scholarly journals LINEAR ALGEBRA AND OPTIMIZATION BASED CONTROLLER DESIGN FOR TRAJECTORY TRACKING OF TYPICAL CHEMICAL PROCESS

2014 ◽  
Vol 44 (4) ◽  
pp. 313-318
Author(s):  
M. E. SERRANO ◽  
G. J. E. SCAGLIA ◽  
P. ABALLAY ◽  
O. A. ORTIZ ◽  
V. MUT
Keyword(s):  
Chemical Process ◽  
Controller Design ◽  
Linear Equations ◽  
Tracking Error ◽  
Optimal Operation ◽  
System Of Linear Equations ◽  
Plant Model ◽  
Control Actions ◽  
Simulation Results ◽  
Tracking Trajectory

This paper presents a new controller design to tracking trajectory of a typical chemical process. The plant model is represented by numerical methods and, from this approach; the control actions for an optimal operation of the system are obtained. Its main advantage is that the condition for the tracking error tends to zero and the calculation of control actions, are obtained solving a system of linear equations. The proofs of convergence to zero of the tracking error are presented. Simulation results show the good performance of the proposed control system.

scholarly journals Improved Computing-Efficiency Least-Squares Algorithm with Application to All-Pass Filter Design

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Lo-Chyuan Su ◽  
Yue-Dar Jou ◽  
Fu-Kun Chen
Keyword(s):  
Least Squares ◽  
Filter Design ◽  
Linear Equations ◽  
Hankel Matrix ◽  
Cholesky Decomposition ◽  
Matrix Inversion ◽  
System Of Linear Equations ◽  
Computationally Efficient ◽  
Pass Filter ◽  
Simulation Results

All-pass filter design can be generally achieved by solving a system of linear equations. The associated matrices involved in the set of linear equations can be further formulated as a Toeplitz-plus-Hankel form such that a matrix inversion is avoided. Consequently, the optimal filter coefficients can be solved by using computationally efficient Levinson algorithms or Cholesky decomposition technique. In this paper, based on trigonometric identities and sampling the frequency band of interest uniformly, the authors proposed closed-form expressions to compute the elements of the Toeplitz-plus-Hankel matrix required in the least-squares design of IIR all-pass filters. Simulation results confirm that the proposed method achieves good performance as well as effectiveness.

Numerical methods based controller design for mobile robots

Robotica ◽  
2009 ◽  
Vol 27 (2) ◽  
pp. 269-279 ◽  
Author(s):  
Gustavo Scaglia ◽  
Lucía Quintero Montoya ◽  
Vicente Mut ◽  
Fernando di Sciascio
Keyword(s):  
Numerical Methods ◽  
Mobile Robot ◽  
Mobile Robots ◽  
Relative Position ◽  
Controller Design ◽  
Tracking Error ◽  
Kinematic Model ◽  
Experimental Results ◽  
Control Actions

SUMMARYThis paper presents the design of four controllers for a mobile robot such that the system may follow a preestablished trajectory. To reach this aim, the kinematic model of a mobile robot is approximated using numerical methods. Then, from such approximation, the control actions to get a minimal tracking error are calculated. Both simulation and experimental results on a PIONEER 2DX mobile robot are presented, showing a good performance of the four proposed mobile robot controllers. Also, an application of the proposed controllers to a leader robot following problem is shown; in it, the relative position between robots is obtained through a laser.

Tracking Controller Design for MIMO Nonlinear Systems With Application to Automotive Cold Start Emission Reduction

2015 ◽  
Vol 137 (10) ◽  
Author(s):  
Selina Pan ◽  
J. Karl Hedrick
Keyword(s):  
Discrete Time ◽  
Model Uncertainty ◽  
Controller Design ◽  
Tracking Error ◽  
Cold Start ◽  
Verification And Validation ◽  
Control Algorithms ◽  
Adaptation Algorithm ◽  
Tracking Controller ◽  
Simulation Results

The main contribution of this paper is the development of a nonlinear multiple-input, multiple-output (MIMO) tracking controller design using a discrete time sliding control approach. A Lyapunov stability analysis is used to prove the asymptotic stability of both the output errors as well as the parameter estimation errors. The application of the “New Invariance Principle” is key to the proof of the parameter error convergence. The developed approach is applied to the cold start emissions problem. The software design process for automotive powertrains on vehicles is growing increasingly complex. Verification and validation provides a systematic procedure to follow for the implementation of control algorithms on physical systems. However, errors can arise that prove costly if not mitigated early on in the verification and validation process. Therefore, the detection and mitigation of potential uncertainties early on in the design process is vital. In this work, the determination of the system model uncertainty is the focus of an adaptation algorithm designed in parallel with a discrete time, MIMO sliding controller. The unknown parameter representing the model uncertainty is updated online in order to decrease tracking error and control effort. The MIMO formulation allows for implementation of both coupled and decoupled frameworks, thus providing a basis for the algorithm to be utilized on a variety of complex vehicle systems. The control algorithms are implemented on a cold start emissions engine model as a case study. A matlab simulink environment is used for simulation results, and an engine test cell is used for experimental validation. Simulation results demonstrate that the algorithm drives tracking error to zero in a fraction of the run time and that the algorithm may be applied with equal efficacy to coupled and decoupled systems. Experimental results demonstrate the ability of the adaptation algorithm to estimate uncertainty in the engine and decrease tracking error.

Anti-Windup Variable Parameter PD Controller Design for Ballistic Missile

2015 ◽  
Vol 742 ◽  
pp. 516-521
Author(s):  
Fei Song ◽  
Hong Chao Zhao ◽  
Ying Xin Mei
Keyword(s):  
Controller Design ◽  
Design Method ◽  
Tracking Error ◽  
Variable Parameter ◽  
Ballistic Missile ◽  
Control Force ◽  
Pd Controller ◽  
Control Effect ◽  
Saturation Problem ◽  
Simulation Results

The conventional PD controller could cause the saturation problem of ballistic missile actuators. A design method of anti-windup variable parameter PD controller was proposed. The proportional coefficient and derivative coefficient were designed to be Gauss functions of system tracking error. Both were small when tracking error was big; whereas both increased as the tracking error decreased. This method not only restrained effectively the saturation problem, but also produced enough control force to drive system outputs to track their commands speedily. The control effect of anti-windup variable parameter PD controller was compared with that of the conventional PD controller in the numerical simulation. The simulation results show that the anti-windup variable parameter PD controller has better control effect.

scholarly journals Tracking Control Design in Nonlinear Multivariable Systems: Robotic Applications

2019 ◽  
Vol 2019 ◽  
pp. 1-15 ◽  
Author(s):  
Gustavo Scaglia ◽  
Emanuel Serrano ◽  
Andres Rosales ◽  
Pedro Albertos
Keyword(s):  
Mobile Robot ◽  
Discrete Time ◽  
Tracking Control ◽  
Controller Design ◽  
Tracking Error ◽  
Control Design ◽  
Multivariable Systems ◽  
Design Technique ◽  
Simulation Results ◽  
Robotic Applications

In this work, a controller design technique called linear algebra based controller (LABC) is presented. The controller is obtained following a systematic procedure that is summarized in this work. In addition, the influence of additive uncertainty on the tracking error is analyzed, and a solution using integrators is proposed. A mobile robot is used as a benchmark to test the performance of the proposed algorithms. In addition, implementation to other systems such as marine vessel is referenced. In this work, the design of controllers in continuous and discrete time is included and experimental and simulation results are shown in a Pioneer 3AT mobile robot. Comparisons are also shown with other controllers proposed in the literature.

scholarly journals Approximate solution of system of equations arising in interior-point methods for bound-constrained optimization

2021 ◽  
Author(s):  
David Ek ◽  
Anders Forsgren
Keyword(s):  
Approximate Solution ◽  
Interior Point ◽  
Interior Point Methods ◽  
Linear Equations ◽  
Approximate Solutions ◽  
System Of Nonlinear Equations ◽  
Intermediate Step ◽  
System Of Linear Equations ◽  
Constrained Nonlinear Optimization ◽  
Asymptotic Error

AbstractThe focus in this paper is interior-point methods for bound-constrained nonlinear optimization, where the system of nonlinear equations that arise are solved with Newton’s method. There is a trade-off between solving Newton systems directly, which give high quality solutions, and solving many approximate Newton systems which are computationally less expensive but give lower quality solutions. We propose partial and full approximate solutions to the Newton systems. The specific approximate solution depends on estimates of the active and inactive constraints at the solution. These sets are at each iteration estimated by basic heuristics. The partial approximate solutions are computationally inexpensive, whereas a system of linear equations needs to be solved for the full approximate solution. The size of the system is determined by the estimate of the inactive constraints at the solution. In addition, we motivate and suggest two Newton-like approaches which are based on an intermediate step that consists of the partial approximate solutions. The theoretical setting is introduced and asymptotic error bounds are given. We also give numerical results to investigate the performance of the approximate solutions within and beyond the theoretical framework.

Study of HVDC System and Subsynchronous Oscillation

2015 ◽  
Vol 1092-1093 ◽  
pp. 356-361
Author(s):  
Peng Fei Zhang ◽  
Lian Guang Liu
Keyword(s):  
Power Plant ◽  
Time Domain ◽  
Simulation Method ◽  
Time Domain Simulation ◽  
Stable Convergence ◽  
Turbine Generator ◽  
Plant Model ◽  
Subsynchronous Oscillation ◽  
Hvdc System ◽  
Simulation Results

With the application and development of Power Electronics, HVDC is applied more widely China. However, HVDC system has the possibilities to cause subsynchronous torsional vibration interaction with turbine generator shaft mechanical system. This paper simply introduces the mechanism, analytical methods and suppression measures of subsynchronous oscillation. Then it establishes a power plant model in islanding model using PSCAD, and analyzes the effects of the number and output of generators to SSO, and verifies the effect of SEDC and SSDC using time-domain simulation method. Simulation results show that the more number and output of generators is detrimental to the stable convergence of subsynchronous oscillation, and SEDC、SSDC can restrain unstable SSO, avoid divergence of SSO, ensure the generators and system operate safely and stably

scholarly journals Numerical approximation for the solution of linear sixth order boundary value problems by cubic B-spline

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
A. Khalid ◽  
M. N. Naeem ◽  
P. Agarwal ◽  
A. Ghaffar ◽  
Z. Ullah ◽  
...  
Keyword(s):  
Numerical Approximation ◽  
Analytic Solution ◽  
Linear Equations ◽  
Computational Cost ◽  
Spline Method ◽  
System Of Linear Equations ◽  
Approximation Solution ◽  
B Spline ◽  
Novel Technique ◽  
Derivatives Of

AbstractIn the current paper, authors proposed a computational model based on the cubic B-spline method to solve linear 6th order BVPs arising in astrophysics. The prescribed method transforms the boundary problem to a system of linear equations. The algorithm we are going to develop in this paper is not only simply the approximation solution of the 6th order BVPs using cubic B-spline, but it also describes the estimated derivatives of 1st order to 6th order of the analytic solution at the same time. This novel technique has lesser computational cost than numerous other techniques and is second order convergent. To show the efficiency of the proposed method, four numerical examples have been tested. The results are described using error tables and graphs and are compared with the results existing in the literature.

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