Classical and intelligent methods in model extraction and stabilization of a dual-axis reaction wheel pendulum: A comparative study

Controlling underactuated open-loop unstable systems is challenging. In this study, first, both nonlinear and linear models of a dual-axis reaction wheel pendulum (DA-RWP) are extracted by employing Lagrangian equa-tions which are based on energy methods. Then to control the system and stabilize the pendulum's angle in the upright position, fuzzy logic based controllers for both x -y directions are developed. To show the efficiency of the designed intelligent controller, comparisons are made with its classical optimal control counterparts. In our simulations, as proof of the reliability and robustness of the fuzzy controller, two scenarios including noise -disturbance-free and noisy-disturbed situations are considered. The comparisons made between the classical and fuzzy-based controllers reveal the superiority of the proposed fuzzy logic controller, in terms of time response. The simulation results of our experiments in terms of both mathematical modeling and control can be deployed as a baseline for robotics and aerospace studies as developing walking humanoid robots and satellite attitude systems, respectively.The work of U.F.-G. was supported by the government of the Basque Country for the ELKARTEK21/10 KK-2021/00014 and ELKARTEK22/85 research programs, respectively

On the robustness of the slotine-Li and the FPT/SVD-based adaptive controllers

A comparative study concerning the robustness of a novel, Fixed Point Transformations/Singular Value Decomposition (FPT/SVD)-based adaptive controller and the Slotine-Li (S&L) approach is given by numerical simulations using a three degree of freedom paradigm of typical Classical Mechanical systems, the cart + double pendulum. The effects of the imprecision of the available dynamical model, presence of dynamic friction at the axles of the drives, and the existence of external disturbance forces unknown and not modeled by the controller are considered. While the Slotine-Li approach tries to identify the parameters of the formally precise, available analytical model of the controlled system with the implicit assumption that the generalized forces are precisely known, the novel one makes do with a very rough, affine form and a formally more precise approximate model of that system, and uses temporal observations of its desired vs. realized responses. Furthermore, it does not assume the lack of unknown perturbations caused either by internal friction and/or external disturbances. Its another advantage is that it needs the execution of the SVD as a relatively time-consuming operation on a grid of a rough system-model only one time, before the commencement of the control cycle within which it works only with simple computations. The simulation examples exemplify the superiority of the FPT/SVD-based control that otherwise has the deficiency that it can get out of the region of its convergence. Therefore its design and use needs preliminary simulation investigations. However, the simulations also exemplify that its convergence can be guaranteed for various practical purposes

Visual Feedback Stabilisation of a Cart Inverted Pendulum A

Vision-based object stabilisation is an exciting and challenging area of research, and is one that promises great technical advancements in the field of computer vision. As humans, we are capable of a tremendous array of skilful interactions, particularly when balancing unstable objects that have complex, non-linear dynamics. These complex dynamics impose a difficult control problem, since the object must be stabilised through collaboration between applied forces and vision-based feedback. To coordinate our actions and facilitate delivery of precise amounts of muscle torque, we primarily use our eyes to provide feedback in a closed-loop control scheme. This ability to control an inherently unstable object by vision-only feedback demonstrates an exceptionally high degree of voluntary motor skill. Despite the pervasiveness of vision-based stabilisation in humans and animals, relatively little is known about the neural strategies used to achieve this task. In the last few decades, with advancements in technology, we have tried to impart the skill of vision-based object stabilisation to machines, with varying degrees of success. Within the context of this research, we continue this pursuit by employing the classic Cart Inverted Pendulum; an inherently unstable, non-linear system to investigate dynamic object balancing by vision-only feedback. The Inverted Pendulum is considered to be one of the most fundamental benchmark systems in control theory; as a platform, it provides us with a strong, well established test bed for this research. We seek to discover what strategies are used to stabilise the Cart Inverted Pendulum, and to determine if these strategies can be deployed in Real-Time, using cost-effective solutions. The thesis confronts, and overcomes the problems imposed by low-bandwidth USB cameras; such as poor colour-balance, image noise and low frame rates etc., to successfully achieve vision-based stabilisation. The thesis presents a comprehensive vision-based control system that is capable of balancing an inverted pendulum with a resting oscillation of approximately ±1º. We employ a novel, segment-based location and tracking algorithm, which was found to have excellent noise immunity and enhanced robustness. We successfully demonstrate the resilience of the tracking and pose estimation algorithm against visual disturbances in Real-Time, and with minimal recovery delay. The algorithm was evaluated against peer reviewed research; in terms of processing time, amplitude of oscillation, measurement accuracy and resting oscillation. For each key performance indicator, our system was found to be superior in many cases to that found in the literature. The thesis also delivers a complete test software environment, where vision-based algorithms can be evaluated. This environment includes a flexible tracking model generator to allow customisation of visual markers used by the system. We conclude by successfully performing off-line optimization of our method by means of Artificial Neural Networks, to achieve a significant improvement in angle measurement accuracy.Goodrich Engine Control Systems and Balfour Beatty Rail Technologie

On Stabilization of Cart-Inverted Pendulum System: An Experimental Study

The Cart-Inverted Pendulum System (CIPS) is a classical benchmark control problem. Its dynamics resembles with that of many real world systems of interest like missile launchers, pendubots, human walking and segways and many more. The control of this system is challenging as it is highly unstable, highly non-linear, non-minimum phase system and underactuated. Further, the physical constraints on the track position control voltage etc. also pose complexity in its control design. The thesis begins with the description of the CIPS together with hardware setup used for research, its dynamics in state space and transfer function models. In the past, a lot of research work has been directed to develop control strategies for CIPS. But, very little work has been done to validate the developed design through experiments. Also robustness margins of the developed methods have not been analysed. Thus, there lies an ample opportunity to develop controllers and study the cart-inverted pendulum controlled system in real-time. The objective of this present work is to stabilize the unstable CIPS within the different physical constraints such as in track length and control voltage. Also, simultaneously ensure good robustness. A systematic iterative method for the state feedback design by choosing weighting matrices key to the Linear Quadratic Regulator (LQR) design is presented. But, this yields oscillations in cart position. The Two-Loop-PID controller yields good robustness, and superior cart responses. A sub-optimal LQR based state feedback subjected to H∞ constraints through Linear Matrix Inequalities (LMIs) is solved and it is observed from the obtained results that a good stabilization result is achieved. Non-linear cart friction is identified using an exponential cart friction and is modeled as a plant matrix uncertainty. It has been observed that modeling the cart friction as above has led to improved cart response. Subsequently an integral sliding mode controller has been designed for the CIPS. From the obtained simulation and experiments it is seen that the ISM yields good robustness towards the output channel gain perturbations. The efficacies of the developed techniques are tested both in simulation and experimentation. It has been also observed that the Two-Loop PID Controller yields overall satisfactory response in terms of superior cart position and robustness. In the event of sensor fault the ISM yields best performance out of all the techniques

Advanced Strategies for Robot Manipulators

Amongst the robotic systems, robot manipulators have proven themselves to be of increasing importance and are widely adopted to substitute for human in repetitive and/or hazardous tasks. Modern manipulators are designed complicatedly and need to do more precise, crucial and critical tasks. So, the simple traditional control methods cannot be efficient, and advanced control strategies with considering special constraints are needed to establish. In spite of the fact that groundbreaking researches have been carried out in this realm until now, there are still many novel aspects which have to be explored

Development of Self-Learning Type-2 Fuzzy Systems for System Identification and Control of Autonomous Systems

Modelling and control of dynamic systems are faced by multiple technical challenges, mainly due to the nature of uncertain complex, nonlinear, and time-varying systems. Traditional modelling techniques require a complete understanding of system dynamics and obtaining comprehensive mathematical models is not always achievable due to limited knowledge of the systems as well as the presence of multiple uncertainties in the environment. As universal approximators, fuzzy logic systems (FLSs), neural networks (NNs) and neuro-fuzzy systems have proved to be successful computational tools for representing the behaviour of complex dynamical systems. Moreover, FLSs, NNs and learning-based techniques have been gaining popularity for controlling complex, ill-defined, nonlinear, and time-varying systems in the face of uncertainties. However, fuzzy rules derived by experts can be too ad-hoc, and the performance is less than optimum. In other words, generating fuzzy rules and membership functions in fuzzy systems is a potential challenge especially for systems with many variables. Moreover, under the umbrella of FLSs, although type-1 fuzzy logic control systems (T1-FLCs) have been applied to control various complex nonlinear systems, they have limited capability to handle uncertainties. Aiming to accommodate uncertainties, type-2 fuzzy logic control systems (T2-FLCs) were established. This thesis aims to address the shortcomings of existing fuzzy techniques by utilisation of type-2 FLCs with novel adaptive capabilities. The first contribution of this thesis is a novel online system identification technique by means of a recursive interval type-2 Takagi-Sugeno fuzzy C-means clustering technique (IT2-TS-FC) to accommodate the footprint-of-uncertainties (FoUs). This development is meant to specifically address the shortcomings of type-1 fuzzy systems in capturing the footprint-of-uncertainties such as mechanical wear, rotor damage, battery drain and sensor and actuator faults. Unlike previous type-2 TS fuzzy models, the proposed method constructs two fuzzifiers (upper and lower) and two regression coefficients in the consequent part to handle uncertainties. The weighted least square method is employed to compute the regression coefficients. The proposed method is validated using two benchmarks, namely, real flight test data of a quadcopter drone and Mackey-Glass time series data. The algorithm has the capability to model uncertainties (e.g., noisy dataset). The second contribution of this thesis is the development of a novel self-adaptive interval type-2 fuzzy controller named the SAF2C for controlling multi-input multi-output (MIMO) nonlinear systems. The adaptation law is derived using sliding mode control (SMC) theory to reduce the computation time so that the learning process can be expedited by 80% compared to separate single-input single-output (SISO) controllers. The system employs the `Enhanced Iterative Algorithm with Stop Condition' (EIASC) type-reduction method, which is more computationally efficient than the `Karnik-Mendel' type-reduction algorithm. The stability of the SAF2C is proven using the Lyapunov technique. To ensure the applicability of the proposed control scheme, SAF2C is implemented to control several dynamical systems, including a simulated MIMO hexacopter unmanned aerial vehicle (UAV) in the face of external disturbance and parameter variations. The ability of SAF2C to filter the measurement noise is demonstrated, where significant improvement is obtained using the proposed controller in the face of measurement noise. Also, the proposed closed-loop control system is applied to control other benchmark dynamic systems (e.g., a simulated autonomous underwater vehicle and inverted pendulum on a cart system) demonstrating high accuracy and robustness to variations in system parameters and external disturbance. Another contribution of this thesis is a novel stand-alone enhanced self-adaptive interval type-2 fuzzy controller named the ESAF2C algorithm, whose type-2 fuzzy parameters are tuned online using the SMC theory. This way, we expect to design a computationally efficient adaptive Type-2 fuzzy system, suitable for real-time applications by introducing the EIASC type-reducer. The proposed technique is applied on a quadcopter UAV (QUAV), where extensive simulations and real-time flight tests for a hovering QUAV under wind disturbances are also conducted to validate the efficacy of the ESAF2C. Specifically, the control performance is investigated in the face of external wind gust disturbances, generated using an industrial fan. Stability analysis of the ESAF2C control system is investigated using the Lyapunov theory. Yet another contribution of this thesis is the development of a type-2 evolving fuzzy control system (T2-EFCS) to facilitate self-learning (either from scratch or from a certain predefined rule). T2-EFCS has two phases, namely, the structure learning and the parameters learning. The structure of T2-EFCS does not require previous information about the fuzzy structure, and it can start the construction of its rules from scratch with only one rule. The rules are then added and pruned in an online fashion to achieve the desired set-point. The proposed technique is applied to control an unmanned ground vehicle (UGV) in the presence of multiple external disturbances demonstrating the robustness of the proposed control systems. The proposed approach turns out to be computationally efficient as the system employs fewer fuzzy parameters while maintaining superior control performance