scholarly journals On PID Controller Design by Combining Pole Placement Technique with Symmetrical Optimum Criterion

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Viorel Nicolau
Keyword(s):  
Transfer Function ◽  
Closed Loop ◽  
Controller Design ◽  
Open Loop ◽  
Pole Placement ◽  
Loop Transfer Function ◽  
Heading Control ◽  
Pid Controller Design ◽  
Analytical Expressions ◽  
Placement Technique

In this paper, aspects of analytical design of PID controllers are studied, by combining pole placement technique with symmetrical optimum criterion. The proposed method is based on low-order plant model with pure integrator, and it can be used for both fast and slow processes. Starting from the desired closed-loop transfer function, which contains a second-order oscillating system and a lead-lag compensator, it is shown that the zero value depends on the real-pole value of closed-loop transfer function. In addition, there is only one pole value, which satisfies the assumptions of symmetrical optimum criterion imposed to open-loop transfer function. In these conditions, by combining the pole placement technique with symmetrical optimum criterion, the analytical expressions of the controller parameters can be simplified. For simulations, PID autopilot design for heading control problem of a conventional ship is considered.

Model-Based Control of Combustion Instabilities

2005 ◽  
Author(s):  
Aimee S. Morgans ◽  
Ann P. Dowling
Keyword(s):  
Transfer Function ◽  
Controller Design ◽  
Open Loop ◽  
Operating Conditions ◽  
Combustion Instabilities ◽  
Lean Premixed Combustion ◽  
Model Based Control ◽  
Model Based ◽  
Loop Transfer Function ◽  
Mathematical Approximation

Model-based control has been successfully implemented on an atmospheric pressure lean premixed combustion rig. The rig incorporated a pressure transducer in the combustor to provide a sensor measurement, with actuation provided by a fuel valve. Controller design was based on experimental measurement of the open loop transfer function. This was achieved using a valve input signal which was the sum of an identification signal and a control signal from an empirical controller to eliminate the non-linear limit cycle. The transfer function was measured for the main instability occurring at a variety of operating conditions, and was found to be fairly similar in all cases. Using Nyquist and H∞-loop shaping techniques, several robust controllers were designed, based on a mathematical approximation to the measured transfer function. These were implemented experimentally on the rig, and were found to stabilise it under a variety of operating conditions, with a greater reduction in the pressure spectrum than had been achieved by the empirical controller.

scholarly journals Analytical Multiloop Control for Multivariable Systems with Time Delays

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Zhiguo Wang ◽  
Peng Wei
Keyword(s):  
Transfer Function ◽  
Process Model ◽  
Controller Design ◽  
Design Method ◽  
Open Loop ◽  
Multivariable Systems ◽  
Performance Improvements ◽  
Loop Transfer Function ◽  
Multiloop Control ◽  
Multiloop Control System

In this paper, a new design method with performance improvements of multiloop controllers for multivariable systems is proposed. Precise expression is developed to show the relationship between the dynamic- and steady-state characteristics of the multiloop control system and its parameters. First, an equivalent transfer function (ETF) is introduced to decompose the multivariable system, based on which the multiloop controller parameters are calculated. According to the ETF matrix property, an analytical expression for the PI controller for multivariable systems is derived in terms of substituting the ETF matrix for the inverse open-loop transfer function. In the proposed controller design method, no approximation of the inverse of the process model is needed, implying that this method can be applied to some multivariable systems with high dimensions. The simulation results obtained from several examples demonstrate the effectiveness of the proposed method.

scholarly journals Direct Synthesis Based Fractional Order PID Controller Design for Non - Integer Order Systems with Time Delay

2020 ◽  
Vol 9 (4) ◽  
pp. 1042-1049
Keyword(s):  
Closed Loop ◽  
Controller Design ◽  
Direct Synthesis ◽  
Tuning Parameter ◽  
Method Performance ◽  
Tuning Parameters ◽  
Integer Order ◽  
Loop Transfer Function ◽  
Pid Controller Design ◽  
Fractional Order Pid

Present study focuses on design and implementation of PI𝝀D𝝁 controller to obtain the closed loop response of for non-integer order systems (NIOS). Controller is designed using direct synthesis (DS) method. Performance analysis in terms of IAE, ISE and ITAE is made and compared with that of literature reported methods. Robustness in terms of Maximum Sensitivity (Ms) is also analyzed. Tuning parameters q and 𝝀, are selected with an arbitrary value for set-point trajectory and disturbance rejection. The closed loop response is studied for various non-integer order systems. Tuning parameters with respect to q (adjustable tuning parameter in assumed closed loop transfer function) and 𝝀 are arrived at for different case studies, q varying from 0.05 to 0.5 and 𝝀 varying from 0.5 to 6. FOMCON tool box of Simulink in MATLAB is employed for the simulation study.

STABILITY OF CLOSED LOOP FRACTIONAL ORDER SYSTEMS AND DEFINITION OF DAMPING CONTOURS FOR THE DESIGN OF CONTROLLERS

2012 ◽  
Vol 22 (04) ◽  
pp. 1230013 ◽  
Author(s):  
PATRICK LANUSSE ◽  
ALAIN OUSTALOUP ◽  
VALERIE POMMIER-BUDINGER
Keyword(s):  
Transfer Function ◽  
Fractional Order ◽  
Half Plane ◽  
Closed Loop ◽  
Open Loop ◽  
Damping Factor ◽  
Closed Loop Systems ◽  
Phase Slope ◽  
Loop Transfer Function ◽  
The Right

Fractional complex order integrator has been used since 1991 for the design of robust control-systems. In the CRONE control methodology, it permits the parameterization of open loop transfer function which is optimized in a robustness context. Sets of fractional order integrators that lead to a given damping factor have also been used to build iso-damping contours on the Nichols plane. These iso-damping contours can also be used to optimize the third CRONE generation open loop transfer function. However, these contours have been built using nonband-limited integrators, even if such integrators reveal to lead to unstable closed loop systems. One objective of this paper is to show how the band-limitation modifies the left half-plane dominant poles of the closed loop system and removes the right half-plane ones. Also presented are how to obtain a fractional order open loop transfer function with a high phase slope and a useful frequency response, and how the damping contours can be used to design robust controllers, not only CRONE controllers but also PD and QFT controllers.

Automated Speed Controller Design of Internal Combustion Engines via Adaptive Control

2000 ◽  
Author(s):  
Patrick J. Cunningham ◽  
Matthew A. Franchek ◽  
John W. Glass
Keyword(s):  
Adaptive Control ◽  
Closed Loop ◽  
Controller Design ◽  
Open Loop ◽  
Feedback Controller ◽  
Ic Engine ◽  
Idle Speed ◽  
Speed Controller ◽  
Online Modeling ◽  
Loop Transfer Function

Abstract Presented in this paper is an adaptive control procedure applied to the idle speed control of an internal combustion (IC) engine. Adaptive control in this investigation is used to automate the design of the engine idle speed controller. The adaptive control process begins by tuning a feedback controller such that the closed loop system is stable. Next, reference step inputs are given to the tuned closed loop system. These transients are used to obtain a model of the IC engine between the by-pass air valve and engine speed. The online modeling procedure is constructed of a filtered derivative method so that the coefficients of the continuous-time model are recovered from the closed loop response. The execution of the proposed online modeling technology is realized using a recursive least squares approach. This online model of the engine process is then used to calculate a new (adapted) feedback controller. The adaptive controller is based on matching the open loop transfer function of the idle speed feedback system to an open loop transfer function that represents the desired transient and steady state performance. To implement the adapted controller, a bumpless transfer approach is used to switch the feedback controller from the tuned controller to the adapted controller. Experimental results performed on a Ford 4.6L fuel injected engine demonstrate the automated controller design process.

Impedance Reduction Controller Design for Mechanical Systems

2013 ◽  
Author(s):  
Hanseung Woo ◽  
Kyoungchul Kong
Keyword(s):  
Case Studies ◽  
Closed Loop ◽  
Controller Design ◽  
Mechanical Impedance ◽  
Open Loop ◽  
Mechatronic Systems ◽  
Closed Loop Systems ◽  
Guaranteed Stability ◽  
Reaction Forces ◽  
Definition Of

Safety is one of important factors in control of mechatronic systems interacting with humans. In order to evaluate the safety of such systems, mechanical impedance is often utilized as it indicates the magnitude of reaction forces when the systems are subjected to motions. Namely, the mechatronic systems should have low mechanical impedance for improved safety. In this paper, a methodology to design controllers for reduction of mechanical impedance is proposed. For the proposed controller design, the mathematical definition of the mechanical impedance for open-loop and closed-loop systems is introduced. Then the controllers are designed for stable and unstable systems such that they effectively lower the magnitude of mechanical impedance with guaranteed stability. The proposed method is verified through case studies including simulations.

scholarly journals The discrete-time tracking problem with H∞ model matching approach plus integral control

2019 ◽  
Vol 292 ◽  
pp. 01018
Author(s):  
Murat Akın ◽  
Tankut Acarman
Keyword(s):  
Discrete Time ◽  
Closed Loop ◽  
Controller Design ◽  
Model Matching ◽  
Matching Problem ◽  
Design Algorithm ◽  
Integral Control ◽  
Loop Transfer Function ◽  
Model Transfer ◽  
Static Output

In this study, the discrete-time H∞ model matching problem with integral control by using 2 DOF static output feedback is presented. First, the motivation and the problem is stated. After presenting the notation, the two lemmas toward the discrete-time H∞ model matching problem with integral control are proven. The controller synthesis theorem and the controller design algorithm is elaborated in order to minimize the H∞ norm of the closed-loop transfer function and to maximize the closed-loop performance by introducing the model transfer matrix. In following, the discrete-time H∞ MMP via LMI approach is derived as the main result. The controller construction procedure is implemented by using a well-known toolbox to improve the usability of the presented results. Finally, some conclusions are given.

scholarly journals Damage Detection and Vibration Control of a Delaminated Smart Composite Plate

2000 ◽  
Vol 9 (1) ◽  
pp. 096369350000900 ◽  
Author(s):  
Aditi Chattopadhyay ◽  
Changho Nam ◽  
Youdan Kim
Keyword(s):  
Composite Plate ◽  
Closed Loop ◽  
Order Theory ◽  
Pole Placement ◽  
Transverse Shear Deformation ◽  
Mean Square ◽  
Smart Composite ◽  
Closed Loop System ◽  
Higher Order Theory ◽  
Placement Technique

In this paper, the effects of delamination on the dynamic characteristics of a composite plate are investigated. The refined higher order theory is used to model the smart composite plate in the presence of delaminations. The theory accurately captures the transverse shear deformation through the thickness, which is important in anisotropic composites, particularly in the presence of discrete actuators and sensors and delaminations. Next, the detection of delamination is investigated using the Root Mean Square (RMS) values of the response of the composite plate subject to disturbances. An active control system is designed to minimise the effect of delamination. The pole placement technique is applied to design the closed loop system by utilising piezoelectric actuators. Numerical results show that the RMS information can be used to estimate the location of the delamination. The controller designed makes the delaminated plate behave like a healthy plate model. The controller also reduces the magnitudes of RMS responses due to disturbance.

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