Synthèse multimodèle d'un régulateur polynomial robuste

Two new approaches are proposed for the multimodel synthesis of a two-degrees-of-freedom polynomial controller : the multimodel pole placement and the multiobjective optimisation. Using several models enables taking into account the parametric variations of the controlled system without introducing conservativeness, be they due to modelling mismatch or changes in the operating conditions. The resulting controller is robust with respect to stability and performances. Multimodel pole placement consists in specifying the closed-loop pole position corresponding to the whole set of models. It is shown that only an approximate pole placement is possible. The distances between the desired and the actual poles are weighted to penalize more the error on the poles which have the most effect on the stability and the performances, and minimized with the least-squares method. An iterative approach is proposed for improving the performances, and an interactive computer-aided design program is developed that enables the user ﬁnding easily which compromises are possible between performances and robustness. In multiobjective optimisation, one considers a set of performance criteria which should be made as close as possible to goal values, also for several models. This results in a minimax problem. Taking into account the H∞ norm of the sensitivity guarantees robust stability. Many different objectives can be included, such as limits on the time- and frequency-domain responses. The result is a compromise between all the speciﬁcations, which is often the purpose of the design. Depending on the optimisation method used, local minima may prevent from reaching the global optimum ; however, this method can signiﬁcantly improve an existing solution. Both approaches are applied to the design of a controller for a ßexible arm. This system exhibits poorly damped modes and large parametric variations. The speciﬁcations concern robust stability and performances. Multimodel pole placement is used to obtain a controller which satisﬁes all of them. Then multiobjective optimisation enables improving the whole set of performance criteria, or more speciﬁcally reducing the amplitude of the control signal.

Fixed-Order H-infinity Controller Design via Convex Optimization Using an Alternative to Youla Prameterization

Alireza Karimi, Hamid Khatibi

All H-infinity controllers of a SISO LTI system are parameterized thanks to the relation between Bounded Real Lemma and Positive Real Lemma and a new concept of strict positive realness of two transfer functions with the same Lyapunov matrix in the matrix inequality of the Kalman-Yakubovic-Popov lemma. This new parameterization shares the same features with Youla parameterization, namely on the convexity of H-infinity norm constraints for the closed-loop transfer functions. However, in contrary to Youla parameterization, it can deal with any controller order and any controller structure such as e.g. PID. The main feature of the proposed method is that it can be extended easily for the systems with polytopic uncertainty. This way, a convex inner approximation of all H-infinity controllers for polytopic systems is given, which can be enlarged by increasing the controller order. In order to design a low-order robust H-infinity controller with less conservatism, rank of the k-th Sylvester resultant matrix of the controller is made to be deficient via a convex approximation of the rank minimization problem. The effectiveness of the proposed method is shown via simulation results.

Institute of Electrical and Electronics Engineers2010

Energy-Efficient Multi-Objective Thermal Control for Liquid-Cooled 3D Stacked Architectures

Mohamed Mostafa Sabry Aly, David Atienza Alonso, Ayse Kivilcim Coskun

3D stacked systems reduce communication delay in multiprocessor system-on-chips (MPSoCs) and enable heterogeneous integration of cores, memories, sensors, and RF devices. However, vertical integration of layers exacerbates temperatureinduced problems such as reliability degradation. Liquid cooling is a highly efficient solution to overcome the accelerated thermal problems in 3D architectures; however, it brings new challenges in modeling and run-time management for such 3D MPSoCs with multi-tier liquid cooling. This paper proposes a novel design-time/run-time thermal management strategy. The design-time phase involves a rigorous thermal impact analysis of various thermal control variables. We then utilize this analysis to design a run-time fuzzy controller for improving energy efficiency in 3D MPSoCs through liquid cooling management and dynamic voltage and frequency scaling (DVFS). The fuzzy controller adjusts the liquid flow rate dynamically to match the cooling demand of the chip for preventing over-cooling and for maintaining a stable thermal profile. The DVFS decisions increase chip-level energy savings and help balance the temperature across the system. Our controller is used in conjunction with temperatureaware load balancing and dynamic power management strategies. Experimental results on 2- and 4-tier 3D MPSoCs show that our strategy prevents the system from exceeding the given threshold temperature. At the same time, we reduce cooling energy by up to 63% and system-level energy by up to 21% in comparison to statically setting a flow rate setting to handle worst-case temperatures.

Institute of Electrical and Electronics Engineers2011

Modeling and Simulation of Energy Efficient Milling Process Plans for Prismatic Parts

Nenad Nesic

The milling process has been continuously optimized from many aspects: forces, velocities, stability, quality. Numerous papers have been published that report results in the domain of toolpath optimization with criteria such as raising the quality of the machined part, obtaining a stable machining process and maximizing the material removal rate. However, only recently researchers have started investigating the ecological impact of machining processes. With the constantly increasing prices of electrical energy and all environmental problems caused by the production and waste of the energy, it has become indispensable to look for ways to optimize machining processes from the energy consumption aspect, too. It is in this domain, then, that the work described in this dissertation contributes – to add a new criterion for the sustainable operation of machine tools: reducing the energy consumption during the use phase of the machine tool. The total energy spent in a machining process is the sum of power spent by all machine tool subsystems multiplied by the time that they are working. Therefore, the operating strategies for increasing energy efficiency for the high-speed machining processes must be oriented towards the reduction of the total machining time (productive and unproductive) and reduction of instantaneous consumed power in the machining process or, preferably, both. There are many causes for milling process time and energy inefficiency. The major sources of potential time reductions include: (i) the issues related to the geometry and topology of the toolpath („air-time”, overlapping segments, gouge and uncut regions, orientation of the toolpath), (ii) the issues related to the kinematics of the feed drives (the feed velocity/acceleration profile). The possible domains for power consumption reduction are related to the forces that exist in the machining process (cutting, inertial, gravitational and friction forces). The power invested to overcome the cutting force is necessary for the machining process but its consumption should be optimized through constant cutting engagement and feedrate scheduling strategies. The other forces are responsible for the pure mechanical power loss and they should be minimized. The optimization variables for inertial and gravitational forces include the feed motion profile and moving mass configuration, while friction losses are load and/or velocity dependent. In addition, there are some power losses in the electric components of machine tool drives (electrical power losses), whose dependency on velocity and mechanical load can also be modeled. Despite many research efforts to analyze and model the phenomena causing inefficiency of the machining process, they are usually not taken into account during milling process planning. In fact, rare are the attempts to use this knowledge to optimize the milling process with more than one of the above mentioned criteria. The reason for that lies in the fact that increasing the instantaneous values of tool engagement and feedrate in order to minimize total machining time also increases the consumed power and, indirectly, deteriorates the tool and/or destabilizes the cutting process. The existence of conflicting criteria in the objective functions imposes the use of evolutionary algorithms for multiobjective optimization. The process of experimental validation of such an optimization model requires costly and complex external hardware setup and it is also time consuming. Hence, there is an emerging need for the development of an accurate model, which would be used for the simulation of the milling process and testing the competing optimization strategies. The ultimate goal of contemporary manufacturing science and engineering is the development of a holistic virtual machine tool system. The motivation of this PhD research is to contribute to this objective by developing the “virtual milling process for prismatic parts (produced by 2.5D milling)”. This category of objects is selected, because the majority of CNC milling tasks can be performed using 2.5D milling. A very large number of mechanical parts are prismatic (their geometry consists exclusively of features that represent 2D contours extruded in a perpendicular direction). Parts that are even more complex are usually produced from a blank by a 2.5D roughing and 3D–5D finishing. Therefore, development of an accurate model of a 2.5D milling process represents a significant contribution to manufacturing engineering. Starting with above given problem description, we have defined the following research objectives: 1. Model power and energy consumption of a 2.5D milling machine as a function of the toolpath geometry (curvature and continuity), cutting engagement, real feedrate profiles and spindle rotational speed, taking into account moving mass configuration, all power losses (mechanical and electrical) in feed-axis and spindle drives and electromechanical constraints of servo drives; 2. Design an integrated software environment for simulation of the developed models; 3. Validate the model experimentally; 4. Demonstrate the potential of its use for multi-objective process optimization. Cutting engagement calculation is performed by using two competing methodologies, in order to make a comparison of their performances. The first one, the pixel based method, is based on discrete image processing, while the other, the exact method, is based on Boolean operations and vector geometry. The tests performed in more than 20 feature/toolpath combinations demonstrate that the exact method is more precise whereas the pixel-based method is computationally much faster. The machine tool operator commands a constant feedrate value. During the process, based on his/her subjective judgment, he/she can manually tune it to keep the process in the desired boundaries. One of the objectives of this research is to predict the real feedrate values so that they can be integrated in the part program before the process start. The feasible profiles of feed velocities for each toolpath segment are analyzed by answering the following questions: can the commanded feedrate be achieved and with what sequence of acceleration and deceleration phases, how much the tool has to slow down in corners and how does the feedrate profile degenerate in segments where the commanded feedrate cannot be reached? In order to determine all forces and torques, a machine tool model is developed. The following subsystems are modeled as rigid bodies (without vibrations): feed motor shaft, transmission, lead screw/nut pair, lead screw bearings, guides (sliding and rolling design), table with the workpiece and electrospindle (rotor, stator and bearings). All kinetic variables (linear and angular speeds; cutting, inertial and friction forces and torques) are then calculated in the joints of this multi-body system. The modeling of all speeds, forces and torques that occur in the machine tool system during the machining process, allows for calculation of various indicators of process time and energy efficiency: material removal rate, total machining time, useful power (invested in cutting), power loss due to the friction in the joints, power losses in electrical motors, electrical energy consumption of feed and spindle drives. In order to assess the accuracy and the reliability of the developed model two sets of experiments have been performed. The model validation is performed on several subsystem levels and the simulation results show a very good compliance with the experimental results. The first experimental setup consists of the force dynamometer, to measure cutting force components in linear axis directions, two laser optical position sensors, to measure the real feedrate and the power sensor, to measure the total power consumption of the machine tool electrical motors. The machining process was performed on the 6-axis machining center C.B. Ferrari A152 and the data acquisition platform was developed in LabVIEW 2010. The second experimental setup consists of the torque dynamometer, to measure the cutting torque directly on the spindle, the built-in current sensor that measures the motor current proportional to the electrical power consumed by the spindle and, again, the power sensor, to measure the total power consumption of the machine tool electrical motors. This time, MIKRON HPM 600U, a 5-axis milling machine equipped with the controller iTNC530, was used for the experimentation. The developed model is ready for practical implementation. Several examples have been prepared to demonstrate its capabilities in the domains of milling process simulation, sensitivity analysis and prospective optimization strategies. These examples include the prediction of various kinetostatic variables for given toolpaths, choice of the optimum machining strategy (minimization of machining time, moving mass and energy consumption) and process optimization by feedrate scheduling (reduction of cutting force fluctuation). As a conclusion, the major contribution of this PhD research is the development of a comprehensive rigid-body dynamics model of a machine tool system, aimed for the generation, simulation and optimization of 21⁄2D milling process plans. The model features several novelties compared to existing approaches: (i) it takes into account the machine tool rigid body dynamics and real tool kinematics in toolpath planning, (ii) it predicts all mechanical and electrical power losses in the machine tool system (iii) it allows the modeling of machine tool system electromechanical constraints. The model was experimentally validated on two real machine tools in different workshops and its capabilities for the simulation of different toolpath patterns and optimization of process parameters were successfully demonstrated using several examples.

EPFL2012

Modeling and Simulation of Energy Efficient Milling Process Plans for Prismatic Parts

Nenad Nesic

EPFL2012