February 1st, 2000
Familiarize ourselves with the MatrixX functionality. To simulate the step response of a boiler plant given the state space model. The simulation is setup to give the students experimental practice with state space control.
The plant is a multiple input multiple output model for a boiler from a power plant. Elkund developed the original model. During the first week this boiler was simulated on the Realsim package. Step inputs were sent into each plant input. The resulting output will show if the plant is stable or unstable without control. The plant without control is unstable as expected.
The computer simulation of the boiler worked, as expected, so the next step was to simulate the control blocks through the AC104 with function generators as the input signals. Function generators were used in place of the step functions. The output from the simulation was expected to go to infinity. When one input was set at 5V, the respected output would saturate. This was the expected result.
The next step is to implement a controller to stabilize
February 8th, 2000
To simulate a boiler plant given the state space model and state space controller. The simulation is setup to give the students experimental practice with state space control.
The plant is a multiple input multiple output model for a boiler from a power plant. Elkund developed the original model. During the first week this boiler was simulated on the Realsim package. This week’s goal is to implement a state space controller. Apurva Naik’s Masters Project Report was used as a guideline for the simulation. The “observer” blocks were created using data from Naik’s report. Step inputs were sent into each plant’s inputs. The outputs from the plant should stabilize at 1. The plant did react in the expected manner.
The plant and controller worked as expected. The next step was to simulate the control blocks through the AC104 with function generators as the input signals. Function generators were used in place of the step functions. The output from the simulation was expected to follow the inputs from the function generators. When one input was set at 5V, the respected output would settle at 5V, after time. This did not work.
February 15th, 2000
We continued analysis of the MIMO system. The output results in a stable system. The next step was to generate the autocode and run the system on the AC-104. During the simulation on the AC-104, we found the outputs diverged to infinity given a step input. This result differed from the MatrixX simulation. We reanalyzed the MatrixX simulation as well as the Realsim hardware connection editor. There was no apparent reason for the differing results.
Our conclusion for the day was to have Dr. Anakwa
contact someone from MatrixX to analyze our system. We suspect that
the AC-104 is not solving the differential equations fast enough.
The problem could also be due to our version of MatrixX being an older
February 22nd, 2000
The AC-104 outputs diverged to infinity when the plant and controller were both continuous. We know from the initial systems simulated during the first few weeks that a discrete controller can control a continuous plant for a simple system. The controller from last week was converted to a discrete block. We simulated this system and the results were a stable output that followed the step input. When we tried this system on the AC-104 the outputs still diverged to infinity. We reanalyzed the MatrixX simulation as well as the Realsim hardware connection editor. There was no apparent reason for the differing results.
From this weeks results and last weeks results we believe that the AC-104 cannot solve the differential equations fast enough. To test this idea we modified the system from a 4-input, 2-output to a 2-input, 2-output system. When running this on the AC-104 we found that the smaller system did function properly. Our conclusion is that the AC-104 cannot handle large matrix calculations. Next week we will try to simulate the same system using transfer functions instead of state variable system blocks.
February 29th, 2000
Simulate the MIMO plant using transfer functions instead of state variable. The AC-104 does not properly simulate the MIMO system using state variables. Taking the system to a more basic format, transfer function, may allow the AC-104 to simulate the system.
The AC-104 does not simulate the MIMO systems. Also, from last week, it was able to simulate the 2-input, 2-output system. The MIMO system will be broken down into its transfer functions and simulated. This system fails when simulated in the Realsim package and the AC-104. The transfer functions were determined using Matlab. After the AC-104 failure, each block was checked to assure that it was properly converted. Once the blocks were checked, the transfer functions were rechecked in Matlab and found to be correct. During the Matlab analysis it was noticed that the poles of some of the transfer functions were close to 1.0. In the Z-plane the system is unstable for values outside of the unit circle. The system runs stable and then goes unstable suddenly. It is believed that the conversion from state space to transfer function form uses a conical form. It can be shown that higher order systems will map to unstable regions in the Z-plane. It is our belief that this is what is occuring in our design. As a result, the system goes unstable.
March 7th, 2000
The AC-104 does not properly simulate the MIMO system using state variables. The only solution is to wait for the upgraded software package. During the wait we will simulate a logic plant using Matlab.
The AC-104 does not simulate the MIMO systems. It has been determined, through conversations with the MatrixX support that our version of the software can not solve the internal equations quickly enough to simulate with the AC104. While we are waitung for the new software to be installed, we were given a logic plant to be simulated. This logic circuit has 2 inputs, position and velocity. Using these inputs an error is calculated as the output. The plant was succesfully created and tested using Matlab. It was tested using various outputs to ensure that it functioned properly. We were unable to simulate this same plant using MatrixX because the proper licenses were not available. From speaking with the MatrixX vendor, we know that there is a program available that will convert Simulink layouts directly to Realsim. This software will be available to Bradley in the near future. The next phase will be to create the controller that will run this plant.
March 21st, 2000
The computers were not working. We spent the entire day waiting on the computer lab director to fix the computers. Someone loaded software onto our computer and then deleted essential path files when they erased their software. Chris Mattus said that it would take an entire day for him to fix. We spent the day catching up on our lab notebooks and analyzing our data.
March 28th, 2000
We discovered a flaw in our original design for the simple SISO system from week 1. We were loading the entire system into the AC104 for simulation purposes. The AC104 has D/A and A/D converters built into its hardware. Therefore when we simulated the system using the Systembuild software , there should have been an A/D to the left of the controller and a D/A to the right of the controller. By loading the entire system into the AC104 we were not getting accurate results because we were not taking into consideration, the built-in A/D and D/A's in the AC104. This is what resulted in such great differences between the AC104 results and the Systembuild results. To address this, we designed the plant using resistors, capacitors and op amps. We will load only the controller into the AC104 and attempt to control the plant that we will build from our design.We took the plant from week 1, and designed it using resistors, capacitors and op amps. The design was not complete at the end of the day. We will continue this next week.
April 4, 2000
We designed the circuit using a simulation package on the computers in the lab. The simulations match the expected results. The circuit is shown below.
April 11, 2000
The circuit designed from last week was built. A step input was put into the system and the resulting output matched the simulated results.
April 18, 2000
The plant built last week was connected to the AC104 and code was generated for the controller portion of the system in MatrixX. The code was downloaded to the AC104 and run at a frequency of 10Hz. The output was found to almost match that of the simulations. The only problem was that the overshoot was still too large and the settling time was also longer. We tried adjusting the scheduler frequency on the AC104 to test different sampling rates. We found that the system behaves better at approximately 15Hz. We also found that above 60Hz or below 9Hz, the system is unstable. We decided to re-discretize the controller to 15Hz and test the output. This will be completed next week.
April 25, 2000
We prepared for our final presentation next week. We also completed the simulation of the SISO systems with a sampling interval of 15Hz. The results still have overshoot, but the system is behaving closer to what is expected.