Pole Placement for Time-Delayed Systems Using Galerkin Approximations

2019 ◽  
Vol 141 (5) ◽  
Author(s):  
Shanti S. Kandala ◽  
Thomas K. Uchida ◽  
C. P. Vyasarayani
Keyword(s):  
Time Delays ◽  
Controller Design ◽  
Galerkin Approximation ◽  
Practical Interest ◽  
Pole Placement ◽  
Design Strategies ◽  
Additional Time ◽  
Delayed Systems ◽  
Pendulum System ◽  
Inverted Pendulum System

Many dynamic systems of practical interest have inherent time delays and thus are governed by delay differential equations (DDEs). Because DDEs are infinite dimensional, time-delayed systems may be difficult to stabilize using traditional controller design strategies. We apply the Galerkin approximation method using a new pseudo-inverse-based technique for embedding the boundary conditions, which results in a simpler mathematical derivation than has been presented previously. We then use the pole placement technique to design closed-loop feedback gains that stabilize time-delayed systems and verify our results through comparison to those reported in the literature. Finally, we perform experimental validation by applying our method to stabilize a rotary inverted pendulum system with inherent sensing delays as well as additional time delays that are introduced deliberately. The proposed approach is easily implemented and performs at least as well as existing methods.

scholarly journals State Space Based Linear Controller Design for the Inverted Pendulum

2019 ◽  
Vol 12 (2) ◽  
pp. 130-147 ◽  
Author(s):  
Miklós Kuczmann
Keyword(s):  
State Space ◽  
Inverted Pendulum ◽  
Controller Design ◽  
Pole Placement ◽  
Space Representation ◽  
Linear Quadratic ◽  
Linear Quadratic Optimal Control ◽  
Pendulum System ◽  
Linear Controller ◽  
Inverted Pendulum System

In a previous survey paper the detailed PID controller design to stabilize the inclination angle as well as the horizontal movement of an inverted pendulum system has been presented. In this paper the linear controller design based on the state space representation is shown step by step. Pendulum model is based on EulerLagrange modeling, and the nonlinear state space model is linearized in the unstable upward position, finally pole placement by Ackermann formula and Bass–Gura equation, moreover linear quadratic optimal control are presented. The pendulum has been inserted into a virtual reality laboratory, which is suitable to use in model based control teaching.

Development of a fuzzy-state feedback regulator for stabilizing a flexible inverted pendulum system

2021 ◽  
pp. 107754632110429
Author(s):  
Pouriya Pourgholam ◽  
Hamid Moeenfard
Keyword(s):  
Fuzzy System ◽  
State Feedback ◽  
Equations Of Motion ◽  
Pole Placement ◽  
Pendulum System ◽  
Inverted Pendulum System ◽  
Reduced Order Observer ◽  
Pole Placement Control ◽  
Fuzzy State

Accurate modeling and efficient control of inverted pendulums have always been a challenge for researchers. So, the current research aims to achieve the following objectives: (I) proposing a comprehensive dynamic model for the inverted pendulums which accounts for the flexibility of the pendulum bar and (II) suggesting an appropriate supervisory fuzzy-pole placement control strategy for stabilizing the pendulum system. Using a Lagrangian formulation, the equations of motion are derived and linearized. Then, a state feedback controller with a reduced-order observer is designed to stabilize the system. Closed-loop simulations reveal that at least six modes shall be considered in the dynamic equations. To improve the quality of the transient response, a novel fuzzy system is developed for real-time assignment of the controller poles. Simulation results demonstrate that the control quality is significantly improved by adding a supervisory fuzzy system to the control loop. The developed approach for dynamic modeling of the system, and the idea of multi-level fuzzy-pole placement control architecture developed in this paper, may be successfully applied to improve the response specifications in other dynamic systems.

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 Integrated SolidWorks and Simscape platform for the design and control of an inverted pendulum system

2020 ◽  
Vol 71 (2) ◽  
pp. 122-126
Author(s):  
Ahmed Alkamachi
Keyword(s):  
Inverted Pendulum ◽  
Controller Design ◽  
State Feedback Control ◽  
Pendulum System ◽  
Inverted Pendulum System ◽  
Control Scheme ◽  
Implicit System ◽  
Physical Elements ◽  
And Control ◽  
The Mathematical Model

AbstractA single inverted pendulum on a cart (SIPC) is designed and modeled physically using SolidWorks. The model is then exported to the Simulink environment to form a Simscape model for simulation and test purposes. This type of modeling uses a physical grid tactic to model mechanical structures. It requires connection of the physical elements with physical signal converter to define the implicit system dynamics to be modeled. The integration between the SolidWorks and Simscape eliminates the need of deriving the mathematical model and provides a platform for the rapid controller design for the system. State feedback control scheme is proposed, designed, and tuned aiming to maintain the pendulum in the upright place while tracking the desired cart position. Several simulation cases are studied to prove the controller abilities. In order to examine the controller robustness, disturbance rejection and noise attenuation capabilities are also discovered.

Optimisation of a PID Controller for an Inverted Pendulum Using the Bees Algorithm

2015 ◽  
Vol 789-790 ◽  
pp. 1039-1044 ◽  
Author(s):  
Muhammed Arif Sen ◽  
Mete Kalyoncu
Keyword(s):  
Pid Controller ◽  
Inverted Pendulum ◽  
Controller Design ◽  
Stable State ◽  
Bees Algorithm ◽  
Pid Controllers ◽  
Pendulum System ◽  
Tuning Method ◽  
Inverted Pendulum System ◽  
Optimal Gains

The inverted pendulum system is a challenging control problem in the control theory, which continually moves away from a stable state. The paper presents the design of a Proportional-Integral-Derivative (PID) controller for a single-input multi-output (SIMO) inverted pendulum system and using the Bees Algorithm (BA) to obtain optimal gains for PID controllers. The Bees Algorithm optimizes the gains so that the controller can move the cart to a desired position with the minimum amount of the change in the pendulum’s angle from the vertically upright position during the movement. The tuning aim is to minimize the control responses of the cart’s position and the pendulum’s angle in time domain. MATLAB/Simulink simulation has been performed to demonstrate that the effects on the system performance of PID controllers with optimal gains. The obtained results show that the tuning method by using the Bees Algorithm produced PID controllers successfully within the controller design criteria. Following a description of the inverted pendulum system and the Bees Algorithm, the paper gives the obtained simulation results for the system demonstrating the efficiency of the design.

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