Regional Pole Placement Design Based Stabilization for Cart Inverted Pendulum System

The inverted pendulum has been considered as a benchmark control problem due to its nonlinearity and stabilization around the unstable equilibrium point. To achieve stabilization, it is well known that all the closed loop system poles should lie in left half of s-plane. In present work, different approaches have taken to shift the system poles to left half of the plane. At first Linear Quadratic Regulator (LQR) is used, where the desired pole locations can be achieved by suitably selecting weight matrix of cost function. With this guaranteed cost control scheme, one does not have to bother about specifying closed-loop poles. Next, a two loop PID is designed based on pole matching conditions. Where the closed loop with unknown controller coefficient characteristic equation is compared with desired characteristics, to find out the controller gains. In both the methods, one has to deal with point wise pole placing, which can be tricky sometimes. With the recent development of LMIs tool, regional pole placement is well suited to achieve the goal. At last, a regional pole placement controller is synthesized, where desired specifications are transformed into LMI regions. In present case, a conical sector of left half plane is taken so that stabilisation with better transient performance can be achieve

Active Structural Control of Single and Multi-Span Beam Structures Subjected to Transient Loads

This study directly addresses the problem of active control of beam structures under the action of moving masses. In this regard, experimental implementations of the particular active control solutions are still rarely seen in the literature. The main objective is to experimentally implement and validate active control solutions for two small-scale test stands with the aim to reduce the structural deflection. The first supporting structure is modelled as an Euler–Bernoulli simply supported beam, acted upon by moving masses of different weights and velocities. The experimental implementation of the proposed optimal controller poses a particular set of challenges as compared with numerical solutions. Specifically, it can include errors due to discretization and the states cannot be directly measured. The resulting limitations of classical optimal observer techniques are stated and consequently the states are estimated by a method utilizing the mode shapes. It is shown both numerically and experimentally that using electromagnetic actuation, a reduced order controller designed using a time-varying algorithm, provides a reduction of the maximum deflection of up to 38% as compared with the uncontrolled structure. Herein an augmented system model is utilised, which includes the moving mass in the system equation. The controller performance and robustness were tested against a representative set of possible moving load parameters. In consequence of the variations in moving mass weight and speed, the controller gain requires a supplementary adaptation. A simple algorithm that schedules the gain as a function of the weight and speed of the moving mass can achieve both a good performance and an adjustment of the control effort to the specific design requirements. In the second part of this study cubic and linear displacement feedback control approaches are studied experimentally for a simply supported beam as well as for the two-span continuous beam. The two-span beam structure is modelled by approximating the support by spring damper elements of high stiffness and damping coefficient. Piezoelectric macro fibre composites serve as actuators. The control methods are, compared to the previous approach, more straightforward to implement and can handle a stream of moving masses. However, optimality and stability cannot be guaranteed and have to be validated experimentally. The linear displacement feedback shows better performance for low weights of the moving masses whereas the cubic displacement feedback achieves higher deflection reduction for higher weights. In the last part, constrained model predictive control is studied numerically for both of the structures. This is currently the only control approach which can take into account saturation limits explicitly by quadratic programming. In this way, better performance is achieved for both test structures as compared to the displacement feedback control approaches

Two-Craft Coulomb Formation Study about Circular Orbits and Libration Points

This dissertation investigates the dynamics and control of a two-craft Coulomb formation in circular orbits and at libration points; it addresses relative equilibria, stability and optimal reconfigurations of such formations. The relative equilibria of a two-craft tether formation connected by line-of-sight elastic forces moving in circular orbits and at libration points are investigated. In circular Earth orbits and Earth-Moon libration points, the radial, along-track, and orbit normal great circle equilibria conditions are found. An example of modeling the tether force using Coulomb force is discussed. Furthermore, the non-great-circle equilibria conditions for a two-spacecraft tether structure in circular Earth orbit and at collinear libration points are developed. Then the linearized dynamics and stability analysis of a 2-craft Coulomb formation at Earth- Moon libration points are studied. For orbit-radial equilibrium, Coulomb forces control the relative distance between the two satellites. The gravity gradient torques on the formation due to the two planets help stabilize the formation. Similar analysis is performed for alongtrack and orbit-normal relative equilibrium configurations. Where necessary, the craft use a hybrid thrusting-electrostatic actuation system. The two-craft dynamics at the libration points provide a general framework with circular Earth orbit dynamics forming a special case. In the presence of differential solar drag perturbations, a Lyapunov feedback controller is designed to stabilize a radial equilibrium, two-craft Coulomb formation at collinear libration points. The second part of the thesis investigates optimal reconfigurations of two-craft Coulomb formations in circular Earth orbits by applying nonlinear optimal control techniques. The objective of these reconfigurations is to maneuver the two-craft formation between two charged equilibria configurations. The reconfiguration of spacecraft is posed as an optimization problem using the calculus of variations approach. The optimality criteria are minimum time, minimum acceleration of the separation distance, minimum Coulomb and electric propulsion fuel usage, and minimum electrical power consumption. The continuous time problem is discretized using a pseudospectral method, and the resulting finite dimensional problem is solved using a sequential quadratic programming algorithm. The software package, DIDO, implements this approach. This second part illustrates how pseudospectral methods significantly simplify the solution-finding process

Galloping and VIV control of square-section cylinder utilizing direct opposing smart control force

An adaptive fuzzy sliding mode controller (AFSMC) is adopted to reduce the 2D flow-induced vibration of an elastically supported square-section cylinder, free to oscillate in stream-wise andtransverse directions in both lock-in and galloping regions. The AFSMC strategy consists of a fuzzy logic inference system intended to follow a sliding-mode controller (SMC), and a robust control system designed to retrieve the variance between the sliding mode and fuzzy controllers.  The sprung square cylinder first experiences vortex-induced vibrations with increasing Reynolds number, and then, after passing the critical flow velocity, it confronts high-amplitude and low-frequencyvibrations of galloping owning to its sharp corners. A co-simulation platform is considered by linking the AFSMC system modeled in Matlab/Simulink to the plant model implemented in Fluent, aiming at the calculation of opposite control force needed for comprehensive annihilation of the cylinder motions. Based on the performed numerical simulations, it becomes clear that the utilized active control system has successfully mitigated the two-degree-of-freedom vibrations of a square cylinder in both the lock-in region and galloping zone. Here, the vibration amplitudes in the transverse andstreamwise directions have decreased by 93% and 94%, for the lock-in region and 93% and 99%, for the galloping zone, respectively

Adaptive and learning-based formation control of swarm robots

Autonomous aerial and wheeled mobile robots play a major role in tasks such as search and rescue, transportation, monitoring, and inspection. However, these operations are faced with a few open challenges including robust autonomy, and adaptive coordination based on the environment and operating conditions, particularly in swarm robots with limited communication and perception capabilities. Furthermore, the computational complexity increases exponentially with the number of robots in the swarm. This thesis examines two different aspects of the formation control problem. On the one hand, we investigate how formation could be performed by swarm robots with limited communication and perception (e.g., Crazyflie nano quadrotor). On the other hand, we explore human-swarm interaction (HSI) and different shared-control mechanisms between human and swarm robots (e.g., BristleBot) for artistic creation. In particular, we combine bio-inspired (i.e., flocking, foraging) techniques with learning-based control strategies (using artificial neural networks) for adaptive control of multi- robots. We first review how learning-based control and networked dynamical systems can be used to assign distributed and decentralized policies to individual robots such that the desired formation emerges from their collective behavior. We proceed by presenting a novel flocking control for UAV swarm using deep reinforcement learning. We formulate the flocking formation problem as a partially observable Markov decision process (POMDP), and consider a leader-follower configuration, where consensus among all UAVs is used to train a shared control policy, and each UAV performs actions based on the local information it collects. In addition, to avoid collision among UAVs and guarantee flocking and navigation, a reward function is added with the global flocking maintenance, mutual reward, and a collision penalty. We adapt deep deterministic policy gradient (DDPG) with centralized training and decentralized execution to obtain the flocking control policy using actor-critic networks and a global state space matrix. In the context of swarm robotics in arts, we investigate how the formation paradigm can serve as an interaction modality for artists to aesthetically utilize swarms. In particular, we explore particle swarm optimization (PSO) and random walk to control the communication between a team of robots with swarming behavior for musical creation

Model Order Reduction

An increasing complexity of models used to predict real-world systems leads to the need for algorithms to replace complex models with far simpler ones, while preserving the accuracy of the predictions. This three-volume handbook covers methods as well as applications. This third volume focuses on applications in engineering, biomedical engineering, computational physics and computer science

Application of non-linear system identification approaches to modelling, analysis, and control of fluid flows.

Flow control has become a topic of great importance for several applications, ranging from commercial aircraft, to intercontinental pipes and skyscrapers. In these applications, and many more, the interaction with a fluid flow can have a significant influence on the performance of the system. In many cases the fluids encountered are turbulent and detrimental to the latter. Several attempts have been made to solve this problem. However, due to the non-linearity and infinite dimensionality of fluid flows and their governing equations, a complete understanding of turbulent behaviour and a feasible control approach has not been obtained. In this thesis, model reduction approaches that exploit non-linear system identification are applied using data obtained from numerical simulations of turbulent three-dimensional channel flow, and two-dimensional flow over the backward facing step. A multiple-input multiple-output model, consisting of 27 sub-structures, is obtained for the fluctuations of the velocity components of the channel flow. A single-input single-output model for fluctuations of the pressure coefficient, and two multiple-input single-output models for fluctuations of the velocity magnitude are obtained in flow over the BFS. A non-linear model predictive control strategy is designed using identified one- and multi-step ahead predictors, with the inclusion of integral action for robustness. The proposed control approach incorporates a non-linear model without the need for expensive non-linear optimizations. Finally, a frequency domain analysis of unmanipulated turbulent flow is perfumed using five systems. Higher order generalized frequency response functions (GFRF) are computed to study the non-linear energy transfer phenomena. A more detailed investigation is performed using the output FRF (OFRF), which can elucidate the contribution of the n-th order frequency response to the output frequency response