Finite-Time State Estimation for an Inverted Pendulum under Input-Multiplicative Uncertainty

A sliding mode observer is presented, which is rigorously proven to achieve finite-time state estimation of a dual-parallel underactuated (i.e., single-input multi-output) cart inverted pendulum system in the presence of parametric uncertainty. A salient feature of the proposed sliding mode observer design is that a rigorous analysis is provided, which proves finite-time estimation of the complete system state in the presence of input-multiplicative parametric uncertainty. The performance of the proposed observer design is demonstrated through numerical case studies using both sliding mode control (SMC)- and linear quadratic regulator (LQR)-based closed-loop control systems. The main contribution presented here is the rigorous analysis of the finite-time state estimator under input-multiplicative parametric uncertainty in addition to a comparative numerical study that quantifies the performance improvement that is achieved by formally incorporating the proposed compensator for input-multiplicative parametric uncertainty in the observer. In summary, our results show performance improvements when applied to both SMC- and LQR-based control systems, with results that include a reduction in the root-mean square error of up to 39% in translational regulation control and a reduction of up to 29% in pendulum angular control

Finite-Time State Estimation for an Inverted Pendulum under Input-Multiplicative Uncertainty

A sliding mode observer is presented, which is rigorously proven to achieve finite-time state estimation of a dual-parallel underactuated (i.e., single-input multi-output) cart inverted pendulum system in the presence of parametric uncertainty. A salient feature of the proposed sliding mode observer design is that a rigorous analysis is provided, which proves finite-time estimation of the complete system state in the presence of input-multiplicative parametric uncertainty. The performance of the proposed observer design is demonstrated through numerical case studies using both sliding mode control (SMC)- and linear quadratic regulator (LQR)-based closed-loop control systems. The main contribution presented here is the rigorous analysis of the finite-time state estimator under input-multiplicative parametric uncertainty in addition to a comparative numerical study that quantifies the performance improvement that is achieved by formally incorporating the proposed compensator for input-multiplicative parametric uncertainty in the observer. In summary, our results show performance improvements when applied to both SMC- and LQR-based control systems, with results that include a reduction in the root-mean square error of up to 39% in translational regulation control and a reduction of up to 29% in pendulum angular control

On periodically pendulum-diven systems for underactuated locomotion: a viscoelastic jointed model

This paper investigates the locomotion principles and nonlinear dynamics of the periodically pendulum-driven (PD) systems using the case of a 2-DOF viscoelastic jointed model. As a mechanical system with underactuation degree one, the proposed system has strongly coupled nonlinearities and can be utilized as a potential benchmark for studying complicated PD systems. By mathematical modeling and non-dimensionalization of the physical system, an insight is obtained to the global system dynamics. The proposed 2-DOF viscoelastic jointed model establishes a commendable interconnection between the system dynamics and the periodically actuated force. Subsequently, the periodic locomotion principles of the actuated subsystem are elaborately studied and synthesized with the characteristic of viscoelastic element. Then the analysis of qualitative changes is conducted respectively under the varying excitation amplitude and frequency. Simulation results validate the efficiency and performance of the proposed system comparing with the conventional system

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

Event-driven observer-based smart-sensors for output feedback control of linear systems

This paper deals with a recent design of event-driven observer-based smart sensors for output feedback control of linear systems. We re-design the triggering mechanism proposed in a previously reported system with the implementation of self-sampling data smart sensors; as a result, we improve its performance. Our approach is theoretically supported by using Lyapunov theory and numerically evidenced by controlling the inverted pendulum on the cart mechanism.Postprint (published version

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 of a mechatronic system for postural control analysis

L'abstract è presente nell'allegato / the abstract is in the attachmen

Bio-inspired robotic control in underactuation: principles for energy efficacy, dynamic compliance interactions and adaptability.

Biological systems achieve energy efficient and adaptive behaviours through extensive autologous and exogenous compliant interactions. Active dynamic compliances are created and enhanced from musculoskeletal system (joint-space) to external environment (task-space) amongst the underactuated motions. Underactuated systems with viscoelastic property are similar to these biological systems, in that their self-organisation and overall tasks must be achieved by coordinating the subsystems and dynamically interacting with the environment. One important question to raise is: How can we design control systems to achieve efficient locomotion, while adapt to dynamic conditions as the living systems do? In this thesis, a trajectory planning algorithm is developed for underactuated microrobotic systems with bio-inspired self-propulsion and viscoelastic property to achieve synchronized motion in an energy efficient, adaptive and analysable manner. The geometry of the state space of the systems is explicitly utilized, such that a synchronization of the generalized coordinates is achieved in terms of geometric relations along the desired motion trajectory. As a result, the internal dynamics complexity is sufficiently reduced, the dynamic couplings are explicitly characterised, and then the underactuated dynamics are projected onto a hyper-manifold. Following such a reduction and characterization, we arrive at mappings of system compliance and integrable second-order dynamics with the passive degrees of freedom. As such, the issue of trajectory planning is converted into convenient nonlinear geometric analysis and optimal trajectory parameterization. Solutions of the reduced dynamics and the geometric relations can be obtained through an optimal motion trajectory generator. Theoretical background of the proposed approach is presented with rigorous analysis and developed in detail for a particular example. Experimental studies are conducted to verify the effectiveness of the proposed method. Towards compliance interactions with the environment, accurate modelling or prediction of nonlinear friction forces is a nontrivial whilst challenging task. Frictional instabilities are typically required to be eliminated or compensated through efficiently designed controllers. In this work, a prediction and analysis framework is designed for the self-propelled vibro-driven system, whose locomotion greatly relies on the dynamic interactions with the nonlinear frictions. This thesis proposes a combined physics-based and analytical-based approach, in a manner that non-reversible characteristic for static friction, presliding as well as pure sliding regimes are revealed, and the frictional limit boundaries are identified. Nonlinear dynamic analysis and simulation results demonstrate good captions of experimentally observed frictional characteristics, quenching of friction-induced vibrations and satisfaction of energy requirements. The thesis also performs elaborative studies on trajectory tracking. Control schemes are designed and extended for a class of underactuated systems with concrete considerations on uncertainties and disturbances. They include a collocated partial feedback control scheme, and an adaptive variable structure control scheme with an elaborately designed auxiliary control variable. Generically, adaptive control schemes using neural networks are designed to ensure trajectory tracking. Theoretical background of these methods is presented with rigorous analysis and developed in detail for particular examples. The schemes promote the utilization of linear filters in the control input to improve the system robustness. Asymptotic stability and convergence of time-varying reference trajectories for the system dynamics are shown by means of Lyapunov synthesis

Active fault-tolerant control of nonlinear systems with wind turbine application

The thesis concerns the theoretical development of Active Fault-Tolerant Control (AFTC) methods for nonlinear system via T-S multiple-modelling approach. The thesis adopted the estimation and compensation approach to AFTC within a tracking control framework. In this framework, the thesis considers several approaches to robust T-S fuzzy control and T-S fuzzy estimation: T-S fuzzy proportional multiple integral observer (PMIO); T-S fuzzy proportional-proportional integral observer (PPIO); T-S fuzzy virtual sensor (VS) based AFTC; T-S fuzzy Dynamic Output Feedback Control TSDOFC; T-S observer-based feedback control; Sliding Mode Control (SMC). The theoretical concepts have been applied to an offshore wind turbine (OWT) application study. The key developments that present in this thesis are:• The development of three active Fault Tolerant Tracking Control (FTTC) strategies for nonlinear systems described via T-S fuzzy inference modelling. The proposals combine the use of Linear Reference Model Fuzzy Control (LRMFC) with either the estimation and compensation concept or the control reconfiguration concept.• The development of T-S fuzzy observer-based state estimate fuzzy control strategy for nonlinear systems. The developed strategy has the capability to tolerate simultaneous actuator and sensor faults within tracking and regulating control framework. Additionally, a proposal to recover the Separation Principle has also been developed via the use of TSDOFC within the FTTC framework.• The proposals of two FTTC strategies based on the estimation and compensation concept for sustainable OWTs control. The proposals have introduced a significant attribute to the literature of sustainable OWTs control via (1) Obviating the need for Fault Detection and Diagnosis (FDD) unit, (2) Providing useful information to evaluate fault severity via the fault estimation signals.• The development of FTTC architecture for OWTs that combines the use of TSDOFC and a form of cascaded observers (cascaded analytical redundancy). This architecture is proposed in order to ensure the robustness of both the TSDOFC and the EWS estimator against the generator and rotor speed sensor faults.• A sliding mode baseline controller has been proposed within three FTTC strategies for sustainable OWTs control. The proposals utilise the inherent robustness of the SMC to tolerate some matched faults without the need for analytical redundancy. Following this, the combination of SMC and estimation and compensation framework proposed to ensure the close-loop system robustness to various faults.• Within the framework of the developed T-S fuzzy based FTTC strategies, a new perspective to reduce the T-S fuzzy control design conservatism problem has been proposed via the use of different control techniques that demand less design constraints. Moreover, within the SMC based FTTC, an investigation is given to demonstrate the SMC robustness against a wider than usual set of faults is enhanced via designing the sliding surface with minimum dimension of the feedback signals

Adaptive Augmentation of Non-Minimum Phase Flexible Aerospace Systems

This work demonstrates the efficacy of direct adaptive augmentation on a robotic flexible system as an analogue of a large flexible aerospace structure such as a launch vehicle or aircraft. To that end, a robot was constructed as a control system testbed. This robot, named “Penny,” contains the command and data acquisition capabilities necessary to influence and record system state data, including the flex states of its flexible structures. This robot was tested in two configurations, one with a vertically cantilevered flexible beam, and one with a flexible inverted pendulum (a flexible cart-pole system). The physical system was then characterized so that linear analysis and control design could be performed. These characterizations resulted in linear and nonlinear models developed for each testing configuration. The linear models were used to design linear controllers to regulate the nominal plant’s dynamical states. These controllers were then augmented with direct adaptive output regulation and disturbance accommodation. To accomplish this, sensor blending was used to shape the output such that the nonminimum phase open loop plant appears to be minimum phase to the controller. It was subsequently shown that augmenting linear controllers with direct adaptive output regulation and disturbance accommodation was effective in enhancing system performance and mitigating oscillation in the flexible structures through the system’s own actuation effort