Robust control of ill-conditioned plants: high-purity distillation

Using a high-purity distillation column as an example, the physical reason for the poor conditioning and its implications on control system design and performance are explained. It is shown that an acceptable performance/robustness tradeoff cannot be obtained by simple loop-shaping techniques (using singular values) and that a good understanding of the model uncertainty is essential for robust control system design. Physically motivated uncertainty descriptions (actuator uncertainties) are translated into the H∞/structured singular value framework, which is demonstrated to be a powerful tool to analyze and understand the complex phenomena

Feedback: Still the Simplest and Best Solution

Most engineers are (indirectly) trained to be "feedforward thinkers" and they immediately think of "model inversion" when it comes to doing control. Thus, they prefer to rely on models instead of data, although feedback solutions in most cases are much simpler and more robust

Feedback control of unstable steady states of flow past a flat plate using reduced-order estimators

We present an estimator-based control design procedure for flow control, using reduced-order models of the governing equations, linearized about a possibly unstable steady state. The reduced models are obtained using an approximate balanced truncation method that retains the most controllable and observable modes of the system. The original method is valid only for stable linear systems, and we present an extension to unstable linear systems. The dynamics on the unstable subspace are represented by projecting the original equations onto the global unstable eigenmodes, assumed to be small in number. A snapshot-based algorithm is developed, using approximate balanced truncation, for obtaining a reduced-order model of the dynamics on the stable subspace. The proposed algorithm is used to study feedback control of 2-D flow over a flat plate at a low Reynolds number and at large angles of attack, where the natural flow is vortex shedding, though there also exists an unstable steady state. For control design, we derive reduced-order models valid in the neighborhood of this unstable steady state. The actuation is modeled as a localized body force near the leading edge of the flat plate, and the sensors are two velocity measurements in the near-wake of the plate. A reduced-order Kalman filter is developed based on these models and is shown to accurately reconstruct the flow field from the sensor measurements, and the resulting estimator-based control is shown to stabilize the unstable steady state. For small perturbations of the steady state, the model accurately predicts the response of the full simulation. Furthermore, the resulting controller is even able to suppress the stable periodic vortex shedding, where the nonlinear effects are strong, thus implying a large domain of attraction of the stabilized steady state.Comment: 36 pages, 17 figure

Beyond the Waterbed Effect: Development of Fractional Order CRONE Control with Non-Linear Reset

In this paper a novel reset control synthesis method is proposed: CRONE reset control, combining a robust fractional CRONE controller with non-linear reset control to overcome waterbed effect. In CRONE control, robustness is achieved by creation of constant phase behaviour around bandwidth with the use of fractional operators, also allowing more freedom in shaping the open-loop frequency response. However, being a linear controller it suffers from the inevitable trade-off between robustness and performance as a result of the waterbed effect. Here reset control is introduced in the CRONE design to overcome the fundamental limitations. In the new controller design, reset phase advantage is approximated using describing function analysis and used to achieve better open-loop shape. Sufficient quadratic stability conditions are shown for the designed CRONE reset controllers and the control design is validated on a Lorentz-actuated nanometre precision stage. It is shown that for similar phase margin, better performance in terms of reference-tracking and noise attenuation can be achieved.Comment: American Control Conference 201

No More Differentiator in PID:Development of Nonlinear Lead for Precision Mechatronics

Industrial PID consists of three elements: Lag (integrator), Lead (Differentiator) and Low Pass Filters (LPF). PID being a linear control method is inherently bounded by the waterbed effect due to which there exists a trade-off between precision \& tracking, provided by Lag and LPF on one side and stability \& robustness, provided by Lead on the other side. Nonlinear reset strategies applied in Lag and LPF elements have been very effective in reducing this trade-off. However, there is lack of study in developing a reset Lead element. In this paper, we develop a novel lead element which provides higher precision and stability compared to the linear lead filter and can be used as a replacement for the same. The concept is presented and validated on a Lorentz-actuated nanometer precision stage. Improvements in precision, tracking and bandwidth are shown through two separate designs. Performance is validated in both time and frequency domain to ensure that phase margin achieved on the practical setup matches design theories.Comment: European Control Conference 201

PENERAPAN PENDEKATAN MATEMATIKA REALISTIK UNTUK MENINGKATKAN PEMAHAMAN KONSEP OPERASI HITUNG PERKALIAN SISWA KELAS 2C SD

Penelitian ini dilatar belakangi oleh banyaknya siswa kelas 2C SDN SKJ I mengalami kesulitan dalam memahami konsep operasi hitung perkalian untuk mengatasi masalah tersebut, peneliti menerapkan Pendekatan Matematika Reaslistik (PMR). Penelitian Tindak Kelas (PTK) ini bertujuan untuk mendeskripsikan : 1) Rencana Pelaksanaan Pembelajaran (RPP) dengan menerapkan Pendekatan Matematika Realistik (PMR) untuk meningkatkan pemahaman konsep operasi hitung perkalian siswa kelas 2SDN SKJ I, Bandung. 2)Pembelajaran dengan menerapkan Pendekatan Matematika Realistik (PMR) untuk meningkatkan pemahaman konsep operasi hitung perkalian siswa kelas 2C SDN SKJ I, bandung. 3) Peningkatan pemahaman konsep operasi hitung perkalian siswa kelas 2C SDN SKJ I Bandung setelah menerapkan Pendekatan Matematika Realistik (PMR). Metode yang digunakan adalah penelitian tindak kelas (PTK) model Kemmis dan Taggart. Pengumpulan data dilakukan dengan observasi dan tes. Data klasifikasi diolah melalui reduksi data, klasifikasi data, display data, penapsiran dan penarikan simpulan, data kuantitatif diolah dengan menggunakan statistik rata-rata dan presentase, temuan penelitian menunjukan bahwa Penerapan Matematika Realistik (PMR) dapat meningkatkan pemahaman konsep operasi hitung perkalian siswa 2C SDN SKJ I. Hal ini ditunjukan dengan nilai rata-rata kelas pada siklus I sebesar 63,75 dan siklus II 85,75. Padahal nilai rata-rata pra siklus sebesar 57,7. Pada pra siklus presentase 16,6 % siswa yang dapat mencapai KKM, sedangkan pada siklus I menjadi 20% dan siklus II 90%.;---The study was based on the number of students in grade 2C SDN SKJ I that have difficulty in understanding of multiplication arithmetic operations concept. to overcome the problem, researchers applied realistic mathematics education. This Classroom Action Research is intended to describe: 1)Learning Implementation Plan by applying the approach Realistic Mathematics Education (RME) to improve understanding of the arithmetic operations of multiplication concept in graders 2 C SDN SKJ I, Bandung. 2) Learning to apply the approach Realistic Mathematics Education (RME) to improve understanding of the operations calculated concept by multiplying grade 2 C SDN SKJ I Bandung. 3) Improved understanding of the arithmetic operations concept of multiplication grade 2 C SDN SKJ I Bandung after applying Approach Realistic Mathematics Education (RME). The method was used Classroom Action Research with model Kemmis and Taggart. The data collection was done by observation and tests. Data classification is processed through data reduction, data classification, data display, interpretation and drawing conclusions, quantitative data were processed using average statistics and percentages, the research findings indicate that the adoption of Realistic Mathematics Education to enhance understanding of the arithmetic operations concept of multiplication students 2 C SDN SKJ I. This is evidenced by the average value of the class in the first cycle of 63.75 and 85.75 second cycle. Where as the value of pre-cycle average of 57.7. In the pre-cycle percentage of 16.6% of students who can be reached KKM, while the first cycle to the second cycle of 20% and 90%

Evaluation of Dynamic Models of Distillation Columns with Emphasis on the Initial Response

The flow dynamics (tray hydraulics) are of key importance for the initial dynamic response of distillation columns. The most important parameters are the liquid holdup, the liquid hydraulic time constant and the vapor constant representing the initial effect of a change in vapor flow on liquid flow. In the paper we present methods for determining these parameters experimentally, and compare the results with estimates from available correlations such as the Francis Weir formula

Two-degree-of-freedom controller design for an ill-conditioned distillation process using µ-synthesis

The structured singular value framework is applied to a distillation benchmark problem formulated for the 1991 IEEE Conference on decision and control (CDC). A two degree of freedom controller, which satisfies all control objectives of the CDC problem, is designed using /spl mu/-synthesis. The design methodology is presented and special attention is paid to the approximation of given control objectives into frequency domain weights

Optimised configuration of sensors for fault tolerant control of an electro-magnetic suspension system

For any given system the number and location of sensors can affect the closed-loop performance as well as the reliability of the system. Hence, one problem in control system design is the selection of the sensors in some optimum sense that considers both the system performance and reliability. Although some methods have been proposed that deal with some of the aforementioned aspects, in this work, a design framework dealing with both control and reliability aspects is presented. The proposed framework is able to identify the best sensor set for which optimum performance is achieved even under single or multiple sensor failures with minimum sensor redundancy. The proposed systematic framework combines linear quadratic Gaussian control, fault tolerant control and multiobjective optimisation. The efficacy of the proposed framework is shown via appropriate simulations on an electro-magnetic suspension system