Comparative Study of Takagi-Sugeno-Kang and Madani Algorithms in Type-1 and Interval Type-2 Fuzzy Control for Self-Balancing Wheelchairs

This study examines the effectiveness of four different fuzzy logic controllers in self-balancing wheelchairs. The controllers under consideration are Type-1 Takagi-Sugeno-Kang (TSK) FLC, Interval Type-2 TSK FLC, Type-1 Mamdani FLC, and Interval Type-2 Mamdani FLC. A MATLAB-based simulation environment serves for the evaluation, focusing on key performance indicators like percentage overshoot, rise time, settling time, and displacement. Two testing methodologies were designed to simulate both ideal conditions and real-world hardware limitations. The simulations reveal distinct advantages for each controller type. For example, Type-1 TSK excels in minimizing overshoot but requires higher force. Interval Type-2 TSK shows the quickest settling times but needs the most force. Type-1 Mamdani has the fastest rise time with the lowest force requirement but experiences a higher percentage of overshoot. Interval Type-2 Mamdani offers balanced performance across all metrics. When a 2.7 N control input cap is imposed, Type-2 controllers prove notably more efficient in minimizing overshoot. These results offer valuable insights for future design and real-world application of self-balancing wheelchairs. Further studies are recommended for the empirical testing and refinement of these controllers, especially since the initial findings were limited to four-wheeled self-balancing robotic wheelchairs

Adaptive Neuro-Fuzzy Control Approach for a Single Inverted Pendulum System

The inverted pendulum is an under-actuated and nonlinear system, which is also unstable. It is a single-input double-output system, where only one output is directly actuated. This paper investigates a single intelligent control system using an adaptive neuro-fuzzy inference system (ANFIS) to stabilize the inverted pendulum system while tracking the desired position. The non-linear inverted pendulum system was modelled and built using MATLAB Simulink. An adaptive neuro-fuzzy logic controller was implemented and its performance was compared with a Sugeno-fuzzy inference system in both simulation and real experiment. The ANFIS controller could reach its desired new destination in 1.5 s and could stabilize the entire system in 2.2 s in the simulation, while in the experiment it took 1.7 s to reach stability. Results from the simulation and experiment showed that ANFIS had better performance compared to the Sugeno-fuzzy controller as it provided faster and smoother response and much less steady-state error

Alternative controller design for rotary inverted pendulum

The inverted pendulum has been considered a classical control problem. Two designs of inverted pendulum are planar and rotary with a nonlinear unstable system characteristic. Inverted pendulum systems are nonlinear. They can be used for testing and studying various observers and controllers. Control of a rotary inverted pendulum is studied here. This paper proposes stabilization of the rotary inverted pendulum at its upright position by using full-state controller. Full-state controllers are designed by using different damping ratios. MATLAB simulation results and the experimental results are taken for 10 degrees step for 5 seconds. The best controller is chosen for SRV02-Rotary inverted pendulum by looking at the simulation and experimental results

Modeling and controller design of a single-linked inverted pendulum using optimized fuzzy logic controller approach

Inverted pendulum (IP) is an underactuated systems, since the input of the system is the force applied to the cart and the outputs are the cart position and pendulum angle (SIMO) system, which makes this system is highly nonlinear and unstable. Inverted pendulum considered as the one the most famous classical systems in the field of control and mechatronics. This project focuses on the design of a fuzzy controller to stabilize an inverted pendulum in a vertical position. A continuous correction mechanism is required to move the cart in a certain way in order to balance the pendulum to prevent it from falling down. This project started by a derivation of the mathematical model of the single linked inverted pendulum system by using Euler-Lagrange method. After that, a fuzzy logic controller (FLC) based Sugeno inference system was designed and genetic algorithm was used to tune the parameters of the controller using MATLAB software. Both controllers were tested using real time inverted pendulum. Experimental results showed that optimized FLC was much better than Sugeno FLC in terms of settling time, overshoot and steady state error

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

Particle swarm optimization and spiral dynamic algorithm-based interval type-2 fuzzy logic control of triple-link inverted pendulum system: A comparative assessment

This paper presents investigations into the development of an interval type-2 fuzzy logic control (IT2FLC) mechanism integrated with particle swarm optimization and spiral dynamic algorithm. The particle swarm optimization and spiral dynamic algorithm are used for enhanced performance of the IT2FLC by finding optimised values for input and output controller gains and parameter values of IT2FLC membership function as comparison purpose in order to identify better solution for the system. A new model of triple-link inverted pendulum on two-wheels system, developed within SimWise 4D software environment and integrated with Matlab/Simulink for control purpose. Several tests comprising system stabilization, disturbance rejection and convergence accuracy of the algorithms are carried out to demonstrate the robustness of the control approach. It is shown that the particle swarm optimization-based control mechanism performs better than the spiral dynamic algorithm-based control in terms of system stability, disturbance rejection and reduce noise. Moreover, the particle swarm optimization-based IT2FLC shows better performance in comparison to previous research. It is envisaged that this system and control algorithm can be very useful for the development of a mobile robot with extended functionality

The Implementation and Comparison of Fuzzy Logic Control Systems to Modern Control Methods on Low-Cost Hardware

Modern control engineering provides many options to automate systems for which a mathematical model is required. Another control does not rely on the mathematical model of the system and is known as fuzzy logic control. In this study, a literature review is conducted on existing control systems strategies such as proportional integral and derivative (PID), linear quadratic regulator (LQR), and fuzzy logic controller (FLC), the complexity of the systems they control, and their strengths and weaknesses. In addition, a series of experiments are conducted, both through simulations in MATLAB Simulink and using their implementation using the actual physical hardware to test the effectiveness of said controllers. The effect of changing fuzzy logic membership functions is also determined. The settling times of controllers are compared using a physical prototype of a mechanical arm. Lastly, dead zone correction techniques are addressed and implemented

Second Order Integral Fuzzy Logic Control Based Rocket Tracking Control

Fuzzy logic is a logic that has a degree of membership in the vulnerable 0 to 1. Fuzzy logic is used to translate a quantity that is expressed using language. Fuzzy logic is used as a control system because this control process is relatively easy and flexible to design without involving complex mathematical models of the system to be controlled. The purpose of this paper is to present a fuzzy control system implemented in a rocket tracking control system. The fuzzy control system is used to keep the rocket on track and traveling at a certain speed. The signal from the fuzzy logic control system is used to control the rocket thrust. The fuzzy Logic System was chosen as the controller because it is able to work well on non-linear systems and offers convenience in program design. Fuzzy logic systems have a weakness when working on systems that require very fast control such as rockets. With this problem, fuzzy logic is modified by adding second-order integral control to the modified fuzzy logic. The proposed algorithm shows that the missile can slide according to the ramp path at 12 m altitude of 12.78 at 12 seconds with a steady-state error of 0.78 under FLC control, at 10 m altitude of 10.68 at 10 seconds with a steady-state error of 0.68 with control integral FCL, at a height of 4 m is 4.689 at 4 seconds with a steady-state error of 0.689 with a second-order integral control of FCL. The missile can also slide according to the parabolic path with the second-order integral control of FCL at an altitude of 15.47 in the 4th minute with a steady-state error of 0