For high-performance distributedparameter motion systems, the dynamics introduced by structural flexibilities need to be considered. Especially at the low frequency region, where most of the energy of the commonly us...
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For high-performance distributedparameter motion systems, the dynamics introduced by structural flexibilities need to be considered. Especially at the low frequency region, where most of the energy of the commonly used reference setpoint is concentrated. The contribution of non-rigid body modes at low frequencies is called the compliance function of the system. It is representative for the quasi-static behaviour of the whole non-rigid body modes. This work proposes a new method for the calculation of the compliance function. It is based on employing the differential equation representation for the flexible structure. The approach is validated for a standard damped second order ODE and a one-dimensional flexible model, i.e., the Euler-Bernoulli beam. We show that we get a major reduction in calculation in comparison with the zero frequency response calculation. The extension of this approach to the general PDE’s will be the scope of the future works.
The microwave drying process is a widely used technology in the drying of porous dielectric materials. Designing a controller for moisture distribution in this process can improve product quality and reduce energy con...
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The microwave drying process is a widely used technology in the drying of porous dielectric materials. Designing a controller for moisture distribution in this process can improve product quality and reduce energy consumption and production time. In this paper, a model-based controller for moisture distribution in an industrial microwave drying process is developed. The moisture and temperature in this process are described by a pair of partial differential equations (PDEs) and have both temporal and spatial variations. In this view, using a semi-discrete finite element approximation, the coupled system of PDEs is transformed into a system of ordinary differential equations (ODEs). Based on the discretized ODEs, a linear quadratic regulator (LQR) controller is designed to determine the power levels of multiple microwave sources in this process to reach and maintain the desired moisture level. Numerical simulations are carried out in three different drying scenarios. The results show that the proposed controller achieves a very good performance in tracking the desired moisture level.
We consider the problem of stability enhancement of an undamped flexible beam with a tip mass in presence of input delay and random disturbances. In absence of delay this problem is classically solved through output f...
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We consider the problem of stability enhancement of an undamped flexible beam with a tip mass in presence of input delay and random disturbances. In absence of delay this problem is classically solved through output feedback based on a suitable approximation of an infinite-dimensional Kalman filter. To cope with the presence of input or output delays we derive and compare two solutions, one based on a predictor from estimates in the past and the other one based on a filter with delayed measurements. An identical delay bound in closed form is derived for both solutions and we show that by an appropriate choice of the control gain it is possible to stabilize the system in presence of arbitrarily large delays. A modular structure is proposed for the case of arbitrary gain and delay bound. Finally, we consider the problem of deriving a finite-dimensional approximation of the predictor.
For systems modeled by partial differential equations, the location and shape of the actuators can be regarded as a design variable and included as part of the controller synthesis procedure. Optimal actuator location...
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For systems modeled by partial differential equations, the location and shape of the actuators can be regarded as a design variable and included as part of the controller synthesis procedure. Optimal actuator location is a special case of optimal design. For linear partial differential equations (PDEs), the existence of an optimal actuator location for a number of cost functions has been established. However, many dynamics are affected by nonlinearities and linearization of the PDE can neglect some important aspects of the model. This paper describes recent results establishing conditions for existence of optimal actuator design and control for important classes of nonlinear PDEs. (C) 2019, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.
We extend the internal model principle for boundary control system to cover robust tracking of sinusoidal reference signals with polynomial coefficients. The internal model principle is presented in the form of both t...
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We extend the internal model principle for boundary control system to cover robust tracking of sinusoidal reference signals with polynomial coefficients. The internal model principle is presented in the form of both the internal model structure and the c-conditions. A controller structure will be presented and its internal model properties will be analyzed in order to solve the tracking problem in a robust manner. As an example, a robust controller is constructed for the one-dimensional heat equation with Dirichlet boundary control at one endpoint and temperature measurement at the other endpoint of the interval. The performance of the controller is demonstrated by numerical simulations. (C) 2019, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.
This paper proposes a framework to assess the stability of an Ordinary Differential Equation (ODE) which is coupled to a 1D-partial differential equation (PDE). The stability theorem is based on a new result on Integr...
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This paper proposes a framework to assess the stability of an Ordinary Differential Equation (ODE) which is coupled to a 1D-partial differential equation (PDE). The stability theorem is based on a new result on Integral Quadratic Constraints (IQCs) and expressed in terms of two linear matrix inequalities with a moderate computational burden. The IQCs are not generated using dissipation inequalities involving the whole state of an infinite-dimensional system, but by using projection coefficients of the infinite-dimensional state. This permits to generalize our robustness result to many other PDEs. The proposed methodology is applied to a time-delay system and numerical results comparable to those in the literature are obtained.
We consider the stabilization problem for an unstable 1-D diffusion-reaction partial differential equation using a so-called folding transformation. The diffusion-reaction equation is transformed into a 2 x 2 system o...
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We consider the stabilization problem for an unstable 1-D diffusion-reaction partial differential equation using a so-called folding transformation. The diffusion-reaction equation is transformed into a 2 x 2 system of coupled parabolic PDEs with exotic boundary conditions. A first backstepping transformation is designed to map the unstable system into a strict-feedback intermediate target system. A second backstepping transformation is designed to stabilize the intermediate target system. Interestingly, the companion gain kernel PDEs contain the folding boundary condition, exhibiting symmetry with the original system. The kernels posses a cascading structure that allows for sequential solution methods. Finally, the controller derived is shown to be exponentially stabilizing in the L-2 sense. (C) 2019, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.
In this paper, an observer-based fault detection scheme is developed for one special kind of distributed parameter systems (DPS) of hyperbolic type. An alternative order reduction approach is utilized to handle the in...
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In this paper, an observer-based fault detection scheme is developed for one special kind of distributed parameter systems (DPS) of hyperbolic type. An alternative order reduction approach is utilized to handle the infinite-dimensional nature of DPS for fault detection purpose, compared with the existing modal analysis based method which relies on the existence of eigen-decomposition of the spatial differential operator. The developed fault detection scheme is finally implemented on a simulation model of the paper drying process in paper production industry, and the achieved results demonstrate the effectiveness of the proposed scheme.
This paper presents a method for tuning simple controllers for distributed parameter systems in the process industry. These systems are usually described by partial differential equations (PDE), which are then simplif...
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This paper presents a method for tuning simple controllers for distributed parameter systems in the process industry. These systems are usually described by partial differential equations (PDE), which are then simplified into lumped parametersystems represented by ordinary differential equations (ODE), providing low order transfer functions used for PID control design. The drawback of this approach is that the control system only performs well at low bandwidths and without disturbances, as relevant system dynamics, such as resonances lying at medium-high frequencies, are not taken into account, limiting the performance of the closed-loop system. This work proposes a method for SISO systems which uses a transfer function that models the resonances (obtained directly from the PDE) to tune a PID controller that incorporates a filter that is designed to fulfill control requirements.
We present a computational framework for stability analysis of systems of coupled linear Partial-Differential Equations (PDEs). The class of PDE systems considered in this paper includes parabolic, elliptic and hyperb...
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We present a computational framework for stability analysis of systems of coupled linear Partial-Differential Equations (PDEs). The class of PDE systems considered in this paper includes parabolic, elliptic and hyperbolic systems with Dirichlet, Neuman and mixed boundary conditions. The results in this paper apply to systems with a single spatial variable. We exploit a new concept of state for PDE systems which allows us to include the boundary conditions directly in the dynamics of the PDE. The resulting algorithms are implemented in Matlab, tested on several motivating and illustrative examples, and the codes have been posted online. Numerical testing indicates the approach has little or no conservatism for a large class of systems and can analyze systems of up to 20 coupled PDEs. (C) 2019, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.
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