Control of the Two Dof Inverted Pendulum

This paper describes how to simulate and control the two DoF inverted pendulum system, a dynamics of multibody system. The control strategy used is based on the conventional feedback method for the stabilisation of the two DoF inverted pendulum system. Simulation study has been done shows that conventional method i.e. pole placement control strategy is capable to control multi input and multi output of the two DoF inverted pendulum system successfully. The result shows that pole placement control strategy gives satisfactory response that is presented in time domain. &nbsp

Desain Sistem Pengaturan Sudut Aero Pendulum Menggunakan Adaptive Neuro Fuzzy Inference System (ANFIS) Berbasis MATLAB

Abstrak Aero pendulum 2dapat 2diartikan 2sebagai pendulum 2yang dilengkapi dengan baling baling di salah satu ujungnya, dan ujung 2lainnya berada pada 2satu titik 2tetap. Aero Pendulum terdiri dari dua posisi ekuilibrium (kesetimbangan) yaitu stabil dan tidak stabil. Salah satu masalah paling sederhana dalam robotika adalah masalah pengendalian posisi sudut. Penelitian ini bertujuan untuk merancang sistem kontrol Aero Pendulum dengan kendali Adaptive Neuro Fuzzy Inference System (ANFIS) yang disimulasikan di perangkat lunak Matlab. Kendali ANFIS telah diterapkan untuk mengontrol suatu sistem dengan pergerakan yang kurang baik. Berdasarkan simulasi pada sistem Aero Pendulum dengan menggunakan kontroler ANFIS, didapatkan hasil terbaik pada setpoint sudut sebesar 80 derajat dengan waktu naik (tr) sebesar 0,8903 detik, waktu tunak (ts) sebesar 1,1035 detik, waktu puncak (Tp) sebesar 1,1484 detik, overshoot maksimum (Mo%) sebesar 0,4868%, dan nilai Error Steady State (Ess%) sebesar 0,006%. Kata Kunci: Adaptive Neuro Fuzzy Inference System (ANFIS), Aero Pendulum, Matlab, Robotik

RANCANG BANGUN STABILISASI SISTEM PENDULUM TERBALIK BERBASIS PENGENDALI PID

Abstrak Pendulum terbalik adalah sistem dinamis, nonlinear, dan sangat tidak stabil yang mensimulasikan permasalahan kestabilan dalam bidang pengaturan. Sistem ini memiliki satu input yaitu gaya dan dua output yaitu sudut pendulum dan posisi kereta sehingga proses pengendaliannya menjadi rumit. Tujuan dari penelitian ini merancang dan mengimplementasikan pengendali PID untuk stabilisasi rancang bangun sistem pendulum terbalik. Perancangan dilakukan dengan berdasar pada model dinamik sistem yang telah divalidasi untuk memastikan kesesuaian dinamika. Skema pengendali yang digunakan adalah two-loop paralel PID Controllers dengan metode penalaan Linear Quadratic Regulator (LQR). Model dinamik sistem memberikan nilai RMSE untuk masing-masing output  dan  berturut-turut sama dengan 0.043 dan 0.016, sehingga model dianggap mampu merepresentasikan dinamika sistem pendulum terbalik. Pada perancangan pengendali diperoleh nilai konstanta-konstanta PID yaitu . Implementasi pengendali pada sistem fisik diketahui bahwa pengendali PID yang dirancang memiliki kemampuan menstabilkan sistem dan ketahanan terhadap gangguan yang baik, dengan nilai RMSE pada masing-masing posisi kereta dan sudut pendulum berturut-turut sama dengan m, dan  radian, serta deviasi maksimum pada uji gangguan sama dengan 0.1 m dan 0.102 radian. Kata Kunci: Pendulum terbalik, pengendali PID, penalaan LQR, stabilisasi sistem Abstract Inverted pendulum is a dynamic, nonlinear, and very unstable system which simulates the problems of stability in control theory. This system has one input which is the force and the two outputs which are the pendulum angle and the cart position so that the control process becomes rather complicated. Aims of this research is to design and to implement PID controller for stabilization of the inverted pendulum system. The design is done based on the dynamical model of the system which has been validated to ensure the suitability of the dynamics. The controller scheme used is two-loop parallel PID Controller with Linear Quadratic Regulator (LQR) tuning method. The system dynamic model gives the RMSE values for each output  and  are 0.043 and 0.016, respectively, so the model is considered capable of representing the dynamics of the inverted pendulum system. On the controllers design, PID constants obtained are Implementation of the designed controllers on the physical systems is known that PID controllers have a good performance in both system stabilization and disturbance rejection, with RMSE values for each cart position and pendulum angle respectively equal to m, and radians. The maximum deviation at the distrubance test are equal 0.1 m and 0.102 radians. Keywords: Inverted pendulum, PID Controllers, LQR Tuning, System stabilizatio

Sliding-Mode Controller Based on Fractional Order Calculus for a Class of Nonlinear Systems

This  paper  presents  a  new  approach  of  fractional  order  sliding  mode controllers  (FOSMC)  for  a  class  of  nonlinear  systems  which  have  a  single input and two outputs (SITO). Firstly, two fractional order sliding surfaces S1 and S2 were proposed with an intermediate variable z transferred from S2 to S1 in order to hierarchy the two sliding surfaces. Secondly, a control law was determined  in  order  to  control  the  two  outputs.  A  sliding  control  stability condition  was  obtained  by  using  the  properties  of  the  fractional  order calculus.  Finally,  the  effectiveness  and  robustness  of  the  proposed  approach  were demonstrated by comparing its performance with the one of the conventional sliding mode controller (SMC), which is based on integer order derivatives. Simulation results were provided for the cases of controlling a ball-beam and inverted pendulum systems

Arm Angle Tracking Control with Pole Balancing Using Equivalent Input Disturbance Rejection for a Rotational Inverted Pendulum

This paper proposes a robust tracking control method for swing-up and stabilization of a rotational inverted pendulum system by applying equivalent input disturbance (EID) rejection. The mathematical model of the system was developed by using a Lagrangian equation. Then, the EID, including external disturbances and parameter uncertainties, was defined; and the EID observer was designed to estimate EID using the state observer dynamics and a low-pass filter. For robustness, the linear-quadratic regulator method is used with EID rejection. The closed-loop stability is proven herein using the Lyapunov theory and input-to-state stability. The performance of the proposed method is validated and verified via experimental results

Comparison of control methods for inverted 2-degree of freedom pendulum mounted on the cart

The paper considers and analyzes the existing methods of controlling systems with a deficit of control actions. Based on the analysis, it was decided to use linear controllers with feedback on the state vector of the system and to compare these methods - modal and linearquadratic. For the study, a dynamic model was chosen, which is an inverted 2-degree of freedom (2DOF) pendulum mounted on a cart. By an iterative method, acceptable system of generalized coordinates that definitely describes the state of the model was selected. Kinematic relations that describe the position of the model in generalized coordinates were derived. Using the Lagrange procedure, a system of nonlinear differential equations describing the motion of a dynamic model was obtained. The procedure of model linearization about the upright equilibrium point was also carried out in order to synthesize control system. Based on the results of modeling, which was carried out by numerical integration method in the Matlab environment, conclusions were drawn on the applicability of these control methods and their effectiveness

Backstepping Sliding Mode Control for Inverted Pendulum System with Disturbance and Parameter Uncertainty

The inverted pendulum system is highly popular in control system applications and has the characteristics of unstable, nonlinear, and fast dynamics. A nonlinear controller is needed to control a system with these characteristics. In addition, there are disturbances and parameter uncertainty issues to be solved in the inverted pendulum system. Therefore, this study uses a nonlinear controller, which is the backstepping sliding mode control. The controller is robust to parameter uncertainty and disturbances so that it is suitable for controlling an inverted pendulum system. Based on testing with step and sine reference signals without interference, the controller can stabilize the system well and has a fast response. In testing with disturbances and mass uncertainty, the backstepping sliding mode controller is robust against these changes and able to make the system reach the reference value. Compared with sliding mode control, backstepping sliding mode control has a better and more robust response to disturbances and parameter uncertainty

Stabilization of elastic inverted pendulum with hysteresis

In this paper, we investigate the elastic inverted pendulum with hysteretic nonlinearity (a back-lash) in the suspension point. Namely, the problems of stabilization and optimization of such a system are considered. The algorithm (based on the bionic model) which provides the effective procedure for finding of optimal parameters is presented and applied to considered system. The results of numerical simulations, namely the phase portraits and the dynamics of Lyapunov function, are also presented and discussed

Cascaded control for balancing an inverted pendulum on a flying quadrotor

SUMMARYThis paper is focused on the flying inverted pendulum problem, i.e., how to balance a pendulum on a flying quadrotor. After analyzing the system dynamics, a three loop cascade control strategy is proposed based on active disturbance rejection control (ADRC). Both the pendulum balancing and the trajectory tracking of the flying quadrotor are implemented by using the proposed control strategy. A simulation platform of 3D mechanical systems is deployed to verify the control performance and robustness of the proposed strategy, including a comparison with a Linear Quadratic Controller (LQR). Finally, a real quadrotor is flying with a pendulum to demonstrate the proposed method that can keep the system at equilibrium and show strong robustness against disturbances.</jats:p