Balancing Inverted Pendulum by Angle Sensing Using Fuzzy Logic ...

More documents

Recommendations

Info

Sensors & Transducers Journal, Vol. 133, Issue 10, October 2011, pp. 74-82supervisor has a rule base in which the fuzzy rules have consequents which address the gains of thePID controller. Hence, the fuzzy supervisor has three “outputs”: KP, KIand KDwhich result indifferent parameters of the PID controller each sampling instant:K'P'I[ kT] K K[ kT](6)PPK [ kT] K K[ kT](7)K'DII[ kT ] K K[ kT](8)DThe inputs of the fuzzy supervisor are: the error e [kT]and its first difference e[kT]. Or in otherwords the error and error rate are given as inputs to fuzzy system. We find that the error depends on K Ponly and the error is reducing with increase in value of K P . For K P 450, the steady state error is 2 %.First we will focus on the error only. We will design such a fuzzy logic supervisory system whichgives output in incremental form of K P for the given inputs e(t) and de/dt. The fuzzy supervisor willchange the value of K P so that the error is less than 2 %.Rewriting the equations:D2.55KDDamping ratio (9)2 2.55K 22.47PSettling time (on 2% basis)ts3.137 (10)KDError 22.47ess(11)2.55K 22.47P Maximum Overshoot = exp 10021 (12)The inverted pendulum system as in eq. (1) is analyzed at different stages. The open loop system(Servomechanism + Inverted Pendulum) has one pole on the right hand side, so the inverted pendulumis unstable in open loop. After introducing position feedback as in Fig. 3 and a feedback transferfunction H(s) =2.86, we get transfer function of the closed loop system. Still one pole is on the righthand side. Hence, this closed loop system is also unstable.[reference of same paper]2. Proposed SystemExisting system incorporates fuzzy controllers for stabilizing an inverted pendulum [9]. The error inthe system depends on K P only and the error is reducing with increase in value of K P , the steady stateerror being less than or equal to 2 % , for K P 450.This design has a fuzzy supervisory system whichgives output in incremental form of K P for the given inputs e(t) and de/dt [11].78
Sensors & Transducers Journal, Vol. 133, Issue 10, October 2011, pp. 74-82In the proposed system we have included a Genetic Algorithm system after the Fuzzy supervisor asshown in Fig. 4. Initially, fuzzy supervisor gives output in incremental form so that error is less than2 %, then the GA system finds the optimal solution in the range 264 K P 529, so that the error andthe overshoot both are minimum. In the proposed system coding of GA system has been done in C++language.Fig. 4. Fuzzy GA supervised PID Controller for IP System.2. Simulation ResultsAfter introducing fuzzy supervised PID-controller, we get a stable response of the system as shown inFig. 5. The fuzzy supervisor changes the value of K P so that the error is less than 2 % [11].Fig. 5. Response of inverted pendulum for an applied input.79
Page 2: Sensors & TransducersVolume 133, Is
Page 6 and 7: Sensors & Transducers Journal, Vol.
Page 14: Sensors & Transducers Journal, Vol.

Balancing Inverted Pendulum by Angle Sensing Using Fuzzy Logic ...

Create successful ePaper yourself

Delete template?

Save as template?