Optimal control-based methodology for active vibration control of pedestrian structures

This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this record.Civil structures such as floor systems with open-plan layouts or lightweight footbridges can be susceptible to excessive levels of vibrations caused by human activities. Active vibration control (AVC) via inertial-mass actuators has been shown to be a viable technique to mitigate vibrations, allowing structures to satisfy vibration serviceability limits. It is generally considered that the determination of the optimal placement of sensors and actuators together with the output feedback gains leads to a tradeoff between the regulation performance and the control effort. However, the "optimal" settings may not have the desired effect when implemented because simplifications assumed in the control scheme components may not be valid and/or the actuator/sensor limitations are not considered. This work proposes a design methodology for multi-input multi-output vibration control of pedestrian structures to simultaneously obtain the sensor/actuator placement and the control law. This novel methodology consists of minimising a performance index that includes all the significant practical issues involved when inertial-mass actuators and accelerometers are used to implement a direct velocity feedback in practice. Experimental results obtained on an in-service indoor walkway confirm the viability of the proposed methodology.The authors acknowledge the financial support provided by the Fundación Caja Madrid through the grant “II Convocatoria de Becas de Movilidad para profesores de las universidades públicas de Madrid durante el curso académico 2012/2013” and also the UK Engineering and Physical Sciences Research Council (EPSRC) though grant EP/J004081/2 entitled “Advanced Technologies for Mitigation of Human-Induced Vibration”

A Novel Predictor Based Framework to Improve Mobility of High Speed Teleoperated Unmanned Ground Vehicles

Teleoperated Unmanned Ground Vehicles (UGVs) have been widely used in applications when driver safety, mission eciency or mission cost is a major concern. One major challenge with teleoperating a UGV is that communication delays can significantly affect the mobility performance of the vehicle and make teleoperated driving tasks very challenging especially at high speeds. In this dissertation, a predictor based framework with predictors in a new form and a blended architecture are developed to compensate effects of delays through signal prediction, thereby improving vehicle mobility performance. The novelty of the framework is that minimal information about the governing equations of the system is required to compensate delays and, thus, the prediction is robust to modeling errors. This dissertation first investigates a model-free solution and develops a predictor that does not require information about the vehicle dynamics or human operators' motion for prediction. Compared to the existing model-free methods, neither assumptions about the particular way the vehicle moves, nor knowledge about the noise characteristics that drive the existing predictive filters are needed. Its stability and performance are studied and a predictor design procedure is presented. Secondly, a blended architecture is developed to blend the outputs of the model-free predictor with those of a steering feedforward loop that relies on minimal information about vehicle lateral response. Better prediction accuracy is observed based on open-loop virtual testing with the blended architecture compared to using either the model-free predictors or the model-based feedforward loop alone. The mobility performance of teleoperated vehicles with delays and the predictor based framework are evaluated in this dissertation with human-in-the-loop experiments using both simulated and physical vehicles in teleoperation mode. Predictor based framework is shown to provide a statistically significant improvement in vehicle mobility and drivability in the experiments performed.PHDMechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/146026/1/zhengys_1.pd

Stability results for constrained dynamical systems

Differential-Algebraic Equations (DAE) provide an appropriate framework to model and analyse dynamic systems with constraints. This framework facilitates modelling of the system behaviour through natural physical variables of the system, while preserving the topological constraints of the system. The main purpose of this dissertation is to investigate stability properties of two important classes of DAEs. We consider some special cases of Linear Time Invariant (LTI) DAEs with control inputs and outputs, and also a special class of Linear switched DAEs. In the first part of the thesis, we consider LTI systems, where we focus on two properties: passivity and a generalization of passivity and small gain theorems called mixed property. These properties play an important role in the control design of large-scale interconnected systems. An important bottleneck for a design based on the aforementioned properties is their verification. Hence we intend to develop easily verifiable conditions to check passivity and mixedness of Single Input Single Output (SISO) and Multiple Input Multiple Output (MIMO) DAEs. For linear switched DAEs, we focus on the Lyapunov stability and this problem forms the basis for the second part of the thesis. In this part, we try to find conditions under which there exists a common Lyapunov function for all modes of the switched system, thus guaranteeing exponential stability of the switched system. These results are primarily developed for continuous-time systems. However, simulation and control design of a dynamic system requires a discrete-time representation of the system that we are interested in. Thus, it is critical to establish whether discrete-time systems, inherit fundamental properties of the continuous-time systems from which they are derived. Hence, the third part of our thesis is dedicated to the problems of preserving passivity, mixedness and Lyapunov stability under discretization. In this part, we examine several existing discretization methods and find conditions under which they preserve the stability properties discussed in the thesis

Stability results for constrained dynamical systems

Differential-Algebraic Equations (DAE) provide an appropriate framework to model and analyse dynamic systems with constraints. This framework facilitates modelling of the system behaviour through natural physical variables of the system, while preserving the topological constraints of the system. The main purpose of this dissertation is to investigate stability properties of two important classes of DAEs. We consider some special cases of Linear Time Invariant (LTI) DAEs with control inputs and outputs, and also a special class of Linear switched DAEs. In the first part of the thesis, we consider LTI systems, where we focus on two properties: passivity and a generalization of passivity and small gain theorems called mixed property. These properties play an important role in the control design of large-scale interconnected systems. An important bottleneck for a design based on the aforementioned properties is their verification. Hence we intend to develop easily verifiable conditions to check passivity and mixedness of Single Input Single Output (SISO) and Multiple Input Multiple Output (MIMO) DAEs. For linear switched DAEs, we focus on the Lyapunov stability and this problem forms the basis for the second part of the thesis. In this part, we try to find conditions under which there exists a common Lyapunov function for all modes of the switched system, thus guaranteeing exponential stability of the switched system. These results are primarily developed for continuous-time systems. However, simulation and control design of a dynamic system requires a discrete-time representation of the system that we are interested in. Thus, it is critical to establish whether discrete-time systems, inherit fundamental properties of the continuous-time systems from which they are derived. Hence, the third part of our thesis is dedicated to the problems of preserving passivity, mixedness and Lyapunov stability under discretization. In this part, we examine several existing discretization methods and find conditions under which they preserve the stability properties discussed in the thesis

A "mixed" small gain and passivity theorem in the frequency domain

We show that the negative feedback interconnection of two causal, stable, linear time-invariant systems, with a "mixed" small gain and passivity property, is guaranteed to be finite-gain stable. This "mixed" small gain and passivity property refers to the characteristic that, at a particular frequency, systems in the feedback interconnection are either both "input and output strictly passive"; or both have "gain less than one"; or are both "input and output strictly passive" and simultaneously both have "gain less than one". The "mixed" small gain and passivity property is described mathematically using the notion of dissipativity of systems, and finite-gain stability of the interconnection is proven via a stability result for dissipative interconnected systems

Characterising Discrete-time Linear Systems With The "mixed" Positive Real And Bounded Real Property

In this paper, we present characterisations of linear, shift-invariant, discrete-time systems that exhibit mixtures of small gain-type properties and positive real-type behaviours in a certain manner. These "mixed" systems are already fairly well characterised in the continuous-time domain, but the widespread adoption of digital controllers makes it necessary to verify whether commonly used discretisation procedures preserve the characteristic of "mixedness". First, we analyse the effects of classical discretisation methods on the "mixed" property using Nyquist methods. A frequency domain feedback stability result is then presented. Finally, we develop a spectral-based characterisation of "mixed" discrete-time systems which provides a practical computational test that can also be applied to the MIMO case. Several examples validate the developed theory.205259268Anderson, B.D.O., Failures of adaptive control theory and their resolution (2005) Commun. Inf. 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