Control System Simulation, Fuzzy Interference System, And TSK Fuzzy Control

Learning Objectives

STAGE 1: Control System Simulation

• To simulate control systems using Simulink
• To evaluate control system performance

Figure 1: Proportional control for the system without disturbance                          

Procedure

1. We opened matlab>>Simulink>>new model.
2. The model as shown in figure 1 above. The blocks were placed on the model by clicking on the library browser>>commonly used blocks/continuous blocks. Eg to add the integrator we clicked library browser>>commonly used blocks, we right clicked the integrator and choose the option Add block to model.
3. The block properties were changed to those of the blocks in figure 1 by double clicking the block.
4. In addition to the blocks as shown figure 1 we added a step input and a scope. Figure 2 below shows the construction of the model Simulink

Figure 2: Model construction in matlab simulink

1. We then defined Kp in MATLAB command window and hit enter to save on the workspace. We clicked run icon to run model the output of the model was as shown below.
2. The values of Kp were varied to 10 and 3 and the outputs plotted as shown below.

Figure 3: output of the model without disturbance Kp=5

Figure 4 output of the model without disturbance Kp=10

Figure 5 output of the model without disturbance Kp =2

From the plots it can be observed that increasing Kp reduces steady state error, increases overshoot and reduces rise time and the vice versa.

1. The value of Kp was set to 5 then we included an integral and differential component. We added a PID controller on our system and plotted the output for the step input into our controller as shown below.

Figure 6: Our proportional control with differentiator and integrator component-PID controller added to it

Figure 7: output of figure 6 Ki=1 Kp=5 Kd =1

1. We adjusted the values of Kd, Ki and Kp of the PID controller so that we can obtain the best response. We obtained Kp=2, Ki=1 and Kd=1 as our best points. The plot was as shown below:

Figure 8: output of figure 6 Ki=1 Kp =2 Kd=1

1. We constructed the system with disturbance as shown below. Its response was as shown below:

Figure 9: system with disturbance

Figure 10: plot for system in figure 9

We then included a PID in the system and repeated the steps in 8

Figure 11: system with disturbance and a PID Kp=5 Kd=10 Ki=20

Figure 12: plot for system in figure11

It is observed that as we varied Kp the transient response varied I was observed that with increased Kp the transient response was short and improved steady state response.

STAGE 2: fuzzy interference system

Objectives

• To build a fuzzy interference system using MATLAB.
• To simulate fuzzy interference systems.
• To draw surface view between the input and output.

Procedure

1. We typed fuzzy and hit enter to load the fuzzy GUI on the command window.
2. From the GUI we defined our inputs and output then saved to workspace.
3. We then defined the membership function by double clicking on one of the inputs then changed the range, types and parameters of the membership function.

Figure 13: FIS GUI

Figure 14: membership function GUI

1. We loaded the Load the tipping example system of the toolbox by typing fuzzy tipper in the MATLAB command window.

Observation:

We compared the tipping system we constructed and they were similar. The membership functions, rules and surface views were the same. It was also observed that as you varied the membership functions the output surfaces varied.

STAGE 3: Mandani fuzzy control

Objectives

• To design Mandani fuzzy controllers.
• To simulate the fuzzy control systems.
• To fine tune fuzzy control systems.

Procedure

1. We designed the block diagram as shown in figure 15 below and simulated it. The block model in Simulink is as shown in figure 15. We varied the PID constants.

Figure 15: Fuzzy Logic control system

Figure 16: Fuzzy logic control system

Figure 17: response of the Fuzzy Logic unit                                                                 Discussions

It is not possible to achieve a fuzzy controller by changing the membership functions only and keeping all the three parameters at unit. The fuzzy controller performs better than PID controller especially when the membership functions and the rules are well defined. When the three normalization constants are varied the performance of the system in both transient and steady state is affected. H0 causes the transient time be longer while h1 reduces as it its value is increased. On the other hand, h2 reduces the transient time however increasing the overshoot.

A tuned fuzzy controller has a high accuracy compared with traditional PID controller in controlling a system. It is also easier to tune it to the desired output of the system under control.

   STAGE4: TSK Fuzzy control

STAGE 1: Control System Simulation

Objectives

• To design TSK fuzzy controllers.
• Simulate TSK fuzzy controller.
• Fine tune TSK control systems.

Procedure

1. We divided the non-linear part of equation 1 2 below into five sections. We used each section and designed a PID controller in Simulink as shown below to form a TSK fuzzy controller.
2. We simulated and fine-tuned the fuzzy controller to achieve the shortest rise time.
3. The difference caused by using alternative fuzzy interference system were studied.
4. Comparison of the TSK fuzzy controller with the traditional PID controller.
5. Comparison of the TSK fuzzy controller with the Mandani fuzzy controller.

Figure 18: Five stages PID

Figure 19: ouptput for TSK fuzzy logic

Derivative action is more often is used to improve transient response of the closed loop system. However D control is not used because it amplifies high frequency noise which is never desired. Derivative action decreases rise time and oscillations. However, it does not have any effect on steady state performance of the closed loop as seen from the figure above.

The following are advantages of TSK fuzzy controller compared to the  Mandani fuzzy controller and the traditional PID controller; works with less precise inputs, doesn’t need fast processors and it is more robust than other non-linear controllers.

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