There are two set of pole in InvertedPendulum system Fast & Slow. Angle Dynamics is determined by fast set of poles and position Dynamics is determined by other set of poles. Performances of different controllers like Sliding Mode, PD, Fuzzy; Neural Network is shown in . Comparison for different Energy based Controllers to stabilization of InvertedPendulum is mentioned in . An Energy based gradient method is described in . A feedback control law is derived in . A method for Controlled Lagrangians described in . A combined Controller is described in . For global stabilization of Invertedpendulum a hybrid Controller is designed in . A non-linear controller is designed in  considering non-linearity for stabilization of InvertedPendulum. A simple design to stabilize the system is described in .
The thesis presents a number of control approaches such as LQR and LQG for CIPS. These design methods have been successful in meeting the stabilization goals of the CIPS, simultaneously satisfying the physical constraints in track limit and control voltage. Due to the non-linear cart friction behavior there is a deviation from the ideal behavior that leads to undesired oscillations mainly in state feedback based control methods. The Linear Quadratic Regulator (LQR) weight selection for the cart-invertedpendulum has been thoroughly presented. The choice of LQR is well known that unlike ordinary state feedback the LQR solution obtained after LQR weight selection automatically takes care of physical constraints. LQG compensator design also considers the white noises such as process noise and measurement noise. While designing LQG compensator a Kalman Filter was used as an optimal estimator. Lastly, Loop Transfer Recovery (LTR) analysis has been performed for suitably selecting the tuning parameter for observer design. By LTR, a set of possible tuning parameters representing the state and process noise covariances can be selected depending on the trade-off between noise suppression and system robustness.
Abstract—The single invertedpendulum (SIP) system is a classic example of a nonlinear under-actuated system. In the past fifty years many nonlinear methods have been proposed for the swing-up and stabilization of a self-erecting invertedpendulum, however, most of these techniques are too complex and impractical for real-time implementation. In this paper, the successful real-time implementation of a nonlinear controller for the stabilization of a SIP on a cart is discussed. The controller is based on the power series expansion of the solution to the Hamilton Jacobi Bellman (HJB) equation. While the performance of the controller is similar to the traditional linear quadratic regulator (LQR), it has some important advantages. First, the method can stabilize the pendulum for a wider range of initial starting angle. Additionally, it can also be used with state dependent weighting matrices, Q and R, whereas the LQR problem can only handle constant values for these matrices. We present results with both constant and state-dependent weighting matrices. Furthermore, we analyze both the stability region and the disturbance rejection of the controller.
T HE double invertedpendulum (DIP) system is an extension of the single invertedpendulum (with one additional pendulum added to the single invertedpendulum), mounted on a moving cart. The DIP sys- tem is a standard model of multivariable, nonlinear, unstable system, which can be used for pedagogy as well as for the introduction of intermediate and advanced control concepts. There are two types of control synthesis for an invertedpendulum, swing- up and stabilization. One of the most popular control methods for swinging up the invertedpendulum is based on the energy method (see  and the refer- ences therein). The stabilization problem of an invertedpendulum is a classical control example for testing of linear and nonlinear controllers (see, e.g., , , ). Several control design approaches have been applied for the stabilization of the double invertedpendulum including the linear quadratic regulator , the state- dependent Riccati equation, optimal neural network , and model predictive control . To our knowl- edge, these studies only use numerical simulations to
experiment done in laboratories. It is found in various control system applications like robotic arm, satellite launching system etc. A Pendulum is a weight suspended from a pivot with its Centre of gravity acting below the pivot. It will come back to equilibrium position if it is displaced sideways. On the other hand, an IP has Centre of gravity acting above its axis of rotation. Hence it is an unstable system. Cart InvertedPendulum (CIP) system is considered here. The basic control objective is to maintain the unstable equilibrium position, by controlling the force applied in the horizontal direction to the mobile cart. The control is challenging as CIP is highly unstable, non-linear and under actuated system. The cart and pendulum is controlled separately. The pendulum is controlled by a Proportional–Integral–Derivative (PID) controller and the cart is controlled using Model Reference Adaptive Control (MRAC) using Lyapunov’s Stability Theory. There is only one control action allowed for CIP so the control actions of pendulum and cart are to be combined into one control force. The stabilization of CIP has been done using MRAC by tracking the cart position. The results are obtained in MATLAB/Simulink environment .
In the first part of this dissertation, the successful real-time implementation of a nonlinear controller for the stabilization of the pendulum is discussed. The controller is based on the power series approximation to the Hamilton Jacobi Bellman (HJB) equation. The derivation of the controller is based on work that can be found in the literature, but the controller has not been used for the stabilization of an invertedpendulum before. It performs similarly to the traditional linear quadratic regulator (LQR), but has some important advantages. First, the method can stabilize the pendulum for a wider range of initial starting angle. Additionally, it can also be used with state dependent weighting matrices, Q and R, whereas the LQR problem can only handle constant values for these matrices. The use of state-dependent weighting matrices for the stabilization of an invertedpendulum in real-time has been discussed in the literature before, but only with controls that use a State Dependent Riccati Equation (SDRE) approach. The benefit of the control presented in this thesis over the SDRE controls is that it is computationally less intense and does not require the solution of complicated matrix equations at every time step. However, the control method presented cannot be used to swing-up the pendulum whereas some of the controls using the online solution of the SDRE can.
The thesis presents a number of control approaches such as LQR, Two-Loop PID Controller, Sub-optimal LQR, and ISM. These design methods have been successful in meeting the stabilization goal of the CIPS, simultaneously satisfying the physical constraints in track limit and control voltage. The LQR, Two-Loop-PID and ISM are successful in ensuring good robustness on the input side of the CIPS. The ISM and Two-Loop-PID give good tolerability towards multichannel gain variation on the output side. Due to the non-linear cart friction behavior there is a deviation from the ideal behavior that leads to undesired stick slip oscillations mainly in state feedback based control methods. The Linear Quadratic Regulator (LQR) weight selection for the cart-invertedpendulum has been systematically presented together with robustness analysis. The choice of LQR is well known that unlike ordinary state feedback the LQR solution obtained after LQR weight selection automatically takes care of physical constraints. The LQR poles guarantee minimum robustness of ± 6 dB gain margin and 60 o phase margin.
spending per month. The question investigating the intention of adopting IoT consists of two stages. In the first stage, all respondents have to answer whether they intend to adopt IoT applications or not. The question in this stage is regardless the time when they plan to use them. Each IoT application is equipped by a description of what the application is and examples of each. IoT applications in this study include smart appliance, smart energy meter, wearable device, connected car, smart health, and home security. Descriptions of each application are presented in Table 2. Those applications refer to the survey question of GSMA , with one additional IoT application, i.e., home security. This part of the questionnaire has only two options each, “0” for indicating has no intention yet, and “1” to show an intention of adopting IoT. This first stage question will be used as dependent variable. To obtain deeper information, all respondents who answer “1” have to respond to the second stage question. The difference between the first and the second stage is the inclusion of the time of adoption, i.e., within five years.
An invertedpendulum is a pendulum that has its center of mass above its pivot point. It is unstable and without additional assist will fall over. It may be suspended stably in this inverted position by means of the usage of a feedback control system to reveal the angle of the pole and flow the pivot factor horizontally returned beneath the center of mass while it begins to fall over, retaining it balanced. The invertedpendulum is a classic problem in dynamics and manage idea and is used as a benchmark for testing control techniques. An invertedpendulum is inherently unstable, and have to be actively balanced with a view to stay upright; this could be accomplished either by applying a torque at the pivot factor, with the aid of
Many studies are found in the area of control issues related to invertedpendulum systems. Some of the studies dealing with invertedpendulum control are summarized herein. Yan  developed a tracking control law for underactuated RIP by applying nonlinear back stepping, differential flatness, and small gain theorem. Mirsaeid and Zarei  presented a mechatronic system case study on adaptive modeling and control of an invertedpendulum. Hassanzadeh et al.  presented an optimum Input-Output Feedback Linearization (IOFL) cascade controller. Genetic Algorithm (GA) was applied for the inner loop with PD controller forming the outer loop for balancing the pendulum in an inverted position. The control criterion was to minimize the Integral Absolute Error (IAE) of the system angles. The optimal controller parameters are found by minimizing the objective function related to IAE using Binary Genetic Algorithm (BGA). Ozbek and Efe  focused on the swing up and stabilization control of a rotary invertedpendulum (RIP) system with linear quadratic regulator (LQR). Sliding Mode Control (SMC) is based on hard boundary switching law and fuzzy logic control (FLC). Akhtaruzzaman et al.  have described different controller designs for rotary pendulum. Experimental and MATLAB based simulation results are given. Hassanzadeh et al.  also studied control by using evolutionary approaches. GA, Particle Swarm Optimization (PSO) and Ant Colony Optimization (ACO) are used for designing the rotational invertedpendulum. Quyen et al.  presented the dynamic model of RIP. ANN controller is used for controlling the system.
A lot of work has been carried out on the invertedpendulum in terms of its stabilization. Many attempts have been made to control it using classical control (,). Thus it is a knowledge which has been widely used in the study of stabilization of space vehicle . It has been used as a test apparatus in computer aided analysis and design thus making iteasier to understand and to experiment different control schemes (,).
Abstract— The InvertedPendulum is one of the most important classical problems of Control Engineering. In this paper, a real-time control for stabilization of invertedpendulum is developed using PID controller. The implementation platform chosen here is FPGA because it exhibits some superior qualities over traditional processors such as parallel processing capability, high sampling rates, flexibility in design, and reliability. In this system controller commands the motor through PWM signal, which drives the cart to balance the pendulum in an inverted position. Pendulum's angular position is fed back by an incremental encoder mounted on its base, which is read by controller. Controller then calculates error and runs the PID algorithm to generate a new command signal.
It is virtually impossible to balance out an invertedpendulum without applying external force into the system. The balancing of an invertedpendulum by moving a cart along a horizontal track is a classic problem in the area of control. They are often useful to demonstrate concepts in linear control such as the stabilization of unstable systems.
ABSTRACT: For at least fifty years, the invertedpendulum has been the most popular benchmark, among others, for teaching and researches in control theory and robotics. This paper presents the key motivations for the use of that system and explains, in details, the main reflections on how the invertedpendulum benchmark gives an effective and efficient application. Several real experiences, virtual models and web-based remote control laboratories will be presented with emphasis on the practical design implementation of this system. A bibliographical survey of different design control approaches and trendy robotic problems will be presented through applications to the invertedpendulum system. In total, 150 references in the open literature, dating back to 1960, are compiled to provide an overall picture of historical, current and challenging develop- ments based on the stabilization principle of the invertedpendulum
Pendulum can be described as a system in a control field theory. An invertedpendulum includes a pendulum rod in vertical, a horizontal pendulum arm, a motor and an encoder. This system was developed by Stephensen about 100 years ago that the controller is needed in order to achieve a stabilization for invertedpendulum in remain upright. The elasticity of the invertedpendulum was studied by Chao under the expectation of beam. This system is widely used in this control engineering that was also applied in many industries such as balancing a broom with only one hand, by launching the rocket from the ground and to stable the arm of robot. Thus, there were many studies on doing a research of the invertedpendulum system that are still in progress of carrying it all over the world. (Tang Jiali Ren Gexue, 2009)
ABSTRACT: Generally the invertedpendulum is unstable, because the pendulum will fall downward due to the gravitational force acting on mass of the pendulum. Keeping the pendulum at vertically inverted position, the position of DC motor shaft needs to be controlled using closed loop analysis. For closed loop analysis, feedback or input device such as encoder is used. To control and set the pendulum at desired inverted position in LABVIEW, fuzzy control logic was selected. Fuzzy control logic provides the stabilization of pendulum at vertical position without using mathematical approach such as conventional approach. Fuzzy logic control system (FLC) was selected as the control technique due to its ability to deal with nonlinear systems such as invertedpendulum. Special feature of fuzzy logic control is that it controls the physical system.
The invertedpendulum system is a standard problem in the area of control systems. They are often useful to demonstrate concepts in linear control such as the stabilization of unstable systems by varying the pendulum position and using the gains. Since the system is inherently nonlinear, it has also been useful in illustrating some of the ideas in nonlinear control . This work consists of two parts of experimental procedures. Part 1 deals with finding or calculating the vectors of gains K using pole placement method and performing the closed loop simulations for the non-linear using simulink model with a full state feedback controller of gains calculated while Part 2 is implementing the controllers by using the gain calculated on the laboratory physical invertedpendulum system and compares their stability.
The number of visual markers used in this study allows a good approximation of subject CoM motion to be obtained. However, in addition to marker locations, an estimate of the distribution of subject body mass must also be made. For this purpose a model of mass distribution proposed by Zatsiorsky et al.  was employed. Based on a data set containing 115 subjects, Zatsiorsky et al. identify individual body segment masses (as a proportion of total subject mass) and CoM locations. Later, de Leva  referenced the mean CoM locations to the relevant proximal and distal joint centres, increasing the practical usability of Zatsiorsky et al’s model. In this work each subject will be modelled as 15 individual body segments divided as follows: feet, shanks, thighs, pelvis, trunk consisting of abdomen and thorax regions, hands, forearms, upper arms and head. The segment masses as a percentage of overall subject mass (table 2) and segment CoM location are as per de Leva’s proposal.
The invertedpendulum system is a typical nonlinear, strong coupling, multivariable, naturally unstable system . In the control process, the invertedpendulum can effectively be used for studies key issues such as the qual- ity of stability, robustness, mobility, tracking and that is why, it is the ideal model for testing various theories in control engineering  . So far, it has been used in classical control, modern control and intelligent control for stability analysis with techniques such as LQR control   fuzzy control method , fuzzy neural net- work method  etc. When fuzzy control is used, the total number of fuzzy rules growth exponentially without the use of real-time processing . Through the fusion of multiple variables, the input variables of the fuzzy controller are reduced, diminishing the difficulty of the design and improving the real-time performance of the system.
point vertically. A simple demonstration of moving the pivot point in a feedback system is achieved by balancing an upturned broomstick on the end of one's finger. The invertedpendulum is a classic problem in dynamics and control theory and is used as a benchmark for testing control strategies. Can anyone balance a ruler upright on the palm of his hand? If he concentrates, he can just barely manage it by constantly reacting to the small wobbles of the ruler (Irza M. A., Mahboob I., Hussain C.,, 2001). This challenge is analogous to a classic problem in the field of control systems design: stabilizing an upside-down (“inverted”) pendulum.