This paper presents the further developments and working principle of the speed-variable switched differential pump (SvSDP) concept proposed, designed and produced in [1]. The SvSDP system is designed to remove the throttling losses associated with typical valve driven control (VDC) systems. The hydraulic and mechanical system is modelled and linearised. The linearisation point is studied to provide an usable basis for controller design. It is proposed, in this paper, to model the converter and motor using a black box approach, where designed and informative input sequences are used to estimate the mathematical behaviour of the electrical drive based on the equivalent output data. The complete non linear model is verified against available trajectory data from the physical system, obtained from [1]. The linear model is analysed through a relative gain array (RGA) analysis to map the input output couplings present in the system. The results show that the system includes heavy cross-couplings. Results presented in [1] indicate, that it is possible to utilise a input output compensated decoupling to redefine the MIMO system into multiple SISO systems. The SvSDP concept is over-determined in relation to the amount of control inputs compared to possible outputs.
It is proposed in [1] to introduce two new input states and two new output states. The decoupling approach has been investigated in this paper. The decoupling results provided a basis of using decentralised control. The linear control strategies are designed independently based on the notion of decoupling. The first controller is related to the level flow, designed to maintain a desired minimum pressure level. The second load flow controller is related to the cylinder motion. The controller results indicate, that it is possible to achieve a good dynamic tracking performance with an error of maximum 0.5 mm for a given position trajectory.
This paper is also considering the energy consumption issues stated in [1], where two conceptual solutions are proposed, to solve the power loss associated with holding a load at a constant cylinder position. This paper is written as the product of an appendix report describing the whole project.
Optimization of Closure Law of Guide Vanes for an Operational Hydropower Plan...Dr. Amarjeet Singh
This paper addresses the optimization of twostage closure law of guide vanes in an operational
hydropower plant of Nepal. The mathematical model
has been established in commercial software Bentley
Hammer, whose correctness has been validated by
comparing the results with the data of experimental
load rejection test. The validated mathematical model
has been employed to find the parameters of optimum
closure pattern, which minimizes the non-linear
objective function of maximum water pressure and
maximum rotational speed of turbine.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
Optimization of Closure Law of Guide Vanes for an Operational Hydropower Plan...Dr. Amarjeet Singh
This paper addresses the optimization of twostage closure law of guide vanes in an operational
hydropower plant of Nepal. The mathematical model
has been established in commercial software Bentley
Hammer, whose correctness has been validated by
comparing the results with the data of experimental
load rejection test. The validated mathematical model
has been employed to find the parameters of optimum
closure pattern, which minimizes the non-linear
objective function of maximum water pressure and
maximum rotational speed of turbine.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
Nonlinear predictive control of a boiler turbine unitISA Interchange
This paper details development of a Model Predictive Control (MPC) algorithm for a boiler-turbine unit, which is a nonlinear multiple-input multiple-output process. The control objective is to follow set-point changes imposed on two state (output) variables and to satisfy constraints imposed on three inputs and one output. In order to obtain a computationally efficient control scheme, the state-space model is successively linearized on-line for the current operating point and used for prediction. In consequence, the future control policy is easily calculated from a quadratic optimization problem. For state estimation the extended Kalman filter is used. It is demonstrated that the MPC strategy based on constant linear models does not work satisfactorily for the boiler-turbine unit whereas the discussed algorithm with on-line successive model linearisation gives practically the same trajectories as the truly nonlinear MPC controller with nonlinear optimization repeated at each sampling instant.
Cooling Towers in Process Industries are part of Utilities design. As the name suggests their primary purpose is to provide cooling requirements to industrial hot water from unit operations & unit processes. Examples include chillers and air conditioners. The principle of operation is to circulate hot water through a tower and allow heat dissipation to the ambient. Cooling towers can operate by natural draft or forced draft methods wherein fans are used to increase heat transfer.
A Study on Performance of Different Open Loop PID Tunning Technique for a Liq...IJITCA Journal
Process control is the application and study of automatic control to maintain a process at the desired
operating condition ,safety,and efficiently while satisfying the environmental and product quality.Like the
Level,Temparature & Pressure, Liquid flow Measurement is one of the major controlling parameter in
process plant. This paper mainly concern about the single tank liquid flow process and designing the
controller with different PID tunning methods.Many process plants controlled by the PID controller with
similar dynamics to find out the possible set of satisfactory controller parameters from the less plant
information but from the mathematical model.With minimum effort adjust the controller parameters by
using three open loop PID controller IMC,CHR & AMIGO and compare their output response in real time
flow tank system.
Chemical Process Calculations – Short TutorialVijay Sarathy
Often engineers are tasked with communicating equipment specifications with suppliers, where process data needs to be exchanged for engineering quotations & orders. Any dearth of data would need to be computed for which process related queries are sometimes sent back to the process engineer’s desk for the requested data.
The following tutorial is a refresher for non-process engineers such as project engineers, Piping, Instrumentation, Static & Rotating Equipment engineers to conduct basic process calculations related to estimation of mass %, volume %, mass flow, actual & standard volumetric flow, gas density, parts per million (ppm) by weight & by volume.
ECONOMIC INSULATION FOR INDUSTRIAL PIPINGVijay Sarathy
Thermal Insulation for Industrial Piping is a common method to reduce energy costs in production facilities while meeting process requirements. Insulation represents a capital expenditure & follows the law of diminishing returns. Hence the thermal effectiveness of insulation needs to be justified by an economic limit, beyond which insulation ceases to effectuate energy recovery. To determine the effectiveness of an applied insulation, the insulation cost is compared with the associated energy losses & by choosing the thickness that gives the lowest total cost, termed as ‘Economic Thickness’.
The following tutorial provides guidance to estimate the economic thickness for natural gas piping in winter conditions as an example case study.
Oil & Gas Pipelines are often subjected to an operation called ‘Pigging’ for maintenance purposes (For e.g., cleaning the pipeline of accumulated liquids or waxes). A pig is launched from a pig launcher that scrapes out the remnant contents of the pipeline into a vessel known as a ‘Slug catcher’. The term slug catcher is used since pigging operations produces a Slug flow regime characterized by the alternating columns of liquids & gases. Slug catcher’s are popularly of two types – Horizontal Vessel Type & Finger Type Slug catcher. However irrespective of the type used, the determination of the slug catcher volume becomes the primary step before choosing the slug catcher type.
Performance investigation of hydraulic actuator based mass lift system using ...Mustefa Jibril
A hydraulic actuator is a system that can provide a large power amplification in industries and
factories. In this paper, mass lifter hydraulic actuator system to a desired displacement is designed
using optimal control theory. MPC and LQR controllers are used to design and improve the
performance of the hydraulic actuator. The hydraulic actuator system is linearized using Taylor
series linearization method and designed using Matlab/Simulink tool. Comparison of the hydraulic
actuator with MPC and LQR controllers using three desired output displacement signals (step, sine
wave and white noise) is done and simulation results have been analyzed successfully. For the
desired step input signal, the hydraulic actuator system with MPC controller lower rise and settling
times with small percentage overshoot as compared to the hydraulic actuator system with LQR
controller and for the desired sine wave signal, the hydraulic actuator system with MPC controller
almost track the desired sine wave input signal correctly as compared to the hydraulic actuator
system with LQR controller. While for the desired white noise input signal, the hydraulic actuator
system with MPC controller have tried to track the desired white noise input signal with small
variation in amplitude as compared to the hydraulic actuator system with LQR controller. Finally
the comparative simulation results prove the effectiveness of the proposed hydraulic actuator
system with MPC controller.
Piping systems associated with production, transporting oil & gas, water/gas injection into reservoirs, experience wear & tear with time & operations. There would be metal loss due to erosion, erosion-corrosion and cavitation to name a few. The presence of corrosion defects provides a means for localized fractures to propagate causing pipe ruptures & leakages. This also reduces the pipe/pipeline maximum allowable operating pressure [MAOP].
The following document covers methods by DNV standards to quantitatively estimate the erosion rate for ductile pipes and bends due to the presence of sand. It is to be noted that corrosion can occur in many other scenarios such as pipe dimensioning, flow rate limitations, pipe performance such as pressure drop, vibrations, noise, insulation, hydrate formation and removal, severe slug flow, terrain slugging and also upheaval buckling. However these aspects are not covered in this document.
Based on the erosional rates of pipes and bends, the Maximum Safe Pressure/Revised MAOP is evaluated based on a Level 1 Assessment procedure for the remaining strength of the pipeline. The Level 1 procedures taken up in this tutorial are RSTRENG 085dL method, DNVGL RP F-101 (Part-B) and PETROBRAS’s PB Equation.
Design and Control of a Hydraulic Servo System and Simulation AnalysisIJMREMJournal
This paper describes the system analysis, modeling and simulation of a Hydraulic Servo System (HSS) for
hydraulic mini press machine. Comparisons among linear output feed back PID control, Fuzzy control and
Hybrid of PID and Fuzzy control are presented. Application of hybrid controller to a nonlinear is investigated
by both position and velocity of the hydraulic servo system. The experiment is based on an 8 bit PIC
16F877 microcontroller, and the simulation is based on MATLAB Simulink. Simulation and hardware
experimental results show that the hybrid controller gave the best performance as it has the smallest overshoot,
oscillation, and setting time.
High pressure common rail injection system modeling and controlISA Interchange
In this paper modeling and common-rail pressure control of high pressure common rail injection system (HPCRIS) is presented. The proposed mathematical model of high pressure common rail injection system which contains three sub-systems: high pressure pump sub-model, common rail sub-model and injector sub-model is a relative complicated nonlinear system. The mathematical model is validated by the software Matlab and a virtual detailed simulation environment. For the considered HPCRIS, an effective model free controller which is called Extended State Observer – based intelligent Proportional Integral (ESO-based iPI) controller is designed. And this proposed method is composed mainly of the referred ESO observer, and a time delay estimation based iPI controller. Finally, to demonstrate the performances of the proposed controller, the proposed ESO-based iPI controller is compared with a conventional PID controller and ADRC.
Adaptive terminal sliding mode control strategy for dc–dc buck convertersISA Interchange
This paper presents an adaptive terminal sliding mode control (ATSMC) strategy for DC–DC buck converters. The idea behind this strategy is to use the terminal sliding mode control (TSMC) approach to assure finite time convergence of the output voltage error to the equilibrium point and integrate an adaptive law to the TSMC strategy so as to achieve a dynamic sliding line during the load variations. In addition, the influence of the controller parameters on the performance of closed-loop system is investigated. It is observed that the start up response of the output voltage becomes faster with increasing value of the fractional power used in the sliding function. On the other hand, the transient response of the output voltage, caused by the step change in the load, becomes faster with decreasing the value of the fractional power. Therefore, the value of fractional power is to be chosen to make a compromise between start up and transient responses of the converter. Performance of the proposed ATSMC strategy has been tested through computer simulations and experiments. The simulation results of the proposed ATSMC strategy are compared with the conventional SMC and TSMC strategies. It is shown that the ATSMC exhibits a considerable improvement in terms of a faster output voltage response during load changes.
Nonlinear predictive control of a boiler turbine unitISA Interchange
This paper details development of a Model Predictive Control (MPC) algorithm for a boiler-turbine unit, which is a nonlinear multiple-input multiple-output process. The control objective is to follow set-point changes imposed on two state (output) variables and to satisfy constraints imposed on three inputs and one output. In order to obtain a computationally efficient control scheme, the state-space model is successively linearized on-line for the current operating point and used for prediction. In consequence, the future control policy is easily calculated from a quadratic optimization problem. For state estimation the extended Kalman filter is used. It is demonstrated that the MPC strategy based on constant linear models does not work satisfactorily for the boiler-turbine unit whereas the discussed algorithm with on-line successive model linearisation gives practically the same trajectories as the truly nonlinear MPC controller with nonlinear optimization repeated at each sampling instant.
Cooling Towers in Process Industries are part of Utilities design. As the name suggests their primary purpose is to provide cooling requirements to industrial hot water from unit operations & unit processes. Examples include chillers and air conditioners. The principle of operation is to circulate hot water through a tower and allow heat dissipation to the ambient. Cooling towers can operate by natural draft or forced draft methods wherein fans are used to increase heat transfer.
A Study on Performance of Different Open Loop PID Tunning Technique for a Liq...IJITCA Journal
Process control is the application and study of automatic control to maintain a process at the desired
operating condition ,safety,and efficiently while satisfying the environmental and product quality.Like the
Level,Temparature & Pressure, Liquid flow Measurement is one of the major controlling parameter in
process plant. This paper mainly concern about the single tank liquid flow process and designing the
controller with different PID tunning methods.Many process plants controlled by the PID controller with
similar dynamics to find out the possible set of satisfactory controller parameters from the less plant
information but from the mathematical model.With minimum effort adjust the controller parameters by
using three open loop PID controller IMC,CHR & AMIGO and compare their output response in real time
flow tank system.
Chemical Process Calculations – Short TutorialVijay Sarathy
Often engineers are tasked with communicating equipment specifications with suppliers, where process data needs to be exchanged for engineering quotations & orders. Any dearth of data would need to be computed for which process related queries are sometimes sent back to the process engineer’s desk for the requested data.
The following tutorial is a refresher for non-process engineers such as project engineers, Piping, Instrumentation, Static & Rotating Equipment engineers to conduct basic process calculations related to estimation of mass %, volume %, mass flow, actual & standard volumetric flow, gas density, parts per million (ppm) by weight & by volume.
ECONOMIC INSULATION FOR INDUSTRIAL PIPINGVijay Sarathy
Thermal Insulation for Industrial Piping is a common method to reduce energy costs in production facilities while meeting process requirements. Insulation represents a capital expenditure & follows the law of diminishing returns. Hence the thermal effectiveness of insulation needs to be justified by an economic limit, beyond which insulation ceases to effectuate energy recovery. To determine the effectiveness of an applied insulation, the insulation cost is compared with the associated energy losses & by choosing the thickness that gives the lowest total cost, termed as ‘Economic Thickness’.
The following tutorial provides guidance to estimate the economic thickness for natural gas piping in winter conditions as an example case study.
Oil & Gas Pipelines are often subjected to an operation called ‘Pigging’ for maintenance purposes (For e.g., cleaning the pipeline of accumulated liquids or waxes). A pig is launched from a pig launcher that scrapes out the remnant contents of the pipeline into a vessel known as a ‘Slug catcher’. The term slug catcher is used since pigging operations produces a Slug flow regime characterized by the alternating columns of liquids & gases. Slug catcher’s are popularly of two types – Horizontal Vessel Type & Finger Type Slug catcher. However irrespective of the type used, the determination of the slug catcher volume becomes the primary step before choosing the slug catcher type.
Performance investigation of hydraulic actuator based mass lift system using ...Mustefa Jibril
A hydraulic actuator is a system that can provide a large power amplification in industries and
factories. In this paper, mass lifter hydraulic actuator system to a desired displacement is designed
using optimal control theory. MPC and LQR controllers are used to design and improve the
performance of the hydraulic actuator. The hydraulic actuator system is linearized using Taylor
series linearization method and designed using Matlab/Simulink tool. Comparison of the hydraulic
actuator with MPC and LQR controllers using three desired output displacement signals (step, sine
wave and white noise) is done and simulation results have been analyzed successfully. For the
desired step input signal, the hydraulic actuator system with MPC controller lower rise and settling
times with small percentage overshoot as compared to the hydraulic actuator system with LQR
controller and for the desired sine wave signal, the hydraulic actuator system with MPC controller
almost track the desired sine wave input signal correctly as compared to the hydraulic actuator
system with LQR controller. While for the desired white noise input signal, the hydraulic actuator
system with MPC controller have tried to track the desired white noise input signal with small
variation in amplitude as compared to the hydraulic actuator system with LQR controller. Finally
the comparative simulation results prove the effectiveness of the proposed hydraulic actuator
system with MPC controller.
Piping systems associated with production, transporting oil & gas, water/gas injection into reservoirs, experience wear & tear with time & operations. There would be metal loss due to erosion, erosion-corrosion and cavitation to name a few. The presence of corrosion defects provides a means for localized fractures to propagate causing pipe ruptures & leakages. This also reduces the pipe/pipeline maximum allowable operating pressure [MAOP].
The following document covers methods by DNV standards to quantitatively estimate the erosion rate for ductile pipes and bends due to the presence of sand. It is to be noted that corrosion can occur in many other scenarios such as pipe dimensioning, flow rate limitations, pipe performance such as pressure drop, vibrations, noise, insulation, hydrate formation and removal, severe slug flow, terrain slugging and also upheaval buckling. However these aspects are not covered in this document.
Based on the erosional rates of pipes and bends, the Maximum Safe Pressure/Revised MAOP is evaluated based on a Level 1 Assessment procedure for the remaining strength of the pipeline. The Level 1 procedures taken up in this tutorial are RSTRENG 085dL method, DNVGL RP F-101 (Part-B) and PETROBRAS’s PB Equation.
Design and Control of a Hydraulic Servo System and Simulation AnalysisIJMREMJournal
This paper describes the system analysis, modeling and simulation of a Hydraulic Servo System (HSS) for
hydraulic mini press machine. Comparisons among linear output feed back PID control, Fuzzy control and
Hybrid of PID and Fuzzy control are presented. Application of hybrid controller to a nonlinear is investigated
by both position and velocity of the hydraulic servo system. The experiment is based on an 8 bit PIC
16F877 microcontroller, and the simulation is based on MATLAB Simulink. Simulation and hardware
experimental results show that the hybrid controller gave the best performance as it has the smallest overshoot,
oscillation, and setting time.
High pressure common rail injection system modeling and controlISA Interchange
In this paper modeling and common-rail pressure control of high pressure common rail injection system (HPCRIS) is presented. The proposed mathematical model of high pressure common rail injection system which contains three sub-systems: high pressure pump sub-model, common rail sub-model and injector sub-model is a relative complicated nonlinear system. The mathematical model is validated by the software Matlab and a virtual detailed simulation environment. For the considered HPCRIS, an effective model free controller which is called Extended State Observer – based intelligent Proportional Integral (ESO-based iPI) controller is designed. And this proposed method is composed mainly of the referred ESO observer, and a time delay estimation based iPI controller. Finally, to demonstrate the performances of the proposed controller, the proposed ESO-based iPI controller is compared with a conventional PID controller and ADRC.
Adaptive terminal sliding mode control strategy for dc–dc buck convertersISA Interchange
This paper presents an adaptive terminal sliding mode control (ATSMC) strategy for DC–DC buck converters. The idea behind this strategy is to use the terminal sliding mode control (TSMC) approach to assure finite time convergence of the output voltage error to the equilibrium point and integrate an adaptive law to the TSMC strategy so as to achieve a dynamic sliding line during the load variations. In addition, the influence of the controller parameters on the performance of closed-loop system is investigated. It is observed that the start up response of the output voltage becomes faster with increasing value of the fractional power used in the sliding function. On the other hand, the transient response of the output voltage, caused by the step change in the load, becomes faster with decreasing the value of the fractional power. Therefore, the value of fractional power is to be chosen to make a compromise between start up and transient responses of the converter. Performance of the proposed ATSMC strategy has been tested through computer simulations and experiments. The simulation results of the proposed ATSMC strategy are compared with the conventional SMC and TSMC strategies. It is shown that the ATSMC exhibits a considerable improvement in terms of a faster output voltage response during load changes.
Hardware-in-the-loop based comparative analysis of speed controllers for a tw...journalBEEI
A comparative study of speed control performance of an induction motor drive system connecting to a load via a non-rigid shaft. The nonrigidity of the coupling is represented by stiffness and damping coefficients deteriorating speed regulating operations of the system and can be regarded as a two-mass system. In the paper, the ability of flatness based and backstepping controls in control the two-mass system is verified through comprehensive hardware-in-the-loop experiments and with the assumption of ideal stator current loop performance. Step-by-step control design procedures are given, in addition, system responses with classical PID control are also provided for parallel comparisons.
The velocity control of the electro hydraulic servo systemeSAT Journals
Abstract In general two basic methods are used for controlling the velocity of a hydraulic cylinder. First by an axial variable-displacement pump for controls flow to the cylinder. This configuration is commonly known as a hydrostatic transmission. Second by proportional valve powered by a constant-pressure source, such as a pressure compensated pump, drives the hydraulic cylinder. In this study, the electro-hydraulic servo system (EHSS) for velocity control of hydraulic cylinder is investigated experimentally and its analysis theoretically. Where the controlled hydraulic cylinder is altered by a swashplate axial piston pump or by proportional valve to achieve velocity control. The theoretical part includes the derivation of the mathematical model equations of combination system. Velocity control system for hydraulic cylinder using simple (PID) controller to get constant velocity range of hydraulic cylinder under applied external variable loads . An experimental set-up is constructed, which consists of the hydraulic test pump unit, the electro-hydraulic proportional valve unit, the hydraulic actuator unit , the external load control unit and interfacing electronic unit. The experimental results show that PID controller can be achieve good velocity control by variable displacement axial piston pump and also by proportional valve under external loads variations. Keywords: Velocity control, Swashplate, Proportional valve, Hydraulic cylinder, PID controller, Axial piston pump
A STUDY ON PERFORMANCE OF DIFFERENT OPEN LOOP PID TUNNING TECHNIQUE FOR A LIQ...IJITCA Journal
Process control is the application and study of automatic control to maintain a process at the desired operating condition ,safety, and efficiently while satisfying the environmental and product quality. Like the Level, Temparature & Pressure, Liquid flow Measurement is one of the major controlling parameter in
process plant. This paper mainly concern about the single tank liquid flow process and designing the controller with different PID tunning methods. Many process plants controlled by the PID controller with similar dynamics to find out the possible set of satisfactory controller parameters from the less plant
information but from the mathematical model. With minimum effort adjust the controller parameters by using three open loop PID controller IMC,CHR & AMIGO and compare their output response in real time flow tank system
A STUDY ON PERFORMANCE OF DIFFERENT OPEN LOOP PID TUNNING TECHNIQUE FOR A LI...IJITCA Journal
Process control is the application and study of automatic control to maintain a process at the desired operating condition ,safety,and efficiently while satisfying the environmental and product quality. Like the Level,Temparature & Pressure, Liquid flow Measurement is one of the major controlling parameter in process plant. This paper mainly concern about the single tank liquid flow process and designing the controller with different PID tunning methods.Many process plants controlled by the PID controller with similar dynamics to find out the possible set of satisfactory controller parameters from the less plant information but from the mathematical model.With minimum effort adjust the controller parameters by using three open loop PID controller IMC,CHR & AMIGOand compare their output response in real time flow tank system.
In this paper, a new topology of Adaptive Hysteresis Band controller for Boost & Buck converter has been proposed, modeled and analyzed. The difficulties caused in Hysteresis Band (HB) controlled dc-dc converter have been eliminated using Adaptive Hysteresis Band (AHB) controller. This novel control topology can be able to maintain the switching frequency constant unlike HB controller. Thus the filter design for the converters will become easier with this controller. Again this control methodology is a robust one as it depends upon the system parameters where there was no possibility with HB controller. The Mathematical modeling of the controller is shown in this paper, further this has been simulated using Matlab /SIMULINK to generate pulse. The steady state analysis to find the parameters and the stability condition of the converter using the dynamic behavior is also portrayed in this paper. The simulation for a Boost and a Buck converter is also shown separately using AHB controller.
MODIFIED DIRECT TORQUE CONTROL FOR BLDC MOTOR DRIVESijctcm
In this paper, a new adaptive reference based approach to direct torque control (DTC) method has been
proposed for brushless direct current (BLDC) motor drives. Conventional DTC method uses two main
reference parameters as: flux and torque. A main difference from the conventional method of it was that
only one reference parameter (speed) was used to control the BLDC motor and the second control
parameter (flux) was obtained from speed error through the proposed control algorithm. Thus, the DTC
performance has been especially improved on systems which need variable speed and torque during
operation, like electric vehicles. The dynamic models of the BLDC and the DTC method have been created
on Matlab/Simulink. The proposed method has been confirmed and verified by the dynamic simulations on
different working conditions. The simulation studies showed that the proposed method reduced remarkably
the speed and the torque ripples when compared the conventional DTC method. Moreover, the proposed
method has also very simple structure to apply the conventional DTC and its extra computational load to
the controller is almost zero.
Applying Parametric Functional Approximations for Teaching Electromechanical ...IOSRJEEE
In this paper functional approximations for the parameters of a DC machine are proposed. These nonlinear algebraic approximations are based on the experimental data that are obtained by carrying out several steady state and transient tests, besides, this method links mathematics and practical analysis of electromechanical systems, allowing students to improve their academic performance and comprehension by comparing estimated values with measured data. An excellent dynamic model results of combining the well known state space description and these parametric functional approximations. This augmented model provides reliable results even during demanding large-excursion transient conditions
MODELING AND DESIGN OF CRUISE CONTROL SYSTEM WITH FEEDFORWARD FOR ALL TERRIAN...cscpconf
This paper presents PID controller with feed-forward control. The cruise control system is one of the most enduringly popular and important models for control system engineering. The system is widely used because it is very simple to understand and yet the control techniques cover many important classical and modern design methods. In this paper, the mathematical modeling for PID with feed-forward controller is proposed for nonlinear model with disturbance effect. Feed-forward controller is proposed in this study in order to eliminate the gravitational and wind disturbance effect. Simulation will be carried out . Finally, a C++ program written and feed to the microcontroller type AMR on our robot
International Journal of Engineering Research and DevelopmentIJERD Editor
Electrical, Electronics and Computer Engineering,
Information Engineering and Technology,
Mechanical, Industrial and Manufacturing Engineering,
Automation and Mechatronics Engineering,
Material and Chemical Engineering,
Civil and Architecture Engineering,
Biotechnology and Bio Engineering,
Environmental Engineering,
Petroleum and Mining Engineering,
Marine and Agriculture engineering,
Aerospace Engineering.
Multi objective control of nonlinear boiler-turbine dynamics with actuator ma...ISA Interchange
This paper investigates multi-objective controller design approaches for nonlinear boiler-turbine dynamics subject to actuator magnitude and rate constraints. System nonlinearity is handled by a suitable linear parameter varying system representation with drum pressure as the system varying parameter. Variation of the drum pressure is represented by suitable norm-bounded uncertainty and affine dependence on system matrices. Based on linear matrix inequality algorithms, the magnitude and rate constraints on the actuator and the deviations of fluid density and water level are formulated while the tracking abilities on the drum pressure and power output are optimized. Variation ranges of drum pressure and magnitude tracking commands are used as controller design parameters, determined according to the boiler-turbine's operation range.
Similar to SvSDP 4113a_emsd3_20122016_article (20)
CFD Simulation of By-pass Flow in a HRSG module by R&R Consult.pptxR&R Consult
CFD analysis is incredibly effective at solving mysteries and improving the performance of complex systems!
Here's a great example: At a large natural gas-fired power plant, where they use waste heat to generate steam and energy, they were puzzled that their boiler wasn't producing as much steam as expected.
R&R and Tetra Engineering Group Inc. were asked to solve the issue with reduced steam production.
An inspection had shown that a significant amount of hot flue gas was bypassing the boiler tubes, where the heat was supposed to be transferred.
R&R Consult conducted a CFD analysis, which revealed that 6.3% of the flue gas was bypassing the boiler tubes without transferring heat. The analysis also showed that the flue gas was instead being directed along the sides of the boiler and between the modules that were supposed to capture the heat. This was the cause of the reduced performance.
Based on our results, Tetra Engineering installed covering plates to reduce the bypass flow. This improved the boiler's performance and increased electricity production.
It is always satisfying when we can help solve complex challenges like this. Do your systems also need a check-up or optimization? Give us a call!
Work done in cooperation with James Malloy and David Moelling from Tetra Engineering.
More examples of our work https://www.r-r-consult.dk/en/cases-en/
Overview of the fundamental roles in Hydropower generation and the components involved in wider Electrical Engineering.
This paper presents the design and construction of hydroelectric dams from the hydrologist’s survey of the valley before construction, all aspects and involved disciplines, fluid dynamics, structural engineering, generation and mains frequency regulation to the very transmission of power through the network in the United Kingdom.
Author: Robbie Edward Sayers
Collaborators and co editors: Charlie Sims and Connor Healey.
(C) 2024 Robbie E. Sayers
Saudi Arabia stands as a titan in the global energy landscape, renowned for its abundant oil and gas resources. It's the largest exporter of petroleum and holds some of the world's most significant reserves. Let's delve into the top 10 oil and gas projects shaping Saudi Arabia's energy future in 2024.
Cosmetic shop management system project report.pdfKamal Acharya
Buying new cosmetic products is difficult. It can even be scary for those who have sensitive skin and are prone to skin trouble. The information needed to alleviate this problem is on the back of each product, but it's thought to interpret those ingredient lists unless you have a background in chemistry.
Instead of buying and hoping for the best, we can use data science to help us predict which products may be good fits for us. It includes various function programs to do the above mentioned tasks.
Data file handling has been effectively used in the program.
The automated cosmetic shop management system should deal with the automation of general workflow and administration process of the shop. The main processes of the system focus on customer's request where the system is able to search the most appropriate products and deliver it to the customers. It should help the employees to quickly identify the list of cosmetic product that have reached the minimum quantity and also keep a track of expired date for each cosmetic product. It should help the employees to find the rack number in which the product is placed.It is also Faster and more efficient way.
Water scarcity is the lack of fresh water resources to meet the standard water demand. There are two type of water scarcity. One is physical. The other is economic water scarcity.
Welcome to WIPAC Monthly the magazine brought to you by the LinkedIn Group Water Industry Process Automation & Control.
In this month's edition, along with this month's industry news to celebrate the 13 years since the group was created we have articles including
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A look back on an article on smart wastewater networks in order to see how the industry has measured up in the interim around the adoption of Digital Transformation in the Water Industry.
1. Speed-variable Switched Differential Pump (SvSDP) System
Peter Sloth-Odgaard, Rasmus Aagaard Hertz, Søren Valentin-Pedersen
Department of Mechanical and Manufacturing Engineering
Aalborg University
DK-9220 Aalborg East
Denmark
Abstract
This paper presents the further developments and working principle of the speed-variable switched differential pump (SvSDP)
concept proposed, designed and produced in [1]. The SvSDP system is designed to remove the throttling losses associated with
typical valve driven control (VDC) systems. The hydraulic and mechanical system is modelled and linearised. The linearisation
point is studied to provide an usable basis for controller design. It is proposed, in this paper, to model the converter and motor
using a black box approach, where designed and informative input sequences are used to estimate the mathematical behaviour of
the electrical drive based on the equivalent output data. The complete non linear model is verified against available trajectory data
from the physical system, obtained from [1]. The linear model is analysed through a relative gain array (RGA) analysis to map the
input output couplings present in the system. The results show that the system includes heavy cross-couplings. Results presented
in [1] indicate, that it is possible to utilise a input output compensated decoupling to redefine the MIMO system into multiple
SISO systems. The SvSDP concept is over-determined in relation to the amount of control inputs compared to possible outputs.
It is proposed in [1] to introduce two new input states and two new output states. The decoupling approach has been investigated
in this paper. The decoupling results provided a basis of using decentralised control. The linear control strategies are designed
independently based on the notion of decoupling. The first controller is related to the level flow, designed to maintain a desired
minimum pressure level. The second load flow controller is related to the cylinder motion. The controller results indicate, that it
is possible to achieve a good dynamic tracking performance with an error of maximum 0.5 mm for a given position trajectory.
This paper is also considering the energy consumption issues stated in [1], where two conceptual solutions are proposed, to solve
the power loss associated with holding a load at a constant cylinder position. This paper is written as the product of an appendix
report describing the whole project.
Keywords: Electro-Hydraulic Drive, Compact Drive, Dynamic Estimation of Electric Drive, Black Box Identification,
Over-determined Control, Decoupling, Input Output Compensation, Pressure Control, Motion Control, Load Hold Efficiency,
Direct Drive
1. Introduction
The focus on the environmental aspect of production lines
have increased in recent years. Hydraulic drive systems
are typically associated with high force operation and
low efficiency. The subject of developing energy efficient
hydraulic solutions is expanding in correlation with the
increased focus on minimising CO2 output and maximising
energy savings. It is common to actuate linear cylinders with
a valve controlled hydraulic drive, where the primary power
loss is related to valve throttling (P = Q·∆p). It was recently
proposed to actuate a linear differential cylinder using only
pumps, thereby fully removing the throttling losses. The
initial concept (SvDP) proved to be unusable in relation to
its achievable tracking performance.
The concept was further developed in multiple student
projects to the stage it has reached today, where the concept
has been built and tested experimentally by [1]. The test
bench finalised in [1] is driven by a speed-variable switched
differential pump (SvSDP) system, where three pumps are
connected to a single motor unit using a common shaft. The
hydraulic diagram of the SvSDP system is shown in figure 1.
The SvSDP system is designed to always build up pressure
in the return side chamber, by switching the support pump P2
in relation to the motor velocity equivalent to a flow difference
defined in equation (1). The pressure build up in the return
side, in relation to motor velocity and pressure, is defined by
Fig. 1 Hydraulic overview of the SvSDP system. The dotted area
indicate the manifold system. [1]
the match ratio χ.
(QP 1 + QP 2) · α > QP 3 for ωm ≥ 0 (1)
QP 1 · α < QP 3 for ωm < 0 (2)
The check valves seen in figure 1 governs the switching
of the second pump (CVAP21) and further adds an anti-
cavitation feature to the system by allowing idling modes in
the pumps. The SvSDP system uses inherited proportional
1
2. valves, which were included in the SvDP design by [2].
The proportional valves adds the possibility of lowering the
chamber pressures during operation, thus adding an extra
necessary control feature. It was proven in [1] that a converter
driven permanent magnet synchronous motor (PMSM) drive
was capable of producing the desired tracking capabilities. It
was later proposed in [3] and [4] that the overall application
cost could be greatly reduced (see table I), if the drive were
to be replaced with a performance equivalent induction motor
(IM, [5]) and Sytronix converter [6], both supplied from
Bosch Rexroth A/S.
Solution Retail price [DKK]
Servo drive + PMSM 45714.00
Frequency converter + IM + Encoder 23000.00
Tab. I Retail price related to different drive solutions. [4]
It was never verified in either [3] or [4], that it is possible to
achieve an equivalent performance of the IM drive compared
to the PMSM solution. The verification of the IM drive is
an essential part of the appendix project, where the related
results are presented, but will not be covered in this paper. It is
chosen to present some of the methods proposed and derived
in [1] in relation to analysis results. The presentation of
methods is done to provide an overview of the mathematical
foundation of the SvSDP system.
2. System model
The hydraulic model is derived and parametrised with respect
to research done in [1] and [3]. It is chosen to follow the
same notation as [1] for easier comparability of results. The
parameter subscripts through this paper are equivalent to the
ones used in figure 1. The governing parts used to model the
SvSDP system are a combination of four different component
categories defined as
• Check valves
• Pumps
• Cylinder
• Proportional valves (2/2 way)
The check valves and manifold dynamics are for simplicity
purposes neglected in this paper. The related dynamic effects
are still included in the non linear system, to ensure the
correct functionality of the designed anti-cavitation system
and switching of the support pump P2. It is chosen to
only represent the equations later used in relation to the
system analysis and controller design. The flows out of
both pump QP 1 and QP 2 are combined to an equivalent
velocity dependent flow QP 12 in relation to the manifold
dynamics. The second order leakage term related to the
mathematical estimate of the pump flow is, for simplicity
purposes, neglected in the paper, such the flow equations are
equivalent to the linearised flow models. The flow equations
are functions of motor velocity ωm and the pressure drop
across the pumps ∆p12
and ∆p3
defined as
QP 12 = K12ω(ωm)ωm − K12p(ωm)∆p12
(3)
QP 3 = K3ωωm − K3p∆p3
(4)
where Kω is the effective displacement constant, propor-
tional to the rotational speed at zero pressure drop across the
pump. The constant Kp describes the pressure depend leakage
over the pump. The motor dependent pump logic is defined
as
K12ω(ωm) =
K1ω + K2ω if ωm ≥ 0
K1ω if ωm < 0
(5)
K12p(ωm) =
K1p + K2p if ωm ≥ 0
K1p if ωm < 0
(6)
The relevant chamber pressure gradients are defined in
equation (7) and (8) where the manifold dynamics, pressure
relief valves and cylinder leakage (KQL·∆pAB
) are neglected.
˙pA
=
βe,A(pA
)
VA,0 + x · Ap
(QP 12 − QAV − ˙x · Ap) (7)
˙pB
=
βe,B(pB
)
VB,0 − x · Ar
(−QP 3 − QBV + ˙x · Ar) (8)
where βe,A and βe,B are defined as the pressure dependent
bulk modulus in relation to the control volumes (VA,0+x·Ap)
and (VB,0 − x · Ar) respectively.
The two proportional valves are identical. The valve model
is formulated based on data sheet data using a combination of
look-up tables and a second order transfer function between
input voltage reference and output. Assuming the look-up
table to be representative for the valve flow, it is possible, by
inverting the look-up table, to only account for the dynamic
behaviour in the valve as
QV (s)
QV,ref (s)
=
133.32
s2 + 2 · 133.3 · s + 133.32
(9)
The mechanical dynamics described by Newton’s second
law of motion, is simplified by neglecting both the Coulomb-
and Stribeck friction terms used in the non linear model thus
only leaving the viscous slider velocity dependent friction
(Bv · ˙x). It is further assumed that the external load can
be considered as a disturbance hence being negligible. The
simplified and linear mechanical model is defined as
¨x =
1
m
(pA
Ap − pB
Ar − Bv · ˙x) (10)
3. Drive model
In this paper it is proposed to use an alternative approach
to describe the dynamics of both the motor and converter
using methods related the subject of system identification. It
is desired to find a usable dynamic estimate which covers both
the motor and controller dynamics without the requirement of
time consuming- and advanced system models.
The achievable performance of the SvSDP system is highly
dependent on the chosen converter and motor. This notion
indicate, that it will be useful to provide a simple black box
tool for estimating drive dynamics in relation to controller
2
3. tuning. The black box tool may increase the application
flexibility of the SvSDP concept, if proper (informative) input
output data can be obtained, such any drive unit can be
modelled and implemented in the tuning process.
The estimated transfer function is describing the relation-
ship between input reference- and output velocity, equivalent
to the transfer function of a closed loop velocity system.
It is chosen to employ a black box estimation using two
methods; ARX and ARMAX presented in [7] and [8]. The
ARMAX method is an extension of the ARX method, with
the difference in its noise handling capabilities. It was seen,
that the velocity signal included noise, thus it was chosen to
utilise ARMAX as the primary estimation method.
The transfer function estimation is employed on results
both related to V/f (voltage/frequency) control and FOC (field
oriented vector control). The estimation results related to the
FOC strategy are seen in figure 2, where the input output data
is related to the estimated and simplified estimated dynamic
models.
Fig. 2 FOC transfer function verification related the simplified
second order model estimate compared to the z-domain model and
actual system.
The results show that the estimated model is capable
of tracking the actual system almost perfectly using a
fifth order z-domain transfer function. The estimated system
dynamics resembled a second order transfer function, up
until the system bandwidth. This notion made it possible
to successfully estimate the drive and motor dynamics with
a second order transfer function, as shown in figure 2.
The tuning process of the proposed Sytronix converter [6]
provided unusable results. The maximum achieved bandwidth
of the FOC controlled closed loop system was 1 Hz, which
is far from the Nyquist frequency [9] stating that a control
system should at least have twice the bandwidth of the plant,
which in this case is equivalent to a minimum required
bandwidth of 30 Hz.
To solve this issue it was concluded by Bosch Rexroth
A/S and the group, that the solution would be to replace
the converter with an equivalent model [10] without the
Sytronix user interface. Based on the data sheet [10] of the
new converter, where no restrictions are mentioned, it was
assumed that it would be possible to achieve the desired
closed loop bandwidth. The tuning results, indicated that
the same unknown performance limitations existed in both
products. The solution was to utilise the PMSM motor [11]
described in [1] for modelling purposes, hence it was not
possible to verify the IM [5] solution at this stage.
4. Linearisation
The non linear system is linearised based on assumptions
related to the operation condition of the hydraulic system. The
primary non linearities are present in the pressure dynamic
equations (7) and (8), in terms of a pressure dependent bulk
modulus and a cylinder position dependent volume. The linear
pump flow equations are presented in equation (3) and (4).
The mechanical system is also, for simplicity purposes, stated
in its linear form in equation (10).
It is chosen to assume a constant bulk modulus for the
controller design. The maximum oil stiffness is achieved
for pressure levels equal or larger than 30 bar, making the
assumption of constant bulk modulus valid based on the
notion that 30 bar is easily reached during operation. The
constant bulk modulus at 30 bar is chosen based on the
assumption of initial velocity. This assumption is deemed
valid based on the notion that the motor is going to follow a
controller reference, which is always varying during reference
tracking. Having a varying motor speed and direction is
assumed to ensure oil pressure levels of minimum 30 bar
throughout the operation with respect to the match ratio.
The validity of this effect is challenged, if the motor is kept
inactive for too long periods of time at zero velocity and load
hold situations.
The position dependent volume changes are analysed using
a pole sweep, to determine the x value where the system has
the minimum possible natural frequency, equivalent to the
slowest dynamic behaviour. The hydraulic system is converted
into its state space form to easily plot the eigenvalues (poles)
in relation to variations in the cylinder position. The dynamic
model between input motor velocity and output cylinder
position consist of four poles and a zero (seen from the
hydraulic transfer function matrix). The free integrator present
when integrating the velocity to position is disregarded. The
root locus plot showed, that the three last poles are equivalent
to a first order system combined with a second order under
damped system. The pole of the first order system is located
closer to ω = 0 rad/s than the second order dynamics. If the
velocity transfer function is stepped (disregarding the free
integrator), it is seen, that the second order dynamics are
dominating the response, thus indicating that the first order
system dynamics are cancelled out by the nearby zero.
5. Model verification
The non linear system model is verified against data from [3].
The inputs used to obtain the experimental data and verify
the non linear model are shown in figure 3a. The dataset is
obtained with an active load side force controller using a load
reference of 0 kN.
3
4. 0 2 4 6 8 10
Time [s]
0
20
40
60
ωm,ref
[rad/s]
0
50
100
xAV,ref
&xBV,ref
[%]
ωm
xAV
xBV
(a) Input sequence for motor and valves.
0 2 4 6 8 10
Time [s]
0
10
20
30
Pressure[bar]
pA:Exp
pA:NL
pB:Exp
pB:NL
(b) Pressure level.
0 2 4 6 8 10
Time [s]
-350
-250
-150
-50
50
x[mm]
Exp
NL
(c) Cylinder position.
0 2 4 6 8 10
Time [s]
0
50
100
˙x[mm/s]
Exp
NL
(d) Cylinder velocity.
Fig. 3 Experimental and simulated responses related to the non linear model verification.
It is seen in [3], that the force controller is incapable of
holding the load of 0 N, thus it is necessary to feed back
the measured load data to compensate for this error in the
model response. The simulated responses are compared with
the experimental data as shown in figure 3.
The responses of the non linear model shows a good
correlation with the experimental data. Both the slider
position and velocity responses are almost identical for the
two systems as seen in figure 3c and 3d respectively. It
should be noted, that the model is showing a less damped
response in comparison to the data. The under damped
behaviour is related to the oscillations present in both the
pressure dynamics and slider velocity seen in figure 3b and
3d respectively.
6. System decoupling
The SvSDP system is a MIMO system, meaning that the
control strategy can be formulated using different approaches.
The system is analysed to verify whether input output
coupling exist or not. If cross-coupling is found, it may prove
beneficial to apply a decoupling approach, thus converting the
MIMO system into multiple SISO systems. An alternative
approach, would be to accept the found cross-couplings and
solve the problem using a non linear control approach.
The input output couplings are analysed for a chosen
frequency range using the relative gain array (RGA) approach.
The transfer function matrix used to obtain the RGA, is
divided into six sub systems. The results show that all sub
systems contain heavy couplings throughout the frequency
sweep, it is further seen that the gain signs changed at the
natural frequency of 102
rad/s. It is proposed and concluded
in [1] that a system decoupling is beneficial based on the
amount of cross coupling in the system.
It is proposed in [1] that by applying both an input-
and output-compensator W1
and W2
respectively, it may
become possible to achieve a fully decoupled system within
the desired frequency range. The original system G(s) is thus
transformed into a compensated system ˜G(s) (see figure 4)
defined as
˜G(s) = W2
G(s) W1
(11)
The input- and output-compensation will modify the inputs
and outputs of ˜G(s) as
˜y = W2
y ˜u = W−1
1
u (12)
The used input- and output compensation structure is
shown in figure 4, where the new decoupling environment
is denoted with tilde.
GAC
(s) GH
(s)W1
W2
G(s)
˜G(s)
˜uref uref u y ˜y
Fig. 4 The compensated system with respect to the original system
consisting of the actuator system GAC
(s) (drive and proportional
valves) and the hydraulic mechanical system GH
(s).
6.1 Output compensation
It is desired to formulate an output-compensation which
makes it possible to consider more appropriate states than
the original control system. It is proposed in [1] to define
a virtual, but measurable, load pressure pL
state and further
introduce a fictive level pressure pH
state. The load pressure
is implicitly describing the available load force seen on the
cylinder shaft, whereas the level pressure can be seen as a
weighted sum between the two chamber pressures. The two
virtual output states are defined as
4
5. pL
= pA
− α · pB
(13)
pH
= pA
+ H · pB
(14)
It is possible to rewrite equations (13) and (14) to describe
both the pA
and pB
pressures in relation to the two defined
output states as
pA
=
H
H + α
· pL
+
α
H + α
· pH
(15)
pB
=
−1
H + α
· pL
+
1
H + α
· pH
(16)
By taking the derivative of both equation (13) and (14)
it is possible to substitute the linear pressure gradients of
chamber A and B from equation (7) and (8). By expanding
the expression of ˙pH
it is possible to show, that by choosing
the parameter H = VB
α·VA
, it is possible to cancel out the piston
velocity ˙x influence in the level pressure dynamics ˙pH
. The
output compensator W2
is defined in equation (17) as the
relation between the actual output states and the two virtual
outputs.
x
pL
pH
˜y
=
1 0 0
0 1 −α
0 1 H
W2
x
pA
pB
y
(17)
6.2 Input compensation
The definition of H is used together with equations (15) and
(16) to rewrite both ˙pH
and ˙pL
in terms of pL
and pH
. This
new definition is used to determine the input compensator
W1
. The load flow QL and level flow QH are defined as the
input related terms of the rewritten ˙pH
and ˙pL
equations. The
input relation is defined as
QL
QH
Q0
˜u
=
H·ΛKω
α+H − H
α+H
1
α+H
(α + H)∆Kω −(α + H) −α+H
α
v31 v32 v33
W −1
1
ωm
QAV
QBV
u
(18)
Q0 is defined as the flow constraint and can be used to
achieve different utilisation methods as described in [1]. This
paper is only considering the flow constraint where Q0 ≡ 0.
Based on the flow constraint chosen, it is possible to create
different input compensations due to the relation between the
compensated input to the original input as
ωm
QAV
QBV
u
=
w11 w12 X
w21 w22 X
w31 w32 X
W1
QL
QH
Q0
˜u
(19)
The column W1
(:, 3) is not of interest due to the definition
of Q0 and is therefore denoted with an "X". It is decided
to utilise the input compensation method 1, described in
[1], where the shaft speed is controlled only by the load
flow QL. The method is obtained by cancelling the term
QAV − QBV
H in the derived load flow gradient ˙pL
. The
dynamic behaviour of the load flow will therefore only be
affected of the shaft speed and not the proportional valve
inputs. It should be noted that both of the proportional valves
are activated for both directions which introduces some losses.
The input compensator is defined as
W1
=
α
H · ΛKω
α+H
α 0 X
∆Kω − H·ΛKω
(α+H)2 X
H · ∆Kω −H2
·ΛKω
(α+H)2 X
(20)
The input QAV and QBV are physically restricted due to
the fact that they can only lead flow away from the cylinder.
This constraint has to be modelled to obtain the proper
performance of the system. The cylinder motion control
is the main focus of the project, which is why it is not
desirable to limit the load flow QL implicitly describing
the allowable force on the cylinder. The restriction of the
proportional valves are therefore related to the level flow QH.
The following relation has to be obtained.
QAV , QBV ≥ 0 ⇒ QH ≤ (α + H)∆Kω · ωm (21)
The relation in equation (22) has to be fulfilled to ensure
a positive flow through the proportional valves and to avoid
discontinuous references with respect to shaft speed.
1
∆K−
ω
≤ (α + H)w12 ≤
1
∆K+
ω
(22)
6.3 Decoupling results
The results related to the implementation of the output
compensation indicate that it is possible to achieve a less
coupled system with only an output compensation. The pure
output compensation is not capable of fully eliminating the
coupling effects, which is why the input compensation is
included. The input and output compensated system ˜G(s) is
manipulated to have the RGA numbers seen in figure 5. The
system is considered fully decoupled, thus proving the validity
of the approach.
100
101
102
103
Frequency [rad/s]
0
2
4
RGAnumber
x(QL
) , PH
(QH
)
x(QH
) , PH
(QL
)
Fig. 5 RGA number of the input and output compensated system
˜G(s).
5
6. 7. Control
The decoupling results indicate, that it will be possible
to utilise a decentralised control approach. The SvSDP is
thought of as a general application to cylinder drives, resulting
in no strict control objective. Instead the difficulty lies in
designing a system that is stable for all pressures and slider
positions. Considering the effective oil stiffness described by
bulk modulus, it is desired to be able to have a minimum
pressure in the cylinder chambers to ensure robustness against
external forces and to improve performance with respect to
position tracking. The control is divided into two parts being
pressure level- and position control. It is tried to design
both control strategies separately based on the notion of
decoupling.
7.1 Pressure level control
The pressure level control is designed to keep a minimum
return side pressure of 30 bar. The controller output is related
to the level flow reference QH. The controller structure is
shown in figure 6.
Level
pressure
reference
generator
pset
+
−
pH,ref
Gc,H
eH
W1
QH
QL
ZZQ0
SCM
ωm,ref
QAV,ref
QBV,ref
W2
pA
x
pB
pL
x
pH
Decoupler
H HH
Fig. 6 Block diagram of the pressure level control structure.
The level pressure error is only dependent on one of
the chamber pressures, which effectively reduces the effect
of pH,ref
to a scaling, dependent on what chamber should
be controlled and the position of the slider. The controller
is designed towards the final goal of finding the optimum
between a maximum possible bandwidth of the compensated
system without being able to excite possibly non decoupled
frequencies caused by possibly occurring errors in the H
estimation. The simplified transfer function between QH and
pH
is defined as
pH(s)
QH(s)
=
1
KHpH
·
1
VA·(α+H)
β·KHpH
· s + 1
(23)
The transfer function in equation (23) is dependent on both
H and VA making it implicitly dependent on the cylinder
position x. The value of x is chosen equivalent to the system
with the largest time constant (slowest possible configuration).
The controller designed is a combination of a PI controller,
a gain and a second order low pass filter. The filter is
used to damp the magnitude after a certain frequency, thus
providing safety against the previously mentioned coupling
effects by ensuring a proper magnitude damping before the
natural frequency is reached. The controller is implemented
and simulated, producing the results shown in figure 7. The
simplified system has a phase margin of 67 degree and a gain
margin of 11.7 dB.
The controller is capable of keeping the minimum set
pressure of 30 bar in the chambers as soon as the set pressure
is reached the first time (see figure 7b), with the exception
of the oscillations present when QL is stepped. The cylinder
velocity response is unaffected by the pressure level control
and still oscillate equivalent to the natural frequency of the
hydraulic system (≈ 16 Hz). It is further seen in figure 7a,
that the valve command signals are strictly positive, governed
by the feasibility bound.
7.2 Motion control
The motion control is divided into three parts, being a
combination of PI position control, pL
feedback damping and
velocity feed forward. A simplified transfer function between
QL and x is constructed based on the load pressure dynamics
˙pL
and (10) rewritten to depend on the load pressure.
x
QL
=
1
s
·
K1
s2 + K2 · s + K3
(24)
where
K1 =
Ap · (α + H) · β
H · VA · M
(25)
K2 =
Bv
m
+
β · KLpL
VA · (α + H)
(26)
K3 =
α + H
H · VA
·
β
m
· A2
p +
Bv · KLpL
α + H
(27)
Assuming perfect decoupling, it is possible to neglect the
term containing pH
. The Kad gained load pressure feedback
is used to achieve a damping coefficient of 0.7 equivalent to
a desired trade off between overshoot and settling time. The
used motion structure is illustrated in figure 8.
+
−
xref
Gpos,P I
ex
Ap
ex +
+
˙xref
+
−
Q∗
L ˜GCM
pset
QL pL
x
pH
Kad
Fig. 8 Block diagram of the motion control structure.
The motion controller is designed such it can ensure
stability for a minimum pressure of 4 bar while still
performing well in the high pressure range. The coherent
stability margins are shown in table II.
Pressure Phase Margin [o] Gain Margin [dB]
Pressure: p0 = 30 bar 52 16
Pressure: p0 = 4 bar 46 6
Tab. II Gain and phase margins of the designed controller and plant,
obtained from the open loop bode plots.
The motion and pressure level controlled system is
simulated and the coherent results are presented in figure 9.
6
7. 0 0.5 1 1.5 2 2.5
Time [s]
0
20
40
Valvesignal[%]
xAV
xBV
(a) Valve opening signals.
0 0.5 1 1.5 2 2.5
Time [s]
0
20
40
60
80
Pressure[bar]
pA
pB
(b) A- and B side pressures.
0 0.5 1 1.5 2 2.5
Time [s]
-20
0
20
QL
[L/min]
(c) Load flow reference.
0 0.5 1 1.5 2 2.5
Time [s]
-200
0
200
˙x[mm/s]
(d) Cylinder velocity.
Fig. 7 Performance of the pressure level control strategy.
The used position reference is shown in figures 9a where the
position is differentiated to produce the velocity reference.
It is seen that the trajectory is followed with a maximum
error of 0.5 mm, which is concluded acceptable. It should
also be noted that the minimum pressure control is unable to
keep minimum 30 bar in chamber B when the reference is
stationary. This effect is caused by the match ratio χ present
in the system.
In correlation to decoupling method 1, it is seen in 9d that
the proportional valves are activated at the same time. The
motion controller is proved to be stable for both small and
large pressure levels and is successfully implemented in the
non linear model. The results indicate, that it is possible to
use the system in a general purpose application.
8. Efficiency analysis
It has previously been proven in [1] that the SvSDP system is
capable of minimising the power consumption compared to a
conventional valve controlled drive (VCD), due to the almost
non-existent throttling losses present in the proportional
valves included in the SvSDP set-up. The power losses
associated with both system types have been experimentally
evaluated in [1] for a predefined load and trajectory case as
shown in figure 10a. The sequence uses an applied load of 20
kN and a maximum slider velocity of 125 mm/s. The input
and output power of both systems, related to this trajectory,
is seen in figure 10b.
It is seen that the tracking performance of both systems are
similar, where the main difference is present in the amount
of input power used compared to output power ( ˙x · FL).
The SvSDP system is drawing much less input power, for
velocities different from zero, compared to the equivalent
VCD solution. The output power of both systems are close to
being the same due to the performance equivalence between
the two solutions. This notion is also indicating the capability
of the SvSDP system since it is possible to obtain the same
tracking performance as the VCD for the given trajectory.
The statement of increased efficiency related to the SvSDP
solution holds true, if the targeted application uses trajectories
with more position variance than periods of constant piston
position.
It is shown in figure 10b that approximately 600 W will be
used at zero slider speed for the SvSDP system. The power
used is both related to the leakage present over the pumps
and the required hold shaft torque. The power consumption
problem has previously been stated, without further analysis
in [1]. The problem is further investigated in this paper to
locate the primary source of loss. The mechanical power over
the pumps is compared to the input power from the converter
bus, thus giving an idea of the power drawn related to both
components separately.
The pump torque multiplied with the shaft velocity will
produce the mechanical power consumption related to the
pumps at standstill of the slider. The pressure drop dependent
pump torque equation [12] is defined as
TP x =
1.56 · KP xω · ∆pP x
η
(28)
where η is the efficiency of the pump, that for simplicity is
chosen to 100 %. For all three pumps the total torque is given
as
TP = TP 1 + TP 2 − TP 3 (29)
The torque equation is only used to provide an estimation of
the power consumption and it has not been possible to test
the coefficients and efficiency in the laboratory. The power
consumption in the three phase induction motor, near zero
velocity, can be described by
PMotor = 3 · Rw · I2
(30)
7
8. 0 5 10 15
Time [s]
-350
-200
-50
100
250
x[mm]
xref
x
(a) Position response.
0 5 10 15
Time [s]
-0.6
-0.3
0
0.3
0.6
ex
[mm]
(b) Maximum tracking error.
0 5 10 15
Time [s]
0
20
40
60
80
Pressure[bar]
pA
pB
(c) A- and B side pressures.
0 5 10 15
Time [s]
0
1
2
3
4
QxV,ref
[L/min]
QAV,ref
QBV,ref
(d) Reference proportional valve flows.
Fig. 9 Simulated response showcasing the motion controller performance.
0 5 10 15
Time [s]
-350
-250
-150
-50
50
150
250
x[mm]
xref
xSvSDP
xVCD
(a) Trajectory used for power consumption analysis. [1]
0 5 10 15
Time [s]
-3
-1.5
0
1.5
3
4.5
6
7.5
9
Power[kW]
Wi
Wi:VCD
WO
WO:VCD
(b) Power consumption results. [1]
Fig. 10 Tracking performance comparison with equivalent input and output power, used to showcase the difference between the SvSDP and
VCD systems.
Rw being the wire resistance and I being the current. The
drawn current at standstill, holding 20 kN equivalent to 28
Nm, can be found in the data sheet [11]. The motor runs slow
in load hold situations and assuming that the current can be
estimated from the pump torque, it is possible to estimate the
power consumption related to the motor by
PMotor = 3 · Rw ·
I · TP
Thold
2
(31)
The values of Rw, Thold and I are found to be 0.79Ω, 28 Nm
and 15.8 A respectively [11]. The Mechanical power used to
actuate the pumps are given as
PP ump = TP · ωm (32)
The low speed input output power consumption related to
both the pumps and motor are shown in figure 11. Note that
the x-axis starts at 6 s, as it corresponds to the load holding
situation shown in figure 10a.
The results in figure 11 indicate that input power measured
at the DC bus, is mainly consumed by the losses in the motor
unit, caused by the large moment acting on the shaft. The
pump leakage makes it impossible to hold constant chamber
pressures over time without activating the motor to counteract
6 6.5 7 7.5 8 8.5 9
Time [s]
-500
0
500
1000
1500
P[W]
PDC:BUS
PPump
PMotor
PPump
+ PMotor
Fig. 11 Power consumption related to different parts of the drive
compared to experimental measured DC-Bus data.
the leakage flow. The variation in backside pressures will
cause slider movement, thus requiring motor actuation to
counteract the leakage dependent changes. The valve based
system has the possibility of fully closing the valve at zero
position error, meaning that the piston velocity and flow
will stay at approximately zero dependent on leakage in the
cylinder, indicating that no power is drawn or lost. The power
loss associated with the motor is the reason why it is essential
to modify the SvSDP design such a load hold feature is
included.
9. Load hold
The load hold problem is investigated in this paper, where
two conceptional solutions are proposed. The first load hold
8
9. concept is a pure mechanical solution using two pilot-operated
check valves (POCV). The check valve implementation (see
figure (12)) is analysed using the non linear model.
Fig. 12 Hydraulic diagram of the modified load hold system using
the POCVs.
The results indicate, that the POCVs are capable of holding
the load, if the motor is forced to zero velocity. The initial
results of the POCV solution shows that it can work with the
designed pressure level control. A better performance can be
achieved, if the influence of the pilot pressures are balanced
in relation to the applied load. The motion controlled system
with included POCVs showed a decrease in performance. This
result indicate that the check valve implementation is less
applicable, at least if the control is not modified to compensate
for the check valve functionality.
It is further chosen to evaluate the proportional valve
load hold (PVLH) concept. The proportional valves should
in theory, only be active during low speed velocity. They
are designed, such maximum flow is achieved at minimum
possible pressure drop. The valve opening diameter should be
equivalent to the tubes diameters, to cause no flow restriction
at fully open position. By adding two new proportional
valves, the system will become even more over-determined
in relation to the number of inputs compared to outputs, thus
increasing the control complexity. If the control problem can
be solved, this solution may provide the wanted effects while
not affecting the performance of the system. The proportional
valve implementation is shown in figure 13.
The PVLH related simulation results are shown in figure
14, where the responses are compared to the non modified
system. It is seen in figure 14c that the expanded SvSDP
system is capable of tracking a position with similar capability
as the non modified system. The existing proportional valve
flows are not affected, indicating no increase in flow related
losses. It is seen in figure 14a and 14b that the chamber
pressures are kept constant for the load hold sequence,
indicated with the constant slider position seen in figure
14c. The overall performance of the PVLH concept is better
compared to the POCV concept.
Fig. 13 Hydraulic diagram of the modified load hold system using
the PVLH approach.
Both proposals showed load hold capabilities on a
conceptual level. It is known, that the maximum achievable
performance is related to the difficulties of choosing the
proper control strategy. The control should be designed to
take advantage of the valve functionalities thus removing the
unwanted power loss associated with load hold sequences
without reducing the current performance of the SvSDP
system.
10. Conclusion
Based on the non linear model verification, it is concluded that
the model of the SvSDP system is capable of representing the
dynamic behaviour of the physical set-up. The results further
indicate that the system will build up a return side pressure
equivalent to the match ratio χ of the pumps for regular non
loaded motion, regardless of input motor direction.
It was proposed to estimate the non linear dynamic be-
haviour of the converter and induction motor, through black
box system identification, using the ARX or ARMAX meth-
ods. Based on the estimation results, it is concluded the esti-
mated models are capable of representing the actual electric
drive. It was further seen that for a given frequency range,
the estimated z-domain models could be described using a
standard second order transfer function. The simplified second
order models is capable of reproducing the output data used
to estimate the system. The identification methods proposed
are concluded to perform well and will provide an increase
in the versatility of the system, related to drive replacements.
The RGA analysis showed that the original system contained
heavy cross couplings, making it difficult to control. It has
been possible to fully decouple the system by employing both
input- and output compensation. The compensation strategies
are both parameter dependent. The decoupling ensures that
the position is controlled by the motor and that the pressure
level is controlled by the two proportional valves. Using
the decoupled system, it was possible to design two linear
controllers; a pressure level controller and a motion controller.
The designed controllers are successfully implemented in the
9
10. 0 2 4 6 8 10
Time [s]
0
50
100
Pressure[bar]
pA
pA
load valve pLVA
(a) A side related pressure levels.
0 2 4 6 8 10
Time [s]
0
20
40
60
Pressure[bar]
pB
pB
load valve pLVA
(b) B side related pressure levels.
0 2 4 6 8 10
Time [s]
-100
0
100
200
Position[mm]
x
x load valve
(c) Position responses.
0 2 4 6 8 10
Time [s]
0
1
2
Flow[L/min]
QAV
QBV
QAV
load valve
QBV
load valve
(d) Proportional valve flows.
Fig. 14 Simulated response related to the implementation of the proportional valve concept.
non linear system, providing a maximum error of 0.5 mm
for a given trajectory. It is concluded, that the SvSDP drive
is ineffective for load hold situations. Experiments show that
approximately 0.6 kW power is drawn when the SvSDP is
used to hold a 20 kN load in a fixed cylinder position.
The distribution of input DC bus power has been analysed,
showing that the majority of the loss associated with load
hold is related to the motor.
To minimise the energy consumption in load hold situa-
tions, two concepts are proposed and analysed with respect
to applicability. The simulation results of the implemented
POCV concept showed moderate performance when used in
relation to the designed controllers. To add the desired feature
of control, it is proposed to implement two proportional valves
(PVLH). The simulated results are promising. Furthermore it
can be assumed that, it is possible to uphold a stiffness in the
return chamber at movement not forced by the pumps actively
moving oil into the chamber. To be able to apply this structure,
a new control strategy has to be devised, that accounts for
the added valve dynamics and further input output cross
couplings. If it is possible to control the PVLHs in a proper
way, that does not influence the tracking performance of the
system in a negative way, it can be concluded to be a viable
solution to the energy consumption problem.
Acknowledgement
The authors would like to thank Bosch Rexroth A/S
Denmark for their interest and support throughout the span
of the project.
References
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