This paper investigates the control of a single-link flexible robot manipulator with a tip payload appointed to rotate about 2 perpendicular axes in space. The control objective is to regulate the rigid body rotation ...
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This paper investigates the control of a single-link flexible robot manipulator with a tip payload appointed to rotate about 2 perpendicular axes in space. The control objective is to regulate the rigid body rotation of the manipulator with guaranteeing the stability of its vibration in the presence of exogenous disturbances. To achieve this, a Lyapunov-based control design procedure is used and accomplished in some steps. First, the partial differential equation (PDE) dynamic model governing the rigid-flexible hybrid motion of the arm is derived by applying Hamilton's principle. Next, based on the developed PDE model, an adaptive robust boundary control is established using the Lyapunov redesign approach. To this end, an adaptation mechanism is proposed so that the robust boundary control gains are dynamically updated online and there is no need for prior knowledge of disturbance upper bounds. The actuators and sensors are fully implemented at the arm boundary without using distributed actuators or sensors. Furthermore, in order to avoid control errors resulting from the spillover, control design is directly based on infinite-dimensional PDE model without resorting to model truncation. Simulation results illustrate the efficacy of the considered method.
We solve the problem of stabilizing a general class of linear first-order hyperbolic systems using actuation at both boundaries of the spatial domain. We design a novel Fredholm transformation similarly to backsteppin...
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We solve the problem of stabilizing a general class of linear first-order hyperbolic systems using actuation at both boundaries of the spatial domain. We design a novel Fredholm transformation similarly to backstepping approaches to derive a boundary controller and a boundary observer enabling stabilization by output feedback. This yields an explicit full-state feedback law that achieves the theoretical lower bound for convergence to zero.
We introduce and solve the stabilization problem of a transport partial differential equation (PDE)/nonlinear ordinary differential equation (ODE) cascade, in which the PDE state evolves on a domain whose length depen...
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We introduce and solve the stabilization problem of a transport partial differential equation (PDE)/nonlinear ordinary differential equation (ODE) cascade, in which the PDE state evolves on a domain whose length depends on the boundary values of the PDE state itself. In particular. we develop a predictor-feedback control design, which compensates such transport PDE dynamics. We prove local asymptotic stability of the closed-loop system in the C(1 )norm of the PDE state employing a Lyapunov-like argument and introducing a backstepping transformation. We also highlight the relation of the PDE-ODE cascade to a nonlinear system with input delay that depends on past input values and present the predictor-feedback control design for this representation as well.
In this paper, a control technique is presented for an undamped, pinned-pinned Euler-Bernoulli beam with control inputs and bounded disturbances on one boundary. The control strategy drives the system to its origin at...
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In this paper, a control technique is presented for an undamped, pinned-pinned Euler-Bernoulli beam with control inputs and bounded disturbances on one boundary. The control strategy drives the system to its origin at an arbitrary exponential rate in the presence of the disturbances. This is achieved in two main steps. First, a backstepping transformation is used to convert the marginally stable Euler-Bernoulli beam system to a new form that has an exponentially stable homogeneous form. Control inputs are needed to fully convert the system to this form;however, since they are distorted by unknown bounded disturbances, the next step implements a sliding mode controller to account for them. The proposed sliding manifolds require a combination of classical and "second order" techniques in order to avoid discontinuous chattering on the physical system. Therefore, the continuous sliding mode controllers developed return the beam to its origin at an arbitrary exponential rate, and do so in the presence of unknown bounded disturbances on the boundary. The main contributions of this paper with respect to previous backstepping designs for the Euler-Bernoulli beam are that all three of the following goals are accomplished together: (i) steady-state position is the origin, (ii) decay rate has no theoretical restrictions, and (iii) is robust to bounded disturbances.
A Kalman filter is optimal in that the variance of the error is minimized by the estimator. It is shown here, in an infinite-dimensional context, that the solution to an operator Riccati equation minimizes the steady-...
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A Kalman filter is optimal in that the variance of the error is minimized by the estimator. It is shown here, in an infinite-dimensional context, that the solution to an operator Riccati equation minimizes the steady-state error variance. This extends a result previously known for lumped parametersystems to distributed parameter systems. It is shown then that minimizing the trace of the Riccati operator is a reasonable criterion for choosing sensor locations. It is then shown that multiple inaccurate sensors, that is, those with large noise variance, can provide as good an estimate as a single highly accurate (but probably more expensive) sensor. Optimal sensor location is then combined with estimator design. A framework for calculation of the best sensor locations using approximations is established and sensor location as well as choice is investigated with three examples. Simulations indicate that the sensor locations do affect the quality of the estimation and that multiple low-quality sensors can lead to better estimation than a single high-quality sensor.
This brief presents a method to design a controller for a system of aggregated thermostatically controlled loads (TCLs) that are represented by two coupled partial differential equations-the Fokker-Planck equations. T...
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This brief presents a method to design a controller for a system of aggregated thermostatically controlled loads (TCLs) that are represented by two coupled partial differential equations-the Fokker-Planck equations. The design goal is to ensure that the cumulative power consumption of the system tracks the desired power. The control algorithm presented in this brief is a design-then-approximate (DTA) method, which helps ensure that the fundamental properties of the system such as stability and controllability are preserved during the controller design process, and not lost as a consequence of discretization. The effects of heterogeneities in the TCL parameters are also considered, and a robust model predictive controller is integrated within the DTA controller structure. This ensures robust tracking of a desired power trajectory even in the presence of heterogeneities in the TCL parameters while also guaranteeing output controllability of the system. The effectiveness of the controller is demonstrated using simulations incorporating actual demand power data.
We consider stabilization problem for reaction-diffusion PDEs with point actuations subject to a known constant delay. The point measurements are sampled in time and transmitted through a communication network with a ...
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We consider stabilization problem for reaction-diffusion PDEs with point actuations subject to a known constant delay. The point measurements are sampled in time and transmitted through a communication network with a time-varying delay. To compensate the input delay, we construct an observer for the future value of the state. Using a time-varying observer gain, we ensure that the estimation error vanishes exponentially with a desired decay rate if the delays and sampling intervals are small enough while the number of sensors is large enough. The convergence conditions are obtained using a Lyapunov-Krasovskii functional, which leads to linear matrix inequalities (LMIs). We design output-feedback point controllers in the presence of input delays using the above observer. The boundary controller is constructed using the backstepping transformation, which leads to a target system containing the exponentially decaying estimation error. The in-domain point controller is designed and analysed using an improved Wirtinger-based inequality. We show that both controllers can guarantee the exponential stability of the closed-loop system with an arbitrary decay rate smaller than that of the observer's estimation error. (C) 2018 Elsevier Ltd. All rights reserved.
In this paper, we describe a dyadic adaptive control framework for output tracking in a class of semilinear systems of partial differential equations with boundary actuation and unknown distributed nonlinearities. The...
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In this paper, we describe a dyadic adaptive control framework for output tracking in a class of semilinear systems of partial differential equations with boundary actuation and unknown distributed nonlinearities. The dyadic adaptive control framework uses the linear terms in the system to split the plant into 2 virtual subsystems, one of which contains the nonlinearities, whereas the other contains the control input. Full-plant-state feedback is used to estimate the unmeasured individual states of the 2 subsystems as well as the nonlinearities. The control signal is designed to ensure that the controlled subsystem tracks a suitably modified reference signal. We prove the well posedness of the closed-loop system rigorously and derive conditions for closed-loop stability and robustness using finite-gain L stability theory.
Dual-cable mining elevator has advantages in the transportation of heavy load to a large depth over the single cable elevator. However challenges occur when lifting a cage via two parallel compliant cables, such as te...
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Dual-cable mining elevator has advantages in the transportation of heavy load to a large depth over the single cable elevator. However challenges occur when lifting a cage via two parallel compliant cables, such as tension oscillation inconformity between two cables and the cage roll, which are important physical variables relating to the fatigue fracture of mining cables. Mining elevator vibration dynamics are modeled by two pairs of 2 x 2 heterodirectional coupled hyperbolic PDEs on a time-varying domain and all four PDE bottom boundaries are coupled at one ODE. We design an output feedback boundary control law via backstepping to exponentially stabilize the dynamic system including the tension oscillation states, tension oscillation error states and the cage roll states. The control law is constructed with the estimated states from the observer formed by available boundary measurements. The exponential stability of the closed-loop system is proved via Lyapunov analysis. Effective suppression of tension oscillations, reduction of inconformity between tension oscillations in two cables, and balancing the cage roll under the proposed controller are verified via numerical simulation. (C) 2018 Elsevier Ltd. All rights reserved.
Motivated by an engineering application in cable mining elevators, we address a new problem on stabilization of 2x2 coupled linear first-order hyperbolic PDEs sandwiched between 2 ODEs. A novel methology combining PDE...
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Motivated by an engineering application in cable mining elevators, we address a new problem on stabilization of 2x2 coupled linear first-order hyperbolic PDEs sandwiched between 2 ODEs. A novel methology combining PDE backstepping and ODE backstepping is proposed to derive a state-feedback controller without high differential terms. The well-posedness and invertibility properties of the PDE backstepping transformation are proved. All states, including coupled linear hyperbolic PDEs and 2 ODEs, are included in the closed-loop exponential stability analysis. Moreover, boundedness and exponential convergence of the designed controller are proved. The performance is investigated via numerical simulation.
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