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Table 1. Parameters for setpoint 23 SI Units for first PSO execution Fig 3: Speed Response for parameters of Table 1

Table 1 Parameters for setpoint 23 SI Units for first PSO execution Fig 3: Speed Response for parameters of Table 1

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Fig 1: Membership Functions and their Parameters As can be seen in Fig! al,bl,cl corresponds to membership function Negative . a2,b2,c2 corresponds to membership function Zero. a3, b3, c3 corresponds to membership function Positive. These parameters have to be tuned such that the steady state error is zero. Again in this case al ,b1 and b3,c3 will be fixed since they deal with extreme or maximum errors or change in errors and b2 will be fixed and centred at zero. Conditions like al<bl<a2 and c2<b3<c3 also need to be satisfied. a2<cl ; cl<b2; b2<a3; a3<c2. These conditions are dealt with by the PSO algorithm to be explicated later. So it can be seen that there are 8 parameters to be tuned. The PSO algorithm is required to be discussed. The PSO is an optimization technique that optimizes a problem by sequentially trying to improve the candidate solution. It does not guarantee an optimal solution[2]. There is a need to produce zero steady state error in speed by we optimising the parameters of the fuzzy controller. In a way fixing the objective function as a function of speed is not possible as it is not the output of the fuzzy controller. The output of the fuzzy controller is voltage. But the voltage more precisely has a dependence on the speed we want. So the objective function should include voltage rather than speed . In other words the Each of the inputs have 3 membership functions — for Negative, Zero and Positive. The MFs are chosen to be triangular in shape. There is only one output i.e. Voltage which is fed to the armature of the DC Motor . The Voltage also has 3 MFs — Negative, Zero, positive but it is not required to be optimised. Since the input to the fuzzy controller deals with the quantity to be controlled only the Input MF is sufficient to be optimised. Mamdani (Fuzzy inference System) FIS has been used. For each triangular membership function there are 3 parameters a,b,c. Since there are 3 MFs for a particular input there are a total of 9 parameters for a particular input. Since there are 2 inputs so there are a total of 18 parameters for each input. The membership functions of one input is shown.
Fig 1: Membership Functions and their Parameters As can be seen in Fig! al,bl,cl corresponds to membership function Negative . a2,b2,c2 corresponds to membership function Zero. a3, b3, c3 corresponds to membership function Positive. These parameters have to be tuned such that the steady state error is zero. Again in this case al ,b1 and b3,c3 will be fixed since they deal with extreme or maximum errors or change in errors and b2 will be fixed and centred at zero. Conditions like al<bl<a2 and c2<b3<c3 also need to be satisfied. a2<cl ; cl<b2; b2<a3; a3<c2. These conditions are dealt with by the PSO algorithm to be explicated later. So it can be seen that there are 8 parameters to be tuned. The PSO algorithm is required to be discussed. The PSO is an optimization technique that optimizes a problem by sequentially trying to improve the candidate solution. It does not guarantee an optimal solution[2]. There is a need to produce zero steady state error in speed by we optimising the parameters of the fuzzy controller. In a way fixing the objective function as a function of speed is not possible as it is not the output of the fuzzy controller. The output of the fuzzy controller is voltage. But the voltage more precisely has a dependence on the speed we want. So the objective function should include voltage rather than speed . In other words the Each of the inputs have 3 membership functions — for Negative, Zero and Positive. The MFs are chosen to be triangular in shape. There is only one output i.e. Voltage which is fed to the armature of the DC Motor . The Voltage also has 3 MFs — Negative, Zero, positive but it is not required to be optimised. Since the input to the fuzzy controller deals with the quantity to be controlled only the Input MF is sufficient to be optimised. Mamdani (Fuzzy inference System) FIS has been used. For each triangular membership function there are 3 parameters a,b,c. Since there are 3 MFs for a particular input there are a total of 9 parameters for a particular input. Since there are 2 inputs so there are a total of 18 parameters for each input. The membership functions of one input is shown.
Vig(k+1)=w.vje(k)+c1 *rand()*(pbestjg—xje(k)) +c2*rand()*(gbest,— xje(k))
Vig(k+1)=w.vje(k)+c1 *rand()*(pbestjg—xje(k)) +c2*rand()*(gbest,— xje(k))
Table 2. Parameters for Set Point 23 SI Units for second PSO execution
Table 2. Parameters for Set Point 23 SI Units for second PSO execution
Fig 4: Speed Response for parameters of Table 2
Fig 4: Speed Response for parameters of Table 2
Fig 5: Speed Response for the parmeters of Table 3 Table 3. Parameters for Set point 25 SI Units
Fig 5: Speed Response for the parmeters of Table 3 Table 3. Parameters for Set point 25 SI Units
Table 4. Parameters for Set point 30 SI Units Fig 6: Speed Response for the parameters of Table 4
Table 4. Parameters for Set point 30 SI Units Fig 6: Speed Response for the parameters of Table 4
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