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Expanding upon the well-established Takagi–Sugeno (T–S) fuzzy model, the T–S fuzzy descriptor model emerges as a robust and flexible framework. This article introduces the development of optimal and robust-optimal controllers grounded in the principles of stability control and fuzzy descriptor systems. By transforming complicated inequalities into linear matrix inequalities (LMI), we establish the essential conditions for controller construction, as delineated in theorems. To substantiate the utility of these controllers, we employ the rotary inverted pendulum as a testbed. Through diverse simulation scenarios, these controllers, rooted in fuzzy descriptor systems, demonstrate their practicality and effectiveness in ensuring the stable control of inverted pendulum systems, even in the presence of uncertainties within the model. This study highlights the adaptability and robustness of fuzzy descriptor-based controllers, paving the way for advanced control strategies in complex and uncertain environments.

This paper presents a novel and comprehensive control framework for the Rotary Inverted Pendulum (RIP), focusing on a hybrid control strategy that addresses the limitations of conventional methods in nonlinear and complex systems. The proposed controller synergistically combines an Optimized Fuzzy Logic Controller (OFLC) with Sliding Mode Control (SMC), leveraging the strengths of both techniques to achieve superior performance. The integration of Particle Swarm Optimization (PSO) into the OFLC significantly enhances its adaptability and precision, while the SMC law provides robust disturbance rejection and system stability. Another key innovation in this framework is the incorporation of an Extended State Observer (ESO), which ensures accurate state estimation and reduces sensor dependency. The most significant physical outcome of this work is the demonstrated improvement in the system’s stability and robustness, even under external disturbances and uncertainties, showcasing the potential of the proposed control framework to achieve precise, stability control in nonlinear systems like the RIP. Extensive simulations validate the effectiveness of the proposed controller, demonstrating significant improvements in stability, disturbance rejection, and control precision, even under disturbance. The results highlight the potential of this approach as a robust solution for complex control systems, offering a significant advancement in the field of nonlinear system control with wide-ranging applications.

A new stable adaptive controller based on a neural network for underactuated systems is proposed in this paper. The control scheme has been developed for two underactuated systems as examples. The Furuta pendulum and the Inertia Wheel Pendulum (IWP) have been examined in this paper. The presented approach aims to address the control problem of the given system in swing up, stabilization, and disturbance rejection. To avoid oscillations, two adaptive neural networks (ANNs) are implemented. The first one is used to approximate the equivalent control online and the second one to minimize the oscillations.

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.

A new stable adaptive neural network (ANN) control scheme for the Furuta pendulum, as a two-degree-of-freedom underactuated nonlinear system, is proposed in this paper. This approach aims to address the control problem of the Furuta pendulum in the steady state and also in the presence of external disturbances. The adaptive classical control laws such as e-modification present some limitations in particular when oscillations are presented in the input. To avoid this problem, two ANNs are implemented using filtered tracking error in the control loop. The first one is a single hidden layer network, used to approximate the equivalent control online, and the second is the feed-forward network, used to minimize the oscillations. The goal of the control is to bring the pendulum close to the upright position in the presence of the various uncertainties and being able to compensate oscillations and external disturbances. The main purpose of the second ANN is to minimize the chattering phenomenon and response time by finding the optimal control input signal, which also leads to the reduction of energy consumption. The learning algorithms of the two ANNs are obtained using the direct Lyapunov stability method. The simulation results are given to highlight the performances of the proposed control scheme.

The Rotary Inverted Pendulum (RIP) is a widely used underactuated mechanical system in various applications such as bipedal robots and skyscraper stabilization where attitude control presents a significant challenge. Despite the implementation of various control strategies to maintain equilibrium, optimally tuning control gains to effectively mitigate uncertain nonlinearities in system dynamics remains elusive. Existing methods frequently rely on extensive experimental data or the designer’s expertise, presenting a notable drawback. This paper proposes a novel tracking control approach for RIP, utilizing a Linear Quadratic Regulator (LQR) in combination with a reduced-order observer. Initially, the RIP system is mathematically modeled using the Newton-Euler-Lagrange method. Subsequently, a composite controller is devised that integrates an LQR for generating nominal control signals and a reduced-order observer for reconstructing unmeasured states. This approach enhances the controller’s robustness by eliminating differential terms from the observer, thereby attenuating unknown disturbances. Thorough numerical simulations and experimental evaluations demonstrate the system’s capability to maintain balance below 50 Hz and achieve precise tracking below 1.4 rad, validating the effectiveness of the proposed control scheme.

We develop a method to simplify the partial differential equations (PDEs) associated to the potential energy for interconnection and damping assignment passivity based control (IDA-PBC) of a class of underactuated mechanical systems (UMSs). Solving the PDEs, also called the matching equations, is the main difficulty in the construction and application of the IDA-PBC. We propose a simplification to the potential energy PDEs through a particular parametrization of the closed-loop inertia matrix that appears as a coupling term with the inverse of the original inertia matrix. The parametrization accounts for kinetic energy shaping, which is then used to simplify the potential energy PDEs and their solution that is used for the potential energy shaping. This energy shaping procedure results in a closed-loop UMS with a modified energy function. This approach avoids the cancellation of nonlinearities, and extends the application of this method to a larger class of systems, including separable and non-separable port-controlled Hamiltonian (PCH) systems. Applications to the inertia wheel pendulum and the rotary inverted pendulum are presented, and some realistic simulations are presented which validate the proposed control design method and prove that global stabilization of these systems can be achieved. Experimental validation of the proposed method is demonstrated using a laboratory set-up of the rotary pendulum. The robustness of the closed-loop system with respect to external disturbances is also experimentally verified.

In this paper, an adaptive controller is proposed to balance a rotary inverted pendulum with time-varying uncertainties. The goal of the control is to bring the pendulum close to the upright position regardless of the various uncertainties and disturbances. Its underactuated dynamics is first decoupled by Olfati’s transformation into a cascade form, and then an adaptive controller is designed to deal with the uncertainties in the new space. Based on the Lyapunov-like theory, the closed loop stability and boundedness of all internal signals can be proved. The simulation results show that the proposed scheme is capable of giving good performance, as desired.

Rotary Inverted Pendulum (RIP) mimics the behavior of many practical control systems like crane mechanism, segway, unicycle robot, traction control in vehicles, rocket stabilization, and launching. RIP is a fourth-order nonlinear open-loop unstable dynamical system and is widely used for testing the effectiveness of the newly developed control algorithms. In this paper, a Hybrid Control Scheme (HCS) based on energy balance and fuzzy logic controllers is proposed to implement the swing up and stabilization control of RIP. In the proposed control scheme, the fuzzy logic-based state feedback gains are dynamically tuned in real-time by minimizing the absolute error between the desired and actual states to get robust control performance. The proposed HCS is also compared with the conventional Linear Quadratic Controller (LQR) for this application. The comparative results show that the proposed fuzzy logic-based hybrid control scheme gives the optimal control performance in terms of achieving satisfactory transient, steady-state, and robust responses from a given RIP system, as compared to the conventional LQR based control scheme. The proposed control scheme is also relatively less complex with a low computational cost and provides desired response characteristics as compared to the existing ones in the literature.