Robust proportional–integral–derivative compensation of an inverted cart–pendulum system: an experimental study

Yapay Arı Kolonisi Algoritması ile Bir Arabalı Ters Sarkacın Lineer Kuadratik Kontrolü: Deneysel Bir Çalışma

“…Pendulum's swinging bound for the proposed method is a bit larger than the other method as shown in Figure 4(b), despite the proposed method managed to keep the pendulum upright position in about 2.2 sec while it took about 2.7 sec for the other method. Overall, the simulation results have shown that the proposed method is more efficient than the method proposed in [10] to select weighting matrices for LQR controller design. Figure 5(a-c), respectively.…”

“…After the LQR training which is performed to determine the matrices and using the ABC algorithm is achieved, the performance of the proposed method is compared with a method proposed by Ghosh et al [10]. Block diagram of the LQR controller of the nonlinear inverted pendulum model with DC motor shown in Figure 3 is employed for the simulation test.…”

“…It is not required to compare the proposed method with one trained by another swarm optimization algorithm since the main goal of this study is to show advantage of the ABC algorithm in comparison with any method based on trial and error instead of its training performance. The method proposed by Ghosh et al [10] is used for comparison purposes in this study. According to this method Q and R matrices can be defined as follows [10] The proposed method and the method proposed in [10] are simulated in the simulation setup which is shown in Figure 3.…”

“…The method proposed by Ghosh et al [10] is used for comparison purposes in this study. According to this method Q and R matrices can be defined as follows [10] The proposed method and the method proposed in [10] are simulated in the simulation setup which is shown in Figure 3. The only differences between these simulations are the feedback gain matrix and the scale factor ̅ .…”

“…According to this method can be taken as Q=C T Q ̅ C. Since matrix includes important outputs, these states are included within the cost. Also another method for choosing weighting matrices for linear quadratic control of an inverted pendulum is proposed by Ghosh et al [10]. According to this method, the matrix can be chosen as = { 11 , 22 , 33 , 44 } and R=r 11 where q 11 =500q, q 22 ,q 33 =20q, q 44 =q and r 11 =10 n .…”