STAGE 1: Control System Simulation
Figure 1: Proportional control for the system without disturbance
Procedure
Figure 2: Model construction in matlab simulink
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.
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
Figure 8: output of figure 6 Ki=1 Kp =2 Kd=1
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
Procedure
Figure 13: FIS GUI
Figure 14: membership function GUI
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
Procedure
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
Objectives
Procedure
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.
Reference
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