Swing-up Control Research Articles

Sparse Variational Deterministic Policy Gradient for Continuous Real-Time Control

Recent advancements in deep reinforcement learning for real control tasks have received interest from many researchers and field engineers in a variety of industrial areas. However, in most cases, optimal policies obtained by deep reinforcement learning are difficult to implement on cost-effective and lightweight platforms such as mobile devices. This can be attributed to their computational complexity and excessive memory usage. For this reason, this article proposes an off-policy deep reinforcement learning algorithm called the sparse variational deterministic policy gradient (SVDPG). SVDPG provides highly efficient policy network compression under the standard reinforcement learning framework. The proposed SVDPG integrates Bayesian pruning, which is known as a state-of-the-art neural network compression technique, with the policy update in an actor–critic architecture for reinforcement learning. It is demonstrated that SVDPG achieves a high compression rate of policy networks for continuous control benchmark tasks while preserving a competitive performance. The superiority of SVDPG in low-computing power devices is proven by comparing the level of compression in terms of the memory requirements and computation time on a commercial microcontroller unit. Finally, it is confirmed that the proposed SVDPG is also reliable in real-world scenarios since it can be applied to the swing-up control of an inverted pendulum system.

A Signal Compensation-Based Robust Swing-Up and Balance Control Method for the Pendubot

This article proposes a novel robust swing-up and balance control method using data-driven compensation signals for the Pendubot system, which is underactuated and subject to dynamic friction, backlash, and modeling uncertainty. The method involves three major developments. First, the uncertainty of the system is described by a previous sampled unknown nonlinear term and its changing rate. Compensation signals are then designed to eliminate the influence of the previous sampled unknown nonlinear term and its changing rate on the outputs of the controlled plant. Second, based on the Lyapunov stability theory, a robust swing-up control method is proposed. Third, in order to eliminate the limit cycle phenomenon caused by the uncertainty near the unstable equilibrium point, a proportional-derivative balance controller based on compensation signals is proposed. The stability and tracking error analysis show that the compensation signals can effectively eliminate the influence of dynamic friction, backlash, and modeling uncertainty on the system. Experimental results verify the effectiveness of the proposed method by showing significant improvements in production rate, accuracy, and cost.

A nonlinear hybrid controller for swinging-up and stabilizing the rotary inverted pendulum

In this paper, we propose a new class nonlinear hybrid controller (NHC) for swinging-up and stabilizing the (under-actuated) rotary inverted pendulum system. First, the swing-up controller, which drives the pendulum up towards the desired upright position, is designed based on the feedback linearization and energy control methods. Then, the modified super-twisting sliding mode control is proposed based on the new sliding surface to stabilize both the fully-actuated (the rotary arm) and under-actuated (the pendulum) state variables. In the proposed NHC, around the upright position, the stabilization controller is applied, and in different circumstances aside from the upright position, the swing-up controller is used. We show that with the proposed NHC: (i) in the swing-up stage, the pendulum is able to reach the desired upright position; and (ii) in the stabilization stage, the closed-loop rotary inverted pendulum is asymptotically stable. We demonstrate the effectiveness of the proposed NHC through extensive experiments. In particular, (i) the faster swing-up under the similar control effort is obtained, compared with the existing fuzzy logic swing-up controller; (ii) the better stabilization control performance for the convergence of the angular positions of the rotary arm and pendulum is attained and the chattering is alleviated, compared with the existing sliding mode stabilization controllers; (iii) the better stabilization control accuracy with the faster convergence time and lower peak overshoot is accomplished, compared with the existing Fuzzy-LQR controller; and (iv) the good robustness against sudden external disturbances is achieved.

Swing-up stabilization control of parallel-rotating inverted pendulum by stable manifold method

Swing-up stabilization control of parallel-rotating inverted pendulum by stable manifold method

Globally Optimal Control of Nonlinear Input-Affine Systems Under Quadratic Objective Functions Based on Trajectory Database

In this paper, an approach to optimally control nonlinear input-affine systems under quadratic objective functions based on a trajectory database is proposed. In the proposed approach, the control input is calculated by solving a two-point boundary value problem of the Euler-Lagrange equation, whose initial solution is searched from the trajectory database. By a mechanism for eliminating trajectories which found to be locally optimal from the database, the proposed approach is able to obtain globally optimal solutions for problems with multiple locally optimal trajectories that are difficult to handle appropriately with existing methods. The effectiveness of the proposed approach is demonstrated through a simulation of swing-up control of one-link inverted pendulum.

Real-Time Swing-Up Control of Non-Linear Inverted Pendulum Using Lyapunov Based Optimized Fuzzy Logic Control

This paper investigates the efficacy of an optimized fuzzy logic controller for real-time swing-up control and stabilization to a rigidly coupled twin-arm inverted pendulum system. The proposed fuzzy controller utilizes Lyapunov criteria for controller design to ensure system stability. The membership functions are further optimized based on the entropy function. The controller design is based on the black-box approach, eliminating the need for an accurate mathematical model of the system. The experimental results shows an improvement in the transient and steady-state response of the controlled system as compared to other state-of-the-art controllers. The proposed controller exhibits a small settling time of 4.0 s and reaches the stable swing-up position within 5 oscillations. Various error indices are evaluated that validates an overall improvement in the performance of the system.

Swing-Up Control Design for Spring Attatched Passive Joint Acrobot

This paper presents the conditions and PD controller to swing-up the Acrobot to which a spring is attached at the passive joint (first joint). Because the motion of the system is in the vertical plane, there are some system parameters associated with gravity. The range of a spring constant and controller gain that allow the PD controller to swing-up the system is defined depending on these parameter values. To prove that the PD controller makes the system approach the equilibrium points, one of which is swing-up state (upright equilibrium point, UEP), the motion of the first link is analyzed according to the motion of the second link and the torque on the active joint (second joint) with an actuator. Among these equilibrium points, the conditions that can only converge to the UEP of the system are found.

Energy-Based Adaptive Oscillation Control of the Electromechanical Systems

The swing-up control of the electromechanical systems is considered. Electromechanical system is the cascade system. The input subsystem is a mechanical plant. The output subsystem is the actuator which dynamics cannot be neglected in particular oscillation control problem. The energy-based objective function is used to design the energy efficient virtual control law of output subsystem. The control objectives are achieving the mechanical subsystem’s reference energy and boundedness of closed-loop cascade system trajectories.In parametric uncertainty, both energy and the control objective depends on unknown parameters of a mechanical subsystem. That complicates the design procedure. The modified Speed bi-gradient method (SBGM) to identify unknown parameters, achieve a desired energy and provide boundedness of the trajectories is proposed. Modifications of SBGM are the introduction of the output subsystem tunable model, and indirect adaptive control design. Swing-up control is calculated based on current estimation performed by the adaptation loop that is without preliminary identification. The design procedure, conditions of applicability and stability analysis are presented. The proposed method is used to design the swing-up control of pendulum under parametric uncertainty. The experimental results coтfirming the performance of a closed-loop system are demonstrated.

Performance Comparisons Of Hybrid Fuzzy-LQR And Hybrid PID-LQR Controllers On Stabilizing Double Rotary Inverted Pendulum

Double Rotary Inverted Pendulum (DRIP) is a member of the mechanical under-actuated system which is unstable and nonlinear. The DRIP has been widely used for testing different control algorithms in both simulation and experiments. The DRIP control objectives include Stabilization control, Swing-up control and trajectory tracking control. In this research, we present the design of an intelligent controller called “hybrid Fuzzy-LQR controller” for the DRIP system. Fuzzy logic controller (FLC) is combined with a Linear Quadratic Regulator (LQR). The LQR is included to improve the performance based on full state feedback control. The FLC is used to accommodate nonlinearity based on its IF-THEN rules. The proposed controller was compared with the Hybrid PID-LQR controller. Simulation results indicate that the proposed hybrid Fuzzy-LQR controllers demonstrate a better performance compared with the hybrid PID-LQR controller especially in the presence of disturbances.

Self tuned Fuzzy PD Control for QNET 2.0 Rotary Inverted Pendulum using lab view

An Inverted pendulum is a nonlinear system and broadly utilized as automated arm. The challenge is to balance the pendulum that can rotate in only two ways, either to the positive or to the negative direction ±180 Degree. This research work is aiming to design a controller based on self-tuned fuzzy logic and (Fuzzy-PD) for QNET-2.0 Rotary Inverted Pendulum using lab-view. This self-tuned fuzzy PD control is responsible to generate computer based signals for stable outputs and can works on errors. Rotary Inverted pendulum (RIP) is used as real time model where self- tuned fuzzy PD control is applied for stabilization. There are two aspects to the control objectives for the inverted pendulum: swing-up and balance in a typical PD system, the balancing controller is generated using a fuzzy logic controller, instead of the proportional term. the swing-up controller is generated in a standard proportional controller by using a fuzzy logic system, instead of the proportional term. To build Lab-VIEW approaches, a software development technique is used to help programmers produce code that has greater potential to solve a problem as opposed to writing code without a design. This approach also helps make coding more accessible, more flexible, and more changeable. Rotary Inverted pendulum systems were operated and managed by means of the PD module and the Fuzzy PD Module in Lab-VIEW. The fuzzy controllers are added into the system after the design of the standard PD and P controllers. The two types of controllers the fuzzy P and the fuzzy P-D, and the common proportional and standard PD, are finally implemented and evaluated on the actual inverted pendulum hardware, and also the Control system output is compared between two different control methods.

Robust Control for Switched Systems With Unmatched Uncertainties Based on Switched Robust Integral Sliding Mode

This paper proposes a robust control design based on a new switched robust integral sliding mode (SRISM) for switched systems with unmatched uncertainties. The SRISM is a sliding surface consisting of multiple sliding modes of subsystems and is robust with respect to the structural decomposed unmatched uncertainties. Each sliding mode of the subsystem can suppress the unmatched uncertainties. Their parameters are given by the conditions of linear matrix inequalities (LMIs), and their reachabilities are guaranteed by the sliding mode controllers. Finally, numerical and application simulation results for an inverted pendulum swing-up control are provided to illustrate the validity of the robust control design.

Automatic Code Generation Tool for Nonlinear Model Predictive Control with Jupyter

We present an automatic code generation tool, AutoGenU for Jupyter, for nonlinear model predictive control (NMPC) with a user-friendly and interactive interface utilizing JupyterLab and Jupyter Notebook. We utilize a symbolic computation package SymPy for automatic C++ code generation. We also developed numerical solvers of NMPC using the continuation/GMRES (C/GMRES) method and multiple-shooting-based C/GMRES method in C++. AutoGenU for Jupyter provides the simulation environment of NMPC with these solvers and visualization of the simulation results. We give an example of code generation and numerical simulation of a swing-up control of a cart pole using AutoGenU for Jupyter.

An Automatic Self-Tuning Control System Design for an Inverted Pendulum

A control problem of an inverted pendulum in the presence of parametric uncertainty has been investigated in this paper. In particular, synthesis and implementation of an automatic self-tuning regulator for a real inverted pendulum have been given. The main cores of the control system are a swing-up control method and a stabilisation regulator. The first one is based on the energy of an inverted pendulum, whereas the second one uses the linear-quadratic regulator (LQR). Because not all of the inverted pendulum parameter values are exactly known an automatic self-tuning mechanism for designed control system has been proposed. It bases on a devised procedure for identifying parameters. The entire derived control system enables effective a pendulum swing-up and its stabilisation at an upper position. The performance of the proposed control system has been validated by simulation in Matlab/Simulink environment with the use of the inverted pendulum model as well as through experimental works using the constructed inverted pendulum on a cart.

Nonlinear Optimal Control for Swing Up and Stabilization of the Acrobot via Stable Manifold Approach: Theory and Experiment

This paper presents a solution for the swing-up and stabilization problem for the Acrobot. The method employed is the stable manifold method for optimal control, which numerically solves Hamilton–Jacobi equations (HJEs). It is shown that the feedback controller derived from the HJE for the optimal control problem exploits an inherent motion in the Acrobot using reactions of arms effectively and, therefore, the control input is kept low. Both the simulation and the experiment confirm the effectiveness and robustness of the controller. This is the first experimental result of a swing-up control for the Acrobot with a single continuous controller. This paper also discusses the comparison with existing approaches for the same problem. It is also shown that nonunique solutions exist for the HJE and the experiment is conducted with one of those.

A holistic optimization approach for inverted cart-pendulum control tuning

The inverted cart-pendulum (ICP) is a nonlinear underactuated system, which dynamics are representative of many applications. Therefore, the development of ICP control laws is important since these laws are suitable to other systems. Indeed, many nonlinear control strategies have emerged from the control of the ICP. For these reasons, the ICP remains a canonical and fundamental benchmark problem in control theory and robotics that is of interest to the scientific community. Till now, the trial-and-error method is still widely applied for ICP controller tuning as well as the sequential tuning referring to tune the swing-up controller and thereafter, the stabilization controller. Therefore, the aim of this paper is to automate and facilitate the ICP control in one step. Thus, this paper proposes to holistically optimize ICP controllers. The holistic optimization is performed by a simplified Ant Colony Optimization method with a constrained Nelder–Mead algorithm (ACO-NM). Holistic optimization refers to a simultaneous tuning of the swing-up, stabilization and switching mode parameters. A new cost function is designed to minimize swing-up time, achieve high stabilization performance and consider system constraints. The holistic approach optimizes four controller structures, which include controllers that have never been tuned by a specific method besides by the trial-and-error method. Simulation results on a ICP nonlinear model show that ACO-NM in the holistic approach is effective compared to other algorithms. In addition, contrary to the majority of work on the subject, all the optimized controllers are validated experimentally. The simulation and experimental results obtained confirm that the holistic approach is an efficient optimization tool and specifically responds to the need of optimization technique for the potential-well controller structure and for the Q [diagonal of the matrix and the full matrix] in the linear–quadratic regulator (LQR) technique. Moreover, ICP experimental response analysis demonstrates that using the full Q provides greater experimental stabilization performance than using its diagonal terms in the LQR technique.

Real-time implementation and analysis of a modified energy based controller for the swing-up of an inverted pendulum on a cart

In this paper we derive a modified energy based swing-up controller using Lyapunov functions. During the derivation, all effort has been made to use a more complex dynamical model for the single inverted pendulum (SIP) system than the simplified model that is most commonly used. We consider the electrodynamics of the DC motor that drives the cart, and incorporate viscous damping friction as seen at the motor pinion. Furthermore, we use a new method to account for the limitation of having a cart-pendulum system with a finite track length. Two modifications to the controller are also discussed to make the method more appropriate for real-time implementation. One of the modifications improves robustness using a modified Lyapunov function for the derivation, while the other one incorporates viscous damping as seen at the pendulum axis. We present both simulation and real-time experimental results implemented in MATLAB Simulink.

Swing-up and Giant-swing Control of Acrobot by Periodic Input Control

Swing-up and Giant-swing Control of Acrobot by Periodic Input Control

An adaptive swing-up sliding mode controller design for a real inverted pendulum system based on Culture-Bees algorithm

This paper presents a new design and implementation of an adaptive swing-up control algorithm for a real inverted pendulum system. The main core of the control algorithm is a sliding mode technique with the Lyapunov stability method. The goal of the proposed adaptive swing-up controller is to get the optimal force control action for the inverted pendulum in the real-time in order to precisely and quickly swing the pendulum up to the inverted position. An on-line auto-tuning hybrid intelligent algorithm based on Culture-Bees algorithms is carried out as a stable and robust algorithm to obtain and adjust the control parameters for the proposed controller. To eliminate the chattering effect of the fast switching surface, the sigmoid function is used as a Signum function for reducing the amplitude of the output function. The numerical simulation results in MATLAB and the experimental work in LabVIEW illustrate the improved performance of the adaptive swing-up controller in terms of robust performance and adaptation effectiveness that minimized the pendulum angle error to a zero value and obtained the best force control action for the pendulum cart, in addition to reducing the fitness evaluation number. These results were confirmed by a comparative study with different nonlinear controller types.

Current development on using Rotary Inverted Pendulum as a benchmark for testing linear and nonlinear control algorithms

Abstract Rotary Inverted Pendulum (RIP) is an under-actuated mechanical system which is inherently nonlinear and unstable. For decades, it has been widely used as an experimental setup to explain and test different kinds of control algorithms. The main control objectives of RIP are: Swing-up control, stabilization control, switching control and trajectory tracking control. All these control objectives are described in this study. State-of-the art works proposed for each control objective have also been reviewed. These comprise the linear, nonlinear time invariant, self-learning and adaptive nonlinear controllers. Moreover, different kinds of nonlinear dynamic models of the RIP together with the developed linear models in the literature have been analyzed. This is because most of the proposed controllers applied on RIP are found to be model dependent since they are mainly based on integral and/or invariant motion. Other types of RIP are also reported along with their advantages. Future research opportunities and challenges of the previous approaches in this area of research are presented. We believe that expert researchers can use this paper as starting point for further advancement while graduate scholars can use it as an initial point.

Smooth Second Order Sliding Mode Control of a Class of Underactuated Mechanical Systems

This paper investigates a framework for the application of robust and smooth second order sliding mode control to a class of underactuated mechanical systems for the realization of high performance control applications. First, using input and state transformations, the dynamics of the class are transformed into a normal form which consists of a set of reduced order nonlinear subsystems and a set of reduced order linear subsystems. Then we present nonlinear sliding manifold and sliding mode control for the reduced order nonlinear subsystem known as the Lagrangian zero dynamics such that stability of the overall system is guaranteed. The control design procedure is illustrated for the Furuta Pendulum, the Overhead Crane, and the Beam-and-Ball system. Numerical simulations verify the effectiveness of the proposed framework. Additionally, we design swingup control law for the Furuta Pendulum to overcome the limitation of the sliding mode control law and achieve global stabilization in the presence of external disturbance.