Optimal control of inverted pendulum system using PID controller, LQR and MPC
01 Nov 2017-Vol. 263, Iss: 5, pp 052007
TL;DR: The control objective is to control the system such that when the cart reaches a desired position the inverted pendulum stabilizes in the upright position.
Abstract: Inverted pendulum is a highly nonlinear system. Here we propose an optimal control technique for the control of an inverted Pendulum - cart system. The system is modeled, linearized and controlled. Here, the control objective is to control the system such that when the cart reaches a desired position the inverted pendulum stabilizes in the upright position. Initially PID controller is used to control the system. Later, Linear Quadratic Regulator (LQR) a well-known optimal control technique which makes use of the states of the dynamical system and control input to frame the optimal control decision is used. Various combinations of both PID and LQR controllers are implemented. To validate the robustness of the controller, the system is simulated with and without disturbance. Finally the system is also controlled using Model Predictive controller (MPC). MPC has well predictive ability to calculate future events and implement necessary control actions. The performance of the system is compared and analyzed.
Citations
More filters
TL;DR: This paper presents the first direct comparison of a PCT controller for a mobile robot with a classical control method, LQR, and results show that the performance of the PCT Controller is comparable to the L QR controller and better at disturbance rejection.
Abstract: Perceptual Control Theory (PCT) theorizes that a creature’s behaviour is varied so that their perception can reach and maintain certain fixed limits, despite external disturbances. The distinguishing characteristic of PCT is that the controlled variables are the inputs (perceptions, as opposed to the system outputs). This paper presents the first direct comparison of a PCT controller for a mobile robot (a two-wheeled ‘inverted pendulum’ balancing robot) with a classical control method, LQR. Simulations and experimental validation results show that the performance of the PCT controller is comparable to the LQR controller and better at disturbance rejection.
14 citations
Cites background from "Optimal control of inverted pendulu..."
...The inverted pendulum is often accepted as an appropriate model for a self-balancing vehicle [19]; its non-linearity and availability in the laboratory mean that inverted pendulum control can be viewed as a benchmark test for evaluating and comparing different control methods [20, 21]....
[...]
14 Jan 2021
TL;DR: In this article, an analysis of the current state-of-the-art technologies in the field of auto-operators used in production during the electroplating process is presented.
Abstract: This paper provides an analysis of the current state-of-the-art technologies in the field of auto-operators used in production during the electroplating process. General schemes of operations are presented, benefits and drawbacks of each scheme are discussed. The paper discusses an increase in the operating efficiency of the auto-operator in transient conditions (braking and acceleration) by reducing suspension oscillations and provides an example of a similar problem from other industries. In addition to the classification of the auto-operators, three main ways and control methods of the auto-operator of a galvanic line are presented. The main ways of eliminating oscillations during the movement of the auto-operator, as well as the rationale for the choice of adaptive (optimal) control, based on and comparing the basic control algorithms of the robot manipulator, are discussed. The comparative analysis of algorithms used to determine the optimal control has been carried out. Application field of each optimal control method described, moreover advantages and disadvantages as well as implementation methods described. Bellman dynamic programming method was chosen to eliminate oscillations of the suspension with details during the auto-operator transient conditions, the chosen method takes into account all necessary conditions to achieve the desired result.
8 citations
TL;DR: In this paper, the robust generalized dynamic inversion control methodology is applied to the problem of stabilizing upright equilibrium configuration of the under-actuated rotary inverted pendulum syste...
Abstract: The article applies the robust generalized dynamic inversion control methodology to the problem of stabilizing upright equilibrium configuration of the under-actuated rotary inverted pendulum syste...
7 citations
Cites methods from "Optimal control of inverted pendulu..."
...The results of the tracking problem of RotIP are presented by Varghese et al. (2017), where model predictive control is applied, which has the ability to predict future state trajectories and implement necessary control actions....
[...]
TL;DR: In this article, a dual-mode fractional-order control with a reference model for pitch and angle control of an inverted pendulum was proposed and an inertia weighted PSO was utilized for optimal tuning of the FOPID parameters to ensure an optimal balance between local and global search.
Abstract: Several control strategies are proposed and developed to enhance the performance of the various underactuated systems, particularly inverted pendulum. This paper presents the dual-mode fractional-order control with a reference model for pitch and angle control of an inverted pendulum. An inertia weighted PSO is utilized for optimal tuning of the FOPID parameters to ensure an optimal balance between local and global search. A cost function of this algorithm is framed based on the error between the reference model output and actual system output along with time-domain performance criteria. The reference model-based tuning improves the performance of the controller and steady-state error tracking. In addition, an optimal state feedback LQR is implemented using pole placement design in the feedback to stabilize and improve the robustness of the inverted pendulum. Compared to the conventional PID, the proposed structure illustrates the FOPID structure has significant performance improvement in both with and without disturbance conditions.
6 citations
References
More filters
Book•
01 Jan 1970
TL;DR: This comprehensive treatment of the analysis and design of continuous-time control systems provides a gradual development of control theory and shows how to solve all computational problems with MATLAB.
Abstract: From the Publisher:
This comprehensive treatment of the analysis and design of continuous-time control systems provides a gradual development of control theoryand shows how to solve all computational problems with MATLAB. It avoids highly mathematical arguments, and features an abundance of examples and worked problems throughout the book. Chapter topics include the Laplace transform; mathematical modeling of mechanical systems, electrical systems, fluid systems, and thermal systems; transient and steady-state-response analyses, root-locus analysis and control systems design by the root-locus method; frequency-response analysis and control systems design by the frequency-response; two-degrees-of-freedom control; state space analysis of control systems and design of control systems in state space.
6,634 citations
TL;DR: It is seen that many PID variants have been developed in order to improve transient performance, but standardising and modularising PID control are desired, although challenging, and the inclusion of system identification and "intelligent" techniques in software based PID systems helps automate the entire design and tuning process to a useful degree.
Abstract: Designing and tuning a proportional-integral-derivative (PID) controller appears to be conceptually intuitive, but can be hard in practice, if multiple (and often conflicting) objectives such as short transient and high stability are to be achieved. Usually, initial designs obtained by all means need to be adjusted repeatedly through computer simulations until the closed-loop system performs or compromises as desired. This stimulates the development of "intelligent" tools that can assist engineers to achieve the best overall PID control for the entire operating envelope. This development has further led to the incorporation of some advanced tuning algorithms into PID hardware modules. Corresponding to these developments, this paper presents a modern overview of functionalities and tuning methods in patents, software packages and commercial hardware modules. It is seen that many PID variants have been developed in order to improve transient performance, but standardising and modularising PID control are desired, although challenging. The inclusion of system identification and "intelligent" techniques in software based PID systems helps automate the entire design and tuning process to a useful degree. This should also assist future development of "plug-and-play" PID controllers that are widely applicable and can be set up easily and operate optimally for enhanced productivity, improved quality and reduced maintenance requirements.
2,461 citations
TL;DR: In this paper, the Industrial Electronics Laboratory at the Swiss Federal Institute of Technology, Lausanne, Switzerland, has built a prototype of a two-wheeled vehicle with two coaxial wheels, each of which is coupled to a DC motor.
Abstract: The Industrial Electronics Laboratory at the Swiss Federal Institute of Technology, Lausanne, Switzerland, has built a prototype of a revolutionary two-wheeled vehicle. Due to its configuration with two coaxial wheels, each of which is coupled to a DC motor, the vehicle is able to do stationary U-turns. A control system, made up of two decoupled state-space controllers, pilots the motors so as to keep the system in equilibrium.
780 citations
TL;DR: The dynamic model of a wheeled inverted pendulum (e.g., Segway, Quasimoro, and Joe) is analyzed from a controllability and feedback linearizability point of view and two novel controllers are designed.
Abstract: In this paper, the dynamic model of a wheeled inverted pendulum (eg, Segway, Quasimoro, and Joe) is analyzed from a controllability and feedback linearizability point of view First, a dynamic model of this underactuated system is derived with respect to the wheel motor torques as inputs while taking the nonholonomic no-slip constraints into considerations This model is compared with the previous models derived for similar systems The strong accessibility condition is checked and the maximum relative degree of the system is found Based on this result, a partial feedback linearization of the system is obtained and the internal dynamics equations are isolated The resulting equations are then used to design two novel controllers The first one is a two-level velocity controller for tracking vehicle orientation and heading speed set-points, while controlling the vehicle pitch (pendulum angle from the vertical) within a specified range The second controller is also a two-level controller which stabilizes the vehicle's position to the desired point, while again keeping the pitch bounded between specified limits Simulation results are provided to show the efficacy of the controllers using realistic data
551 citations
TL;DR: A model predictive control algorithm for the solution of a state-feedback robust control problem for discrete-time nonlinear systems and guarantees robust stability in the face of a class of bounded disturbances and/or parameter uncertainties is described.
Abstract: This paper describes a model predictive control (MPC) algorithm for the solution of a state-feedback robust control problem for discrete-time nonlinear systems. The control law is obtained through the solution of a finite-horizon dynamic game and guarantees robust stability in the face of a class of bounded disturbances and/or parameter uncertainties. A simulation example is reported to show the applicability of the method. Copyright © 2003 John Wiley & Sons, Ltd.
231 citations