Paper
Content
A Mini Thesis entitled Creating a Control System in Matlab/Simulink for a Hydraulic Tool Power Supply System on a Hydraulic Hybrid Vehicle by James Sweetman and Dr. Walter Olson
Abstract
Hybrid Hydraulic Vehicles (HHVs) have the potential to double the efficiency of currently available hybrids, and are therefore, on the rise. They are mainly being used in large vehicles, like military trucks. These trucks have to make daily rounds to ensure safety of military personnel and to help soldiers with reconnaissance. The trucks will now be equipped with a power system for peripheral tools to be attached. This system is called the Hydraulic Tool Power Supply system, or HyToPS system. In order to utilize this system, a software program had to be developed and customized to control as many variables as possible, so the user would only have to be concerned with using the tool itself, and not concerned with setting a pressure, flow, or torque rating. The software was written using Matlab/Simulink using control theory and experimental data. This system made use of a conventional PI
controller, a lead compensator, and a negative feedback loop. The derivation of model transfer functions, PI transfer functions, lead compensator functions, and general control theory will be discussed. The results of the model have been produced and will be discussed later.
Introduction
There are flaws with energy sources in the world today. Three crucial flaws that have led to a surge in research are finances, pollution, and lack of resources. The world today has been using nonrenewable energy sources for a long time. It is becoming more apparent that these resources will not last us forever. The viable solutions that have come up for cleaning car exhaust are to just have cleaner energy sources. A hybrid energy system has been developed; this system is called an HHV (hydraulic hybrid vehicle). HHVs are capable of a high power density and an efficient energy conversion process. They are able to release stored energy quickly , but their long term efficiency leaves some qualities to be desired due to a low energy density. (2) This type of setup is favored in a stop-and-go setting. This can be utilized in garbage trucks, delivery services, and even military vehicles. Aside from these advantages, an HHV is capable of powering peripheral systems to a vehicle. An example of this system is on a military vehicle called Hydraulic Tool Power Supply system, or HyToPS system. This HyToPS system uses the power of the already present hydraulic system and makes an extension to tools for use in the field. Military personnel in a vehicle may need to use a jackhammer, impact wrench, or a number of tools, in the field at any time without an outlet. They can now connect the tool to their vehicle and it will supply a tremendous amount of power, due to the high power density. A software application must be developed to coincide with this system. The system being installed makes use of Rotary Power s A70 hydraulic pump/motor. This motor will be the driving motor in a hydraulic circuit that will supply power to the HyToPS system on a mobile
military vehicle. The motor must be characterized in order to determine its potential. In order to accomplish this task, research on control theory was necessary and tests had to be run on the motor in a controlled environment. Once the research was done and the data had been collected, it was analyzed for values such as moment of inertia, static friction force, speed limits, pressure limits, and torque produced. Using the experimental data to model the pump and theoretical values to create a controller, a computer model was created that saved time and money. This model was compiled using Matlab/Simulink software. This model was capable of showing shaft speed of the motor, flow rate of the hydraulic fluid through the motor, the pressure of the fluid before and after passing through the motor, and the torque produced by the fluid. The model was absolutely necessary in order to create a control system for the HyToPS circuit.
Literature Review
Many articles and papers relating to hydraulic hybrids and control theory were reviewed as work toward the model progressed. Articles about general hybrid vehicles were read. These articles compared electric hybrid vehicles to hydraulic hybrid vehicles, and to internal combustion engines (ICEs). It was through these articles that information pertaining to the hydraulic hybrid vehicles was discovered. The advantages were discussed, and the type of vehicle where an HHV system would work best was discovered. A journal paper was examined to figure out how to tune a PID controller in a proper and efficient way. General help files, websites, and classroom notes were read to figure out how to use certain Simulink commands. There are many reasons why an HHV is advantageous compared to an EHV (electric hybrid vehicle), or an ICE. An ICE engine is propelled by multiple little explosions that happen inside an engine. Air and gasoline are pushed into a cylinder in an engine block, then the fuel and air mixture in compressed as much as possible. After the compression, a spark plug ignites the mixture causing an
explosion, or combustion, which propels the piston in the chamber down and, in turn, spins the crankshaft powering the vehicle motion. The problem with an ICE is that it produces a lot of harmful emissions and fuel is becoming increasingly expensive. An EHV system includes an ICE. An EHV system catches braking energy and stores it in a battery pack. This battery takes this saved energy and uses it to propel the car when the ICE would operate at an inefficient level or anytime a vehicle is stopped. The problem with EHVs is it has a low power density, meaning it stores and releases energy at a slow rate, so not as much braking energy is recovered. An HHV system is also used with an ICE. The concept is very similar to the EHV system with a few differences. The HHV system captures brake energy by charging a high pressure fluid accumulator. The force from braking helps pump hydraulic fluid into an accumulator at a high pressure so it can be used to power the vehicle later. The HHVs have a high power density, meaning it can store and release large amounts of energy very quickly, but it cannot store a high volume of energy. An article was read discussing Ziegler-Nichols rules for tuning a PI controller. This article, in association with classroom notes, helped make a PI controller functional for the motor model. The sources indicated that a step function was to be used to supply an input signal to the model of the A70 motor, to get a response worth analyzing. This first order response is in Figure 1. A tangent line was drawn off of the graph at 68% of the total rise. This line, and the initial lag of the signal, were evaluated and led to the values needed for a PI controller. This will be discussed in further detail for this specific motor later on.
Figure 1 - First order response of the Rotary Power A70 motor model.
Model
An accumulator/pump system will provide fluid at a constant high pressure (4600 psi) to the A70 motor. This motor will be mechanically linked with a fixed displacement, variable pressure pump. This pump will circulate hydraulic oil at a medium pressure (2000 psi) throughout the peripheral system. The system is an open loop hydraulic circuit. This circuit will constantly run at a consistent flow. In order to save as much energy as possible, the pressure in the loop (2000 psi) will need to be reduced when the tool is not in use. In this case, the circulating pressure can be decreased by lowering the amount of torque on the mechanical linkage shaft. To lower the torque, the volume of the A70 motor must be minimized, because torque is the product of pressure, which is constant in the motor, and volume. In summary, the volume of the motor chamber has to be controlled to make sure the flow of the fluid is constant, but the pressure must be minimal when not in use. It is with this information that people can
create a simple negative feedback loop using the shaft speed as a reference number, to control the volume of the chamber in the motor. A control system of this type had been written using Matlab/Simulink. An initial model was built using the test data determined in the lab. A motor model transfer function was created using the equation in Figure 2, and then calibrated, by use of a gain, to match this data.
Figure 2 - General motor transfer function Using the data that was acquired, the motor model had some figures to match. For the model, the output speed, flow, and torque of the motor could be matched to the test data. This model presented some problems as it may not have been accurate enough in its responses because it was merely a manipulation of values with constants that forced the outputs to match the data in the tested scenarios. The model resulted in correct answers for the previously tested setups only. This was not necessarily an accurate portrayal of the motor because it was unknown how the motor would respond in EVERY circumstance. Problems arose using a controller and compensator, and unexpected results were displayed. A new model was needed. It was at this point that the new model was set to be in the discrete, or z, domain. The next step was to create a mathematical model using values obtained from testing and creating transfer functions from control theory. Two transfer functions were created, one to model the output of the motor, and one to model the load that the motor propels. The formula used was in the continuous domain. Tustin s method, or a bilinear transformation, was used to convert the new transfer function. The conversion equation is shown in Figure 3. The new transfer function, in the continuous domain, of the motor is shown in Figure 4. The new transfer function, in the discrete domain, of the motor is shown in Figure 5.
Figure 3 - Tustin's method for converting from the continuous to discrete domain
Figure 4 - Motor transfer function in the continuous domain
Figure 5 - Motor transfer function in the discrete domain This transfer function is the basis for the A70 motor model. It was calibrated with a gain of 12.5 and is shown in Figure 6.
Figure 6 - A70 Motor model in Simulink The load transfer function was determined by some assumptions based on data from a similar pump. It was determined in a similar manner to the motor model, with the exception of the load transfer function. The equation for the load transfer function in the continuous and discrete domains are shown below in Figure 7. The model of the load is shown in Figure 8.
Figure 7 - Load transfer functions in different domains
Figure 8 - Load model in Simulink
Experimental
In order to get the values needed for the model, the moments of inertia and frictional losses, the motor needed to be characterized. The moment of inertia value came from examining coast down test data. (Note to Dr. Olson: Admittedly, I did struggle with getting the actual value of the moment of inertia like you had predicted, and I am aware that the previous sentence is a copout and does not explain how to get the value, I will have to fix this in the rewrite.) The motor was put at a high speed, then the driving force was removed, and the motor coasted to a stop. In Figure 9a, the coast down data is displayed. For a better picture, Figure 9b shows the key area, between 7400 and 8500.
Figure 9a - Full Torque vs. Time (.1 seconds)
Figure 9b - Zoomed in Torque vs. Time
The frictional losses were in a time relationship with the moment of inertia.
The control system regulates the amount of fluid needed and the time at which the system actuates with a necessary precision. There are many methods and tools used in control theory. The tools used for this case were a PI controller and a lead compensator. Both of these controllers are represented by a discrete transfer function. They need to be first order transfer functions because the motor in question has a first order response. A PI (Proportional-Integral) controller uses the current data and past data to tell the system what its next move should be. A lead compensator is used to minimize the overshoot in the transient response of a signal. The PI controller has to be "tuned" in order to get the desired results. The lead compensator was easy to choose because the theory behind it is simple. It is a transfer function with a pole as close to the stability limit as possible, which is one. The zero of the transfer function has to be less than a pole value in order to be a lead compensator. If it is greater, then it would be a lag compensator. The ideal value for the zero is to be as close to the value of the pole as possible, but have enough of a difference to make sure an alias signal isn t produced. This is where the signal has action going on in between pulses but the system does not know it because the sampling time is too great. The PI controller requires a little more analysis. The basic steps of creating a PI controller for a first order response motor are as follows: 1) Put a step function into the motor, 2) Analyze the result and draw a linear curve fit line of the rising portion of the graph, 3) Determine critical values, R and L, from the graph with the sampling time, 4) Use these values to create the coefficients in the PI controller. Another step was taken in this case, and that was, again, the bilinear transformation. In order to create
the coefficients in the PI controller, also called tuning the controller, a method needed to be selected. The method chosen was the Zeigler-Nichols method. This says that Ti=3L and Kp=.9/RL. Figure 9 shows the equation and variables of the transfer function. (1)
Figure 9 PI controller equation
Results
At this point the model has been successfully created and the controllers around it are in the loop. The results of the system are shown in Figures 10a-10d.
Figure 10a - Speed results of the controller on the model
Figure 10b - Flow rate results of the controller on the model
Figure 10c - Displacement results of the controller on the model
Figure 10d - Torque demanded from the provided work cycle The goal of this system was to keep the speed at a constant 2000 RPM thereby keeping the flow at a constant 4-4.5 GPM. The linear displacement graph represents a percentage of the total volume of the motor chamber. It must fall between the values of 0 and 1. The results in the graphs reflect the independent working pressure cycle. The displacement must increase to raise the amount of supplied torque to meet the demand from the pressure cycle. It also must decrease when the torque is not needed. The speed shows change when the loads are suddenly applied and removed. The flow rate graph is a product of the variable speed, and a fixed volume for the pump/load, so it has the same signature as the speed plot. This program accurately depicts the correct values, and the controller works satisfactorily. The future work from this point is to get hardware from the client. Once the hardware is received it will be fully assembled and added to other hardware in a hydraulics testing lab. There, a control and operating system will be used to operate the supply pump and apply a load to this hydraulic system. With successful results, it will be ready for a field demonstration in early 2012.
This demonstration will, hopefully, lead to more interest in this technology. This technology solves some of the previously mentioned problems. There is plenty of information out there about tests and vehicles that have already been completed. This test setup and model has been completed with basic control theory and simple modeling practices. The results for the model were displayed as expected, and this was an overall success.
Works Cited
1) Astrom, K J. Revisiting the Ziegler-Nichols step response method for PID control. Journal of Process Control, v. 14 issue 6, 2004, p. 635. 2) Hui, Sun. Control strategy of hydraulic/electric synergy system in heavy hybrid vehicles. Energy Conversion & Management, v. 52 issue 1, 2011, p. 668-674. 3) Hydraulic hybrid truck undergoes field tests. Machine Design, v. 79 issue 19, 2007, p. 38-38. 4) Gannon, Mary C. Hydraulic hybrids on the rise. Hydraulics & Pneumatics, v. 62 issue 7, 2009, p. 28-31. 5) http://www.nrdc.org/energy/gasprices/default.asp 6) http://www.livestrong.com/article/156537-facts-of-car-pollution/ 7) http://journals.ohiolink.edu/ejc/article.cgi?issn=10069321&issue=v42i0002&article=215_rbfcapc&searc h_term=%28refkey%3D%28Li%231999%23215%23224%23H%29volkey%3D%2810069321%2342%2321 5%232%29%29 Li, Hongxing. Relationship between fuzzy controllers and PID controllers. Science in China Series E: Technological Sciences, v. 42 issue 2, 1999, p. 215-224. 8) http://journals.ohiolink.edu/ejc/article.cgi?issn=02561115&issue=v26i0003&article=622_adopccalfftp& search_term=%28refkey%3D%28Lee%232009%23622%23630%23S%29volkey%3D%2802561115%2326 %23622%233%29%29 Lee, Seunghyun. Analytical design of PID controller cascaded with a lead-lag filter for time-delay processes. Korean Journal of Chemical Engineering, v. 26 issue 3, 2009, p. 622-630.
9) http://journals.ohiolink.edu/ejc/article.cgi?issn=08883270&issue=v22i0006&article=1274_sosotpsothfs &search_term=%28refkey%3D%28Macha%232008%231274%231288%23E%29volkey%3D%2808883270 %2322%231274%236%29%29 Macha, Ewald. Selection of settings of the PID controller by automatic tuning at the control system of the hydraulic fatigue stand. Mechanical Systems and Signal Processing, v. 22 issue 6, 2008, p. 12741288. 10) Ntogramatzidis, L. Exact tuning of PID controllers in control feedback design. IET Control Theory & Applications, v. 5 issue 4, 2011, p. 565-578. 11) http://journals.ohiolink.edu/ejc/article.cgi?issn=00981354&issue=v28i0011&article=2201_asmotpfsaufs &search_term=%28refkey%3D%28Srinivas%232004%232201%232218%23M%29volkey%3D%28009813 54%2328%232201%2311%29%29 Srinivas, M. A simple method of tuning PID controllers for stable and unstable FOPTD systems. Computers and Chemical Engineering, v. 28 issue 11, 2004, p. 2201-2218. 12) http://journals.ohiolink.edu/ejc/article.cgi?issn=01651684&issue=v86i0010&article=2771_tofpcwzr&sea rch_term=%28refkey%3D%28Valerio%232006%232771%232784%23D%29volkey%3D%2801651684%23 86%232771%2310%29%29 Valerio, Duarte. Tuning of fractional PID controllers with Ziegler-Nichols-type rules. Signal Processing, v. 86 issue 10, 2006, p. 2771-2784. 13) http://content.epnet.com/pdf9/pdf/2008/DES/28Apr08/31885455.pdf?T=P&P=AN&K=31885455&Ebsco Content=dGJyMMvl7ESeqLQ40dvuOLCmr0mep7NSr6q4Sa%2BWxWXS&ContentCustomer=dGJyMO3e5 4fq3%2ByDuePfgeyx%2BEu3q64A&D=a9h Ogando, Joseph. NO BATTERIES REQUIRED: Hydraulic hybrid technology has been aimed at trucks, but it could make sense for smaller vehicles. Design News, v. 63 issue 6, 2008, p. 45-48.
14) http://content.epnet.com/pdf23_24/pdf/2009/0W3/01Oct09/44681755.pdf?T=P&P=AN&K=44681755& EbscoContent=dGJyMMvl7ESeqLQ40dvuOLCmr0mep7NSr6q4Sa%2BWxWXS&ContentCustomer=dGJyM O3e54fq3%2ByDuePfgeyx%2BEu3q64A&D=a9h Partnership set to provide hybrid systems for fleet vehicles. Hydraulics & Pneumatics, v. 62 issue 10, 2009, p. 11-11. 15) http://www.nrdc.org/energy/gasprices/default.asp 16) http://www.livestrong.com/article/156537-facts-of-car-pollution/ 17) http://auto.howstuffworks.com/engine1.htm 18) http://auto.howstuffworks.com/hybrid-car2.htm
Abstract
Hybrid Hydraulic Vehicles (HHVs) have the potential to double the efficiency of currently available hybrids, and are therefore, on the rise. They are mainly being used in large vehicles, like military trucks. These trucks have to make daily rounds to ensure safety of military personnel and to help soldiers with reconnaissance. The trucks will now be equipped with a power system for peripheral tools to be attached. This system is called the Hydraulic Tool Power Supply system, or HyToPS system. In order to utilize this system, a software program had to be developed and customized to control as many variables as possible, so the user would only have to be concerned with using the tool itself, and not concerned with setting a pressure, flow, or torque rating. The software was written using Matlab/Simulink using control theory and experimental data. This system made use of a conventional PI
controller, a lead compensator, and a negative feedback loop. The derivation of model transfer functions, PI transfer functions, lead compensator functions, and general control theory will be discussed. The results of the model have been produced and will be discussed later.
Introduction
There are flaws with energy sources in the world today. Three crucial flaws that have led to a surge in research are finances, pollution, and lack of resources. The world today has been using nonrenewable energy sources for a long time. It is becoming more apparent that these resources will not last us forever. The viable solutions that have come up for cleaning car exhaust are to just have cleaner energy sources. A hybrid energy system has been developed; this system is called an HHV (hydraulic hybrid vehicle). HHVs are capable of a high power density and an efficient energy conversion process. They are able to release stored energy quickly , but their long term efficiency leaves some qualities to be desired due to a low energy density. (2) This type of setup is favored in a stop-and-go setting. This can be utilized in garbage trucks, delivery services, and even military vehicles. Aside from these advantages, an HHV is capable of powering peripheral systems to a vehicle. An example of this system is on a military vehicle called Hydraulic Tool Power Supply system, or HyToPS system. This HyToPS system uses the power of the already present hydraulic system and makes an extension to tools for use in the field. Military personnel in a vehicle may need to use a jackhammer, impact wrench, or a number of tools, in the field at any time without an outlet. They can now connect the tool to their vehicle and it will supply a tremendous amount of power, due to the high power density. A software application must be developed to coincide with this system. The system being installed makes use of Rotary Power s A70 hydraulic pump/motor. This motor will be the driving motor in a hydraulic circuit that will supply power to the HyToPS system on a mobile
military vehicle. The motor must be characterized in order to determine its potential. In order to accomplish this task, research on control theory was necessary and tests had to be run on the motor in a controlled environment. Once the research was done and the data had been collected, it was analyzed for values such as moment of inertia, static friction force, speed limits, pressure limits, and torque produced. Using the experimental data to model the pump and theoretical values to create a controller, a computer model was created that saved time and money. This model was compiled using Matlab/Simulink software. This model was capable of showing shaft speed of the motor, flow rate of the hydraulic fluid through the motor, the pressure of the fluid before and after passing through the motor, and the torque produced by the fluid. The model was absolutely necessary in order to create a control system for the HyToPS circuit.
Literature Review
Many articles and papers relating to hydraulic hybrids and control theory were reviewed as work toward the model progressed. Articles about general hybrid vehicles were read. These articles compared electric hybrid vehicles to hydraulic hybrid vehicles, and to internal combustion engines (ICEs). It was through these articles that information pertaining to the hydraulic hybrid vehicles was discovered. The advantages were discussed, and the type of vehicle where an HHV system would work best was discovered. A journal paper was examined to figure out how to tune a PID controller in a proper and efficient way. General help files, websites, and classroom notes were read to figure out how to use certain Simulink commands. There are many reasons why an HHV is advantageous compared to an EHV (electric hybrid vehicle), or an ICE. An ICE engine is propelled by multiple little explosions that happen inside an engine. Air and gasoline are pushed into a cylinder in an engine block, then the fuel and air mixture in compressed as much as possible. After the compression, a spark plug ignites the mixture causing an
explosion, or combustion, which propels the piston in the chamber down and, in turn, spins the crankshaft powering the vehicle motion. The problem with an ICE is that it produces a lot of harmful emissions and fuel is becoming increasingly expensive. An EHV system includes an ICE. An EHV system catches braking energy and stores it in a battery pack. This battery takes this saved energy and uses it to propel the car when the ICE would operate at an inefficient level or anytime a vehicle is stopped. The problem with EHVs is it has a low power density, meaning it stores and releases energy at a slow rate, so not as much braking energy is recovered. An HHV system is also used with an ICE. The concept is very similar to the EHV system with a few differences. The HHV system captures brake energy by charging a high pressure fluid accumulator. The force from braking helps pump hydraulic fluid into an accumulator at a high pressure so it can be used to power the vehicle later. The HHVs have a high power density, meaning it can store and release large amounts of energy very quickly, but it cannot store a high volume of energy. An article was read discussing Ziegler-Nichols rules for tuning a PI controller. This article, in association with classroom notes, helped make a PI controller functional for the motor model. The sources indicated that a step function was to be used to supply an input signal to the model of the A70 motor, to get a response worth analyzing. This first order response is in Figure 1. A tangent line was drawn off of the graph at 68% of the total rise. This line, and the initial lag of the signal, were evaluated and led to the values needed for a PI controller. This will be discussed in further detail for this specific motor later on.
Figure 1 - First order response of the Rotary Power A70 motor model.
Model
An accumulator/pump system will provide fluid at a constant high pressure (4600 psi) to the A70 motor. This motor will be mechanically linked with a fixed displacement, variable pressure pump. This pump will circulate hydraulic oil at a medium pressure (2000 psi) throughout the peripheral system. The system is an open loop hydraulic circuit. This circuit will constantly run at a consistent flow. In order to save as much energy as possible, the pressure in the loop (2000 psi) will need to be reduced when the tool is not in use. In this case, the circulating pressure can be decreased by lowering the amount of torque on the mechanical linkage shaft. To lower the torque, the volume of the A70 motor must be minimized, because torque is the product of pressure, which is constant in the motor, and volume. In summary, the volume of the motor chamber has to be controlled to make sure the flow of the fluid is constant, but the pressure must be minimal when not in use. It is with this information that people can
create a simple negative feedback loop using the shaft speed as a reference number, to control the volume of the chamber in the motor. A control system of this type had been written using Matlab/Simulink. An initial model was built using the test data determined in the lab. A motor model transfer function was created using the equation in Figure 2, and then calibrated, by use of a gain, to match this data.
Figure 2 - General motor transfer function Using the data that was acquired, the motor model had some figures to match. For the model, the output speed, flow, and torque of the motor could be matched to the test data. This model presented some problems as it may not have been accurate enough in its responses because it was merely a manipulation of values with constants that forced the outputs to match the data in the tested scenarios. The model resulted in correct answers for the previously tested setups only. This was not necessarily an accurate portrayal of the motor because it was unknown how the motor would respond in EVERY circumstance. Problems arose using a controller and compensator, and unexpected results were displayed. A new model was needed. It was at this point that the new model was set to be in the discrete, or z, domain. The next step was to create a mathematical model using values obtained from testing and creating transfer functions from control theory. Two transfer functions were created, one to model the output of the motor, and one to model the load that the motor propels. The formula used was in the continuous domain. Tustin s method, or a bilinear transformation, was used to convert the new transfer function. The conversion equation is shown in Figure 3. The new transfer function, in the continuous domain, of the motor is shown in Figure 4. The new transfer function, in the discrete domain, of the motor is shown in Figure 5.
Figure 3 - Tustin's method for converting from the continuous to discrete domain
Figure 4 - Motor transfer function in the continuous domain
Figure 5 - Motor transfer function in the discrete domain This transfer function is the basis for the A70 motor model. It was calibrated with a gain of 12.5 and is shown in Figure 6.
Figure 6 - A70 Motor model in Simulink The load transfer function was determined by some assumptions based on data from a similar pump. It was determined in a similar manner to the motor model, with the exception of the load transfer function. The equation for the load transfer function in the continuous and discrete domains are shown below in Figure 7. The model of the load is shown in Figure 8.
Figure 7 - Load transfer functions in different domains
Figure 8 - Load model in Simulink
Experimental
In order to get the values needed for the model, the moments of inertia and frictional losses, the motor needed to be characterized. The moment of inertia value came from examining coast down test data. (Note to Dr. Olson: Admittedly, I did struggle with getting the actual value of the moment of inertia like you had predicted, and I am aware that the previous sentence is a copout and does not explain how to get the value, I will have to fix this in the rewrite.) The motor was put at a high speed, then the driving force was removed, and the motor coasted to a stop. In Figure 9a, the coast down data is displayed. For a better picture, Figure 9b shows the key area, between 7400 and 8500.
Figure 9a - Full Torque vs. Time (.1 seconds)
Figure 9b - Zoomed in Torque vs. Time
The frictional losses were in a time relationship with the moment of inertia.
The control system regulates the amount of fluid needed and the time at which the system actuates with a necessary precision. There are many methods and tools used in control theory. The tools used for this case were a PI controller and a lead compensator. Both of these controllers are represented by a discrete transfer function. They need to be first order transfer functions because the motor in question has a first order response. A PI (Proportional-Integral) controller uses the current data and past data to tell the system what its next move should be. A lead compensator is used to minimize the overshoot in the transient response of a signal. The PI controller has to be "tuned" in order to get the desired results. The lead compensator was easy to choose because the theory behind it is simple. It is a transfer function with a pole as close to the stability limit as possible, which is one. The zero of the transfer function has to be less than a pole value in order to be a lead compensator. If it is greater, then it would be a lag compensator. The ideal value for the zero is to be as close to the value of the pole as possible, but have enough of a difference to make sure an alias signal isn t produced. This is where the signal has action going on in between pulses but the system does not know it because the sampling time is too great. The PI controller requires a little more analysis. The basic steps of creating a PI controller for a first order response motor are as follows: 1) Put a step function into the motor, 2) Analyze the result and draw a linear curve fit line of the rising portion of the graph, 3) Determine critical values, R and L, from the graph with the sampling time, 4) Use these values to create the coefficients in the PI controller. Another step was taken in this case, and that was, again, the bilinear transformation. In order to create
the coefficients in the PI controller, also called tuning the controller, a method needed to be selected. The method chosen was the Zeigler-Nichols method. This says that Ti=3L and Kp=.9/RL. Figure 9 shows the equation and variables of the transfer function. (1)
Figure 9 PI controller equation
Results
At this point the model has been successfully created and the controllers around it are in the loop. The results of the system are shown in Figures 10a-10d.
Figure 10a - Speed results of the controller on the model
Figure 10b - Flow rate results of the controller on the model
Figure 10c - Displacement results of the controller on the model
Figure 10d - Torque demanded from the provided work cycle The goal of this system was to keep the speed at a constant 2000 RPM thereby keeping the flow at a constant 4-4.5 GPM. The linear displacement graph represents a percentage of the total volume of the motor chamber. It must fall between the values of 0 and 1. The results in the graphs reflect the independent working pressure cycle. The displacement must increase to raise the amount of supplied torque to meet the demand from the pressure cycle. It also must decrease when the torque is not needed. The speed shows change when the loads are suddenly applied and removed. The flow rate graph is a product of the variable speed, and a fixed volume for the pump/load, so it has the same signature as the speed plot. This program accurately depicts the correct values, and the controller works satisfactorily. The future work from this point is to get hardware from the client. Once the hardware is received it will be fully assembled and added to other hardware in a hydraulics testing lab. There, a control and operating system will be used to operate the supply pump and apply a load to this hydraulic system. With successful results, it will be ready for a field demonstration in early 2012.
This demonstration will, hopefully, lead to more interest in this technology. This technology solves some of the previously mentioned problems. There is plenty of information out there about tests and vehicles that have already been completed. This test setup and model has been completed with basic control theory and simple modeling practices. The results for the model were displayed as expected, and this was an overall success.
Works Cited
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