Design of Sliding Mode PID Controller with Improved reaching laws for Nonlinear Systems

In this thesis, advanced design technique in sliding mode control (SMC) is presented with focus on PID (Proportional-Integral-Derivative) type Sliding surfaces based Sliding mode control with improved power rate exponential reaching law for Non-linear systems using Modified Particle Swarm Optimization (MPSO). To handle large non-linearities directly, sliding mode controller based on PID-type sliding surface has been designed in this work, where Integral term ensures fast finite convergence time. The controller parameter for various modified structures can be estimated using Modified PSO, which is used as an offline optimization technique. Various reaching law were implemented leading to the proposed improved exponential power rate reaching law, which also improves the finite convergence time. To implement the proposed algorithm, nonlinear mathematical model has to be decrypted without linearizing, and used for the simulation purposes. Their performance is studied using simulations to prove the proposed behavior. The problem of chattering has been overcome by using boundary method and also second order sliding mode method. PI-type sliding surface based second order sliding mode controller with PD surface based SMC compensation is also proposed and implemented. The proposed algorithms have been analyzed using Lyapunov stability criteria. The robustness of the method is provided using simulation results including disturbance and 10% variation in system parameters. Finally process control based hardware is implemented (conical tank system)

Model-free controller design for nonlinear underactuated systems with uncertainties and disturbances by using extended state observer based chattering-free sliding mode control

MakaleWOS:000912458400001Most of the control strategies require a mathematical model or reasonable knowledge that is difficult to obtain for complex systems. Model-free control is a good alternative to avoid the difficulties and complex modeling procedures, especially if the knowledge about the system is insufficient. This paper presents a new control scheme completely independent of the system model. The proposed scheme combines sliding mode control (SMC) with intelligent proportional integral derivative (iPID) control based on a local model and extended state observer (ESO). Although the iPID control makes the proposed method model-free, it cannot guarantee that the tracking errors converge to zero asymptotically except the system is in a steady-state regime. Therefore, the SMC is added to the control scheme to ensure the convergence by minimizing the estimation errors of the observer. The proposed iPIDSMC controller is tested in the presence of different parameter variations and external disturbances on an inverted pendulum - cart (IPC), which is a highly unstable underactuated system with nonlinear coupled dynamics. The proposed controller is compared with the PID, iPID and Hierarchical Sliding Mode Control (HSMC) for a clearer evaluation. Simulation results showed that the proposed controller is extremely insensitive to parameter variations, matched and mismatched disturbances and the control signal of the proposed method is chattering-free, even though it is based on a discontinuous control action

Modified PSO based PID Sliding Mode Control using Improved Reaching Law for Nonlinear systems

In this paper, a new model based nonlinear control technique, called PID (Proportional-Integral-Derivative) type sliding surface based sliding mode control is designed using improved reaching law. To improve the performance of the second order nonlinear differential equations with unknown parameters modified particle swarm intelligent optimization (MPSO) is used for the optimized parameters. This paper throws light on the sliding surface design, on the proposed power rate exponential reaching law, parameters optimization using modified particle swarm optimization and highlights the important features of adding an integral term in the sliding mode such as robustness and higher convergence, through extensive mathematical modeling. Siding mode control law is derived using Lyapunov stability approach and its asymptotic stability is proved mathematically and simulations showing its validity. MPSO PID-type Sliding mode control will stabilize the highly nonlinear systems, will compensate disturbances and uncertainty and reduces tracking errors. Simulations and experimental application is done on the non-linear systems and are presented to make a quantitative comparison.Comment: arXiv admin note: substantial text overlap with arXiv:2207.1112

Control of DC Motor Using Integral State Feedback and Comparison with PID: Simulation and Arduino Implementation

The Direct Current (DC) motor is widely applied in various implementations. The main problem in the DC motor is controlling the angular speed on the specific reference. This research then proposed an integral state feedback design for tracking control in DC motor, with Simulink Matlab simulation and the Arduino hardware implementation. The results will be compared with the implementation of the PID controller. The integral state feedback controller can handle the system to reach the setpoint with good performance in the simulations, even with changing different poles and setpoints. In the hardware implementation, the current sensor (INA219) and encoder sensor are used since all state variables need to be calculated. Based on the result, the controller can reach the setpoint stably with oscillation. Similar results are showed in simulations with different setpoints. Compared with the PID Controller, the integral state feedback controller has a better response with faster rise time and faster settling time

Implementation and Control of an Inverted Pendulum on a Cart

An Inverted Pendulum on a Cart is a common system often used as a benchmark problem for control systems. The system consists of a cart that can move in one direction on the horizontal plane and a pendulum attached to the cart through a hinge point. The pendulum can rotate 360° on the plane made up of the vertical direction and the direction the cart can move. The system is controlled by applying a force to the cart, to make it move. This thesis consists of two goals. The first goal is to build a lab model of the Inverted Pendulum on a Cart system. The second goal is to create a controller that can swing the pendulum from a pendulum down position to a pendulum up position, and balance it in this position. The lab model is built using a track that the cart can move along, a stepper motor for applying force to the cart and a microcontroller for controlling the system. The pendulum angle and the cart position are measured using incremental encoders. A Mathematical model of the system have been derived. This forms the basis for the design of the controller and is also used for simulating and testing the system and controller in MATLAB/Simulink before it is implemented on the real system. The controller consists of three parts. An extended Kalman filter is implemented to estimate the non-measurable state. An energy-based controller is used to swing the pendulum from the down position to the up position. This controller regulates the energy in the pendulum to be close to the energy the pendulum should have when it is balanced in the upright position. When the pendulum is close to the upright position the controller will switch to a linear quadratic regulator to balance the pendulum. This controller is based on a linearized version of the mathematical system model. The lab model and the controllers have been successfully built and implemented

Design, Control, and Optimization of Robots with Advanced Energy Regenerative Drive Systems

We investigate the control and optimization of robots with ultracapacitor based regenerative drive systems. A subset of the robot joints are conventional, in the sense that external power is used for actuation. Other joints are energetically self-contained passive systems that use ultracapacitors for energy storage. An electrical interconnection known as the star configuration is considered for the regenerative drives that allows for direct electric energy redistribution among joints, and enables higher energy utilization efficiencies. A semi-active virtual control strategy is used to achieve control objectives. We find closed-form expressions for the optimal robot and actuator parameters (link lengths, gear ratios, etc.) that maximize energy regeneration between any two times, given motion trajectories. In addition, we solve several trajectory optimization problems for maximizing energy regeneration that admit closed-form solutions, given system parameters. Optimal solutions are shown to be global and unique. In addition, closed-form expressions are provided for the maximum attainable energy. This theoretical maximum places limits on the amount of energy that can be recovered. Numerical examples are provided in each case to demonstrate the results. For problems that don\u27t admit analytical solutions, we formulate the general nonlinear optimal control problem, and solve it numerically, based on the direct collocation method. The optimization problem, its numerical solution and an experimental evaluation are demonstrated using a PUMA manipulator with custom regenerative drives. Power flows, stored regenerative energy and efficiency are evaluated. Experimental results show that when following optimal trajectories, a reduction of about 10-22% in energy consumption can be achieved. Furthermore, we present the design, control, and experimental evaluation of an energy regenerative powered transfemoral prosthesis. Our prosthesis prototype is comprised of a passive ankle, and an active regenerative knee joint. A novel varying impedance control approach controls the prosthesis in both the stance and swing phase of the gait cycle, while explicitly considering energy regeneration. Experimental evaluation is done with an amputee test subject walking at different speeds on a treadmill. The results validate the effectiveness of the control method. In addition, net energy regeneration is achieved while walking with near-natural gait across all speeds

Solar Panel Control System Using an Intelligent Control: T2FSMC and Firefly Algorithm

Solar panel is a solar energy converter to electrical energy. On solar tracker, there is a controller which sets the movement of solar panel such that it is perpendicular with solar rays. Previous research had designed Type 2 Fuzzy Sliding Mode Control (T2FSMC) controller to control the position of solar panel. However, there was trial and error process to determine gain scale factor so the development of optimization method is needed. This paper aims to modify gain scale factor using Firefly algorithm to increase performance of system. The simulation shows that T2FSMC Firefly has better performance than T2FSMC. T2FSMC Firefly shows the increase of performance on rise time, settling time, and integral time absolute error

Observer-based robust fault estimation for fault-tolerant control

A control system is fault-tolerant if it possesses the capability of optimizing the system stability and admissible performance subject to bounded faults, complexity and modeling uncertainty. Based on this definition this thesis is concerned with the theoretical developments of the combination of robust fault estimation (FE) and robust active fault tolerant control (AFTC) for systems with both faults and uncertainties.This thesis develops robust strategies for AFTC involving a joint problem of on-line robust FE and robust adaptive control. The disturbances and modeling uncertainty affect the FE and FTC performance. Hence, the proposed robust observer-based fault estimator schemes are combined with several control methods to achieve the desired system performance and robust active fault tolerance. The controller approaches involve concepts of output feedback control, adaptive control, robust observer-based state feedback control. A new robust FE method has been developed initially to take into account the joint effect of both fault and disturbance signals, thereby rejecting the disturbances and enhancing the accuracy of the fault estimation. This is then extended to encompass the robustness with respect to modeling uncertainty.As an extension to the robust FE and FTC scheme a further development is made for direct application to smooth non-linear systems via the use of linear parameter-varying systems (LPV) modeling.The main contributions of the research are thus:- The development of a robust observer-based FE method and integration design for the FE and AFTC systems with the bounded time derivative fault magnitudes, providing the solution based on linear matrix inequality (LMI) methodology. A stability proof for the integrated design of the robust FE within the FTC system.- An improvement is given to the proposed robust observer-based FE method and integrated design for FE and AFTC systems under the existence of different disturbance structures.- New guidance for the choice of learning rate of the robust FE algorithm.- Some improvement compared with the recent literature by considering the FTC problem in a more general way, for example by using LPV modeling