed idea.

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