On the Linear Quadratic Optimal Systems Design in the Frequency Domain

1997 ◽  
Vol 119 (3) ◽  
pp. 581-584
Author(s):  
Chih-Min Lin ◽  
Tarn-Sea Lu
Keyword(s):  
Optimal Control ◽  
Control System ◽  
Frequency Domain ◽  
Flight Control ◽  
Design Method ◽  
Systems Design ◽  
Linear Quadratic ◽  
Stability Margins ◽  
Single Input Single Output ◽  
Single Output

By frequency-domain approach, a synthesis methodology of single-input-single-output optimal control system is developed to ensure closed-loop stability and to minimize a linear quadratic cost function. Furthermore, the equivalent two-degree-of-freedom system is designed so that the feedback-loop can satisfy the return difference equality, i.e., this system possesses the system performance with the optimal control sense and the stability margins properties as in time-domain approach LQR optimal systems. The F-4E flight control system is considered as the design example to illustrate the validity of the design method.

H ∞ Frequency-Domain Identification of Flight Control System

2008 ◽  
Author(s):  
D. T. W. Yau ◽  
E. H. K. Fung ◽  
Y. K. Wong
Keyword(s):  
Frequency Domain ◽  
Flight Control ◽  
Transfer Functions ◽  
Linear Time ◽  
Identification Algorithm ◽  
Discrete Time System ◽  
Worst Case ◽  
Single Input Single Output ◽  
Domain Identification ◽  
Single Output

In this paper, H∞ identification is performed in frequency domain for the longitudinal pitch and speed channels of a commercial Boeing 747 transport aircraft flying at a particular flight condition. The plant (i.e. the longitudinal pitch and speed transfer functions) to be identified is a causal, bounded-input/bounded-output (BIBO) stable, single-input/single-output (SISO), linear time-invariant (LTI) discrete-time system. The frequency response data is generated by simulation of the plant transfer functions and is corrupted by unknown but bounded measurement noise. An identification algorithm is used to map the experimental data into an identified model such that the worst case identification error converges in a particular sense. In this paper, untuned linear algorithm and two-stage nonlinear algorithm are used respectively for computing the identified models for the pitch and speed transfer function of the aircraft. Different window sequence (rectangular, triangular, traperzoidal, etc.) are used in these algorithms. The error response and worst case error bound computed by these two algorithms are also compared. The paper demonstrates the effectiveness of the two algorithms for computing the identified model. Unlike classical identification which is inadequate for robust control, the results of H∞ identification can be used for designing the H∞ robust controllers.

System Identification and Optimal Control of a 6-DOF Magnetic Levitation Stage With Nanopositioning Capabilities

2004 ◽  
Author(s):  
Huzefa Shakir ◽  
Won-Jong Kim ◽  
Shobhit Verma
Keyword(s):  
Optimal Control ◽  
Magnetic Levitation ◽  
Current Model ◽  
Euler Angle ◽  
Linear Quadratic ◽  
Single Input Single Output ◽  
Single Output ◽  
Linear Quadratic Regulation ◽  
Lqr Controller ◽  
System Equations

A systematic procedure for modeling and optimal control of a multivariable 6-DOF (degree-of-freedom) magnetically levitated (maglev) stage has been described in this paper. In our previous publications, we have presented the design, SISO (single-input single-output) control, and testing of the maglev stage with nanometer-precision positioning capability and several-hundred-micrometer travel range. In the present work, we extended the current model to a more rigorous LQR (linear quadratic regulation) controller for the lateral control to reduce the coupling between axes. Independent lead-lag controllers have been used for the vertical control. The system equations have been derived using the Euler angle methodology and linearized about an operating point. The performance of this multivariable control has been analyzed and compared with all the six decoupled SISO controllers. The effect of adding the integrators to eliminate the steady-state error has also been discussed and the performance of the LQR controller with different weight matrices has been compared. In this paper, we also address the issues related to the stochastic modeling of the stage to analyze the coupling between different axes and transfer function identification.

scholarly journals Comparative study of zero effects in pole-placement control system design via the shift and delta transforms

2005 ◽  
Vol 18 (3) ◽  
pp. 439-451
Author(s):  
Milica Naumovic
Keyword(s):  
Control System ◽  
System Design ◽  
Pole Placement ◽  
Control System Design ◽  
Single Input Single Output ◽  
Single Output ◽  
Continuous Time Systems ◽  
Single Input ◽  
Pole Placement Control ◽  
Time Systems

This paper deals with the special replacement of the shift operator and its associated z transform by delta operator and ? transform, respectively. The aim of the paper is to clarify the role of zeros of discretized linear single input single output continuous-time systems modeled by shift and delta operators. In particular, the effect of zero dynamics on the control system design based on classical pole-zero assignment in the case of both operators is considered. The analysis is illustrated by simulation results.

scholarly journals D-Optimal Design for Information Driven Identification of Static Nonlinear Elements

2021 ◽  
Author(s):  
Nalika Ulapane ◽  
Karthick Thiyagarajan ◽  
sarath kodagoda ◽  
Linh Nguyen
Keyword(s):  
Optimal Design ◽  
Model Calibration ◽  
Design Method ◽  
Single Input Single Output ◽  
Single Output ◽  
Order Polynomial ◽  
Information Maximization ◽  
Pros And Cons ◽  
Single Input ◽  
Optimal Design Method

<div>Identification of static nonlinear elements (i.e., nonlinear elements whose outputs depend only on the present value of inputs) is crucial for the success of system identification tasks. Identification of static nonlinear elements though can pose several challenges. Two of the main challenges are: (1) mathematical models describing the elements being unknown and thus requiring black-box identification; and (2) collection of sufficiently informative measurements. With the aim of addressing the two challenges, we propose in this paper a method of predetermining informative measurement points offline (i.e., prior to conducting experiments or seeing any measured data), and using those measurements for online model calibration. Since we deal with an unknown model structure scenario, a high order polynomial model is assumed. Over fit and under fit avoidance are achieved via checking model convergence via an iterative means. Model dependent information maximization is done via a D-optimal design of experiments strategy. Due to experiments being designed offline and being designed prior to conducting measurements, this method eases off the computation burden at the point of conducting measurements. The need for in-the-loop information maximization while conducting measurements is avoided. We conclude by comparing the proposed D-optimal design method with a method of in-the-loop information maximization and point out the pros and cons. The method is demonstrated for the single-input-single-output (SISO) static nonlinear element case. The method can be extended to MISO systems as well.</div>

scholarly journals MODEL PREDICTIVE CONTROL TOOLBOX DESIGN FOR NONSTATIONARY PROCESS

2021 ◽  
Author(s):  
Oleksandr V. Stepanets ◽  
Yurii I. Mariiash
Keyword(s):  
Optimal Control ◽  
Control System ◽  
Model Predictive Control ◽  
Predictive Control ◽  
Complex Structure ◽  
Nonstationary Process ◽  
Actual State ◽  
Quadratic Functional ◽  
Linear Quadratic ◽  
Prediction Horizon

Background. Model predictive control (MPC) approach is the basic feedback scheme, combined with high adaptive properties, which determines its successful use in the practice of design and operation of control systems. These advantages allow managing multidimensional objects with a complex structure, including nonlinearity, optimizing processes in real time within the constraints on controlled and managed variables, taking into account uncertainties in the task of objects and perturbations. Objective. The purpose of the paper is to design and analyse control system of carbon monoxide oxidation in the convector cavity based on MPC with linear-quadratic cost functional with constraint. Methods. The design of MPC is based on mathematical model of an object (relatively simple). At the current step, the prediction of object dynamic response on some final period of time (prediction horizon) is carried out; control optimization is performed, the purpose of which is to approximate the control variables of the prediction model to the corresponding setpoint on the predict horizon. The found optimal control is applied and measurement of an actual state of object at the end of a step is carried out. The prediction horizon is shifted one step further, and this algorithm are repeated. Results. The results of modeling the automatic control system show that the MPC approach provides maintenance of carbon dioxide content when changing oxygen consumption and overshoot caused by introduction bulk does not exceed 0.6 % that meets the technological requirements of the process. Conclusions. A fuse of the MPC and the quadratic functional given the constraints on the input signals is proposed. The problems of control degree of carbon oxidation in the convector cavity include non-stationarity, so the use of classical control methods is difficult. The MPC approach minimizes the cost function that characterizes the quality of the process. The predicted behaviour of a dynamic system will usually differ from its actual motion. The obtained quadratic functional is optimized to find the optimal control of degree of CO oxidation to CO2.

Isotropic Compliance in E(3): Feasibility and Workspace Mapping

2016 ◽  
Vol 8 (6) ◽  
Author(s):  
Matteo Verotti ◽  
Nicola P. Belfiore
Keyword(s):  
Control System ◽  
Euclidean Space ◽  
Joint Control ◽  
Control Law ◽  
Single Input Single Output ◽  
Gain Ratio ◽  
Single Output ◽  
Control Gain ◽  
Single Input ◽  
Manipulator Control

A manipulator control system, for which isotropic compliance holds in the Euclidean space E(3), can be significantly simplified by means of diagonal decoupling. However, such simplification may introduce some limits to the region of the workspace where the sought property can be achieved. The present investigation reveals how to detect which peculiar subset, among four different classes, a given manipulator belongs to. The paper also introduces the concept of control gain ratio for each specific single-input/single-output joint control law in order to limit the maximum gain required to achieve the isotropic compliance condition.

scholarly journals MIMO Passive Control Systems Are Not Necessarily Robust

2015 ◽  
Vol 2015 ◽  
pp. 1-6
Author(s):  
Jesús U. Liceaga-Castro ◽  
Irma I. Siller-Alcalá ◽  
Eduardo Liceaga-Castro ◽  
Luis A. Amézquita-Brooks
Keyword(s):  
Control System ◽  
Structure Function ◽  
Control Systems ◽  
Passive Control ◽  
Linear Control System ◽  
Linear Control ◽  
Single Input Single Output ◽  
Single Output ◽  
Single Input

Via several cases of study it is shown that a passive multivariable linear control system, contrary to its single input single output counterpart, may not be robust. Moreover, it is shown that lack of robustness can be exposed via the multivariable structure function.

Optimal Design of ADAS Damped MDOF Structures

1999 ◽  
Vol 15 (2) ◽  
pp. 317-330 ◽  
Author(s):  
Yuri Ribakov ◽  
Jacob Gluck
Keyword(s):  
Optimal Control ◽  
Control System ◽  
Numerical Analysis ◽  
Optimal Control Theory ◽  
Passive Control ◽  
Design Method ◽  
Viscous Damping ◽  
Viscous Dampers ◽  
Structural Frame ◽  
Different Levels

Incorporated at various levels of a structural frame, ADAS devices may be used to improve the response of the structure during earthquakes. A design method of a passive control system for multistory structures using optimal Adding Damping And Stiffness (ADAS) dampers is presented. Optimal Control Theory (OCT) is commonly used to obtain the levels of viscous damping at each story. The optimization leads to different levels of damping at each story. Therefore, a solution with viscous dampers is inconvenient and can be expensive. The proposed method enables the use of relatively less expensive optimal ADAS devices dissipating energy which is equivalent to that of viscous dampers. The method is examined in a numerical analysis of a seven-story shear framed structure. Significant improvement was obtained in the behavior of the ADAS damped structure compared to the uncontrolled one.

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