Oupa NhambeStudent No: 587899CHMT 4011: Process ControlProject Part Two: MIMO Control of Ferrosilicon Pilot PlantSubmission date: 06 July 2015

Executive SummaryProportional, integral and derivative (PID) controllers are the most widely used controllers in Multiple-Input-Multiple-Output (MIMO) in most process industries. This is due to their simplicity, easy implementation and their robustness. Various tuning methods like the Cohen-Coon (C-C) method and the Zeigler-Nichols (Z-N) method have been recommended for optimum set-up of PID controllers. In the project the performance of a three tank MIMO system was tuned based on the Cohen-Coon and Zeigler-Nichols method to determine the optimum PID parameters. The Relative Gain Array of the system was also determined for best pairing suggestions. The PID parameters, gain, integral time and derivative time were calculated to be 1, 600 and 120 for optimum performance of the controller. The RGA suggested that it is best to pair water inflow with tank level, and solids inflow with outlet slurry density.Keywords: Cohen-Coon, Zeigler-Nichols, PID Controller, MIMO, RGA

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Table of Contents

1.Introduction12.Model Development and Description13.Results and Discussion23.1.PID Controller Tuning for Water Only System23.1.1.Cohen & Coon Tuning Method23.1.2.Zeigler-Nichols Tuning Method43.2.PID Controller Fine Tuning for Water Only Operation43.3.Solids Effect on Tank 3 Height and Final Slurry Flowrate53.4.Spillage Effects on Tank 3 Outlet Density63.5.The Relative Gain Array (RGA)73.6.Recommended Instruments for Measuring the Level in Tank 3 and Density of Qout74.Conclusions75.References86.Appendix9

2. 3. IntroductionAccording to Fichte (2005), Ferrosilicon is a ferroalloy, an alloy of iron and silicon with average silicon content in the range of 15 and 90 per cent by weight. In this project ferrosilicon is used ain a pilot plant to make a dense-medium bath utilising three identical tanks. The main objective of this project is to develop a Simulink model that can control the level in each tank and also the final slurry density as recommended. This will be done by determining the optimum PID controller parameters, and also determine the Relative Gain Array (RGA) for controlling the level of tank 3 to a desired value and to also maintain the final slurry density at a desired constant value. The RGA will help in such a way that it gives the possible way for pairing the inputs and outputs for a Multiple-Inputs-Multiple-Outputs (MIMO) system.4. Model Development and DescriptionDeveloping Equations:Mass balance equations were set-up as follows to prepare block diagrams in Simulink.Tank 1:

Where and refers to tank 1 outlet flowrate and density respectivelyTank 2:

Tank 3: Volume change with height

Divide throughout by , and take limit as goes to 0

Assuming constant density in the tank, we have:

For perfect mixing, density within the tank is the same as the density of outlet stream;

From the overall mass balance we have the following:

Also the dynamic volume balance was performed. These equations were used to construct the simulation for the project. See appendix for block diagrams.5. Results and Discussion5.1. PID Controller Tuning for Water Only System5.1.1. Cohen & Coon Tuning MethodThe method used for tuning the PID controller was the process reaction curve tuning technique. According to Svrcek et al., (2014), in this method a process reaction curve is produced in response to step disturbance. The curve was then used to determine the controller gain, integral time, and the derivative time. This technique was done on an open loop, which implies that no control action occurs, and thus the process response can be isolated. To generate the curve, the process was allowed to reach steady state, then a small disturbance was introduced, and the input and output responses to the step disturbance were recorded. The two figures below depict the input and output reaction curves, respectively. The curves were generated assuming that the maximum water flow is 30l/min.

Figure 3.1 Input reaction curve in response to a step disturbance from initial steady state to final steady state of 30l/min

Figure 3.2 Output reaction curve in response to a step change from initial steady state to final steady state of 30l/minThe process parameters that were obtained from the reaction curves above were as follows.

Cohen & Coon recommended the following expressions for calculating PID parameters:

5.1.2. Zeigler-Nichols Tuning MethodThe reaction curve tuning method for a PID controller was also used for the Z-N tuning method. Figure 3.1 and figure 3.2 were utilised to determine process parameters as outlined above. Zeigler-Nichols recommended the following expressions for estimating the process gain, integral time and the derivative time:

5.2. PID Controller Fine Tuning for Water Only OperationThe improved PID parameters were obtained as follows. The gain, K, was obtained to be 1, which implies that the proportional band, Xp is 100. The integral time, Ti is 600, and the derivative time, Td, is 120. At this values a steady state height is quickly reached for tank 3. This minimises the error in the system, and shortens the dead time. 5.3. Solids Effect on Tank 3 Height and Final Slurry FlowrateAt time, t = 200s, V2 was opened to 50%. The figure below shows the response to this step input.

Figure 3.3 Reaction curve to step change disturbance of V2 opening. The final solids flowrate when V2 is opened to 50% was recorded to be approximately 4.26l/min.

Figure 3.4 Curve depicting the effect of V2 opening at 50% on tank 3 outlet flowrateThe figure above shows that when the step change of V2 opening to 50% is introduced, the systems established steady state is disturb, thus the system moves away from this initial steady state until a new steady state operation is reached. The new steady state flow is established at approximately 1.5 seconds, and Qout moves from 20l/min to a new value of 24.26l/min. The density of the slurry is maintained at 2000kg/m3 using the density control loop. The same phenomenon is observed for the height of tank 3. The height level moved from the initial steady state value until new steady state was established.

Figure 3.5 Curve depicting the effect of V2 opening to 50% on height of tank 35.4. Spillage Effects on Tank 3 Outlet DensityAt time t = 2000, a stream with 40% FeSi was introduced into tank 2. The figure below shows the systems response to this disturbance.

Figure 3.6 Curve showing the effects of spillage disturbance on tank 3 outlet density.Upon introduction of the spillage stream, the density of tank 3 outlet stream decreased. The density PID controller was used to maintain the density at the required value of 2000kg/m3. The control valve, V2, was opened slightly above 50%.5.5. The Relative Gain Array (RGA)

From the RGA above it advisable to pair water inflow with tank 3 level and the solids (FeSi) with the slurry density since and are greater than and respectively.5.6. Recommended Instruments for Measuring the Level in Tank 3 and Density of QoutLevel Measurement:To measure the level in tank 3, it is recommended that an ultrasonic level transmitter is used. An ultrasonic transmitter comprises of a sensor unit, installed above the maximum liquid level, and a remote mounted transmitter and a display unit. The sensor directs an ultrasonic signal downwards onto the liquid surface and time taken for the reflected signal to return is used to calculate the distance. These units are very reliable, reasonable priced and very robust.Density Measurement: Sampling methods this is a direct method for measuring solids concentrations. It is important to ensure that the sample is representative of the slurry flow stream. In small pipelines is preferable to sample the total discharge. Method is not practical for large pipes. Nuclear density meters for all pipe sizes.6. ConclusionsThe aim of the project was to simulate a three tank system with multiple inputs and outputs in order to tune the PID controller and to also study the effects of disturbances on the plant. Also the RGA of the system was determined to determine the best coupling of the systems parameters. After fine tuning the controller, the PID parameters, gain, integral time and derivative time were determined to be 1, 600 and 120 respectively. The RGA suggested that it is best to couple the water inlet flowrate with tank 3 level and the solids flowrate with the outlet density.

7. ReferencesFichte R. (2005). Ferroalloys, Ullmans enclopedia of industrial chemistry, Weinheim: Wiley-VHC, doi: 1002/14356007.a10_305Svrcek W.Y., Mahoney D.P., Young B.R. (2014). A Real-Time Approach to Process Control, 3rd ed. UK: Wiley. Pp., 303-305

8. Appendix

Figure 6.1 Tank 1 solids balance

Figure 6.2 Tank 2 Solids Balance

Figure 6.3 Tank 3 solids balance

Figure 6.4 Tank 1 Volume Balance

Figure 6.5 Tank 2 Volume balance

Figure 6.6 Tank 3 Volume balance

Figure 6.7 PID controller controlling tank level

Figure 6.8 PID controller controlling outlet slurry density

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