A transient arbitrary Lagrangian Eulerian based finite element method is used to simulate the effects of varying the die gap during the extrusion of Newtonian fluids. The transient change of the extrudate shape, velocity, and pressure due to the die gap variation is described and studied. Moreover, varying the die gap creates oscillations on the simulated free surface of the extrudate at higher Reynolds number values thus requiring a finer mesh. A new method for defining the free surface is introduced to avoid free surface oscillations. The new method enables the use of a coarse mesh which makes it possible to run simulations with shorter computational time at higher Reynolds numbers.

A new transport PDE/nonlinear ODE cascade model is proposed to simulate extrudate thickness for polymer extrusion with varying die gap. The model is developed to simulate extrusion in extrusion blow moulding. A finite element method simulator is used as a reference for the proposed model to replicate its time dependent extrudate thickness profile. The parameters of the proposed model are identified by minimizing the response error between the proposed model and the finite element method simulator due to step inputs. The novel model is computationally cheap, suitable for controller design, and effective in simulating the extrudate thickness.

A sampling-rate-dependent (SRD) controller is proposed for the uniform output tracking problem of multiinput multioutput discrete time-varying linear systems. A proportional-integral-derivative (PID) controller is a special case of the proposed controller. The SRD controller aims at achieving uniform output tracking in the sense of attaining arbitrary small steady-state errors as well as arbitrary small settling time. The SRD controller makes use of higher sampling rates for larger variations in the desired trajectories. An analytic approach for finding the parameters of the SRD controller that guarantees reference output trajectory tracking is presented. Four different numerical examples and two different experimental applications are provided in order to illustrate the output tracking capability of the proposed SRD controller. Performance is compared to a PID controller with fuzzy gain scheduling, four multivariable PID controllers, an H ∞ optimal controller, and an iterative-learning-control algorithm.Index Terms-Discrete-time systems, multi-input multioutput (MIMO) systems, multivariable control, output feedback, PID controller, tracking.

Neglecting the armature inductance, L a , is a common approach for model order reduction for a class of brush DC motors. Some authors, however, make a partial or incomplete interpretation for neglecting L a , leading students to wrong results and misunderstandings. The existing conditions in the literature and in introductory control systems textbooks are either based on the time constant of the mechanical system being greatly larger than that of the electrical system, or L a & 0. These conditions are not supported analytically and no corresponding error analysis of any kind is provided. This paper analyzes and criticizes the eligibility of these conditions and provides an error model that corresponds to the model order reduction associated with neglecting L a , and another that corresponds to neglecting the non-dominant pole. Experimental results are included to illustrate the suitability of the proposed error models and the suitability of employing such models in basic control designs.

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