This paper presents the first results of an optimal control approach to piezoceramic actuators. A one-dimensional free energy model for piezoceramics recently proposed by Smith and Seelecke is briefly reviewed first. It is capable of predicting the hysteretic behavior along with the frequency-dependence present in these materials. The model is implemented into an optimal control package, and two exemplary cases are simulated to illustrate these features and the potential of the method.
The paper presents an optimal control approach to shape memory alloy (SMA) actuators. Like other active materials, e.g., piezoceramics or magnetostrictive materials, SMAs exhibit a highly non-linear and hysteretic behavior. In certain applications, in particular those with high driving frequencies like MEMS (Micro-Electro-Mechanical Systems) applications, this is known to lead to a breakdown of standard control algorithms. The optimal control approach overcomes this problem by including a model for the hysteretic behavior, and allows criteria like maximal speed and minimal energy consumption to be taken into account. To illustrate the potential benefits of the method, the performance is compared to that of a standard PI control.
The prediction of the temperature profile for radio frequency ablation-a minimal form of tumor treatment-depends on a variety of material parameters (e.g. electric and thermal conductivities) as the coefficients of a system of partial differential equations. We discuss a basic model for the identification of such material parameters from measured temperature data, which bases on an objective function of tracking type which is constrained by the system of PDE. After the discretization of the PDE system with a standard finite element method we optimize the discrete system with an SQP solver. Numerical results are shown for a test scenario consisting of an artificial tumor and artificially generated target temperature profile. Simulation and Parameter IdentificationFor the treatment of tumor diseases there exists a wide variety of approaches ranging from transplantation or surgical resection over chemotherapy to non-invasive techniques. One of these minimally invasive treatments is the radio-frequency (RF) ablation, which is widely used for the destruction of hepatic tumors. In RF ablation a probe, which is connected to an electric generator, is inserted into the tumor. Due to the resistance of the tissue the electric current generates heat, which destroys the cells around the probe. If the temperature reaches a certain critical value the proteins of the tissue coagulate and the cells die. If all malignant tissue cells are destroyed, the therapy is considered to be successful. To a high extent the success of an RF ablation depends on the experience of the radiologist. This motivates the desire for a numerical support (cf. e.g. The main aspect of the model is the description of the temperature profile which induces a volume of destroyed tissue. This part consists of two coupled partial differential equations (PDEs), the electrostatic equation, which describes the electric potential of the tissue, and the heat equation, which takes a heat source due to the electric current into account [2]:and appropriate boundary conditions on ∂D.• Heat equation:with source and sinkand appropriate boundary and initial conditions.The sink term Q perf accounts for the cooling effect of the blood perfusion [2]. The source term Q rf describes the energy, which enters the domain through the electric field of the probe. Here, P eff is a nonlinear function, which models the characteristics of the electric generator. Moreover, these PDEs depend on material parameters like the electric conductivity σ, the density ρ, the heat capacity c, the thermal conductivity λ and the perfusion coefficient ν. Although there exist studies concerning these material parameters, they are in fact not known for a specific patient. Moreover, the existing studies have been performed
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