Optimization of Emotional Learning Approach to Control Systems with Unstable Equilibrium - Software Engineering, Artificial Intelligence, Networking and Parallel/Distributed Computing - page 51

Ta b l e 3 Evaluation measures of second disturbance test

Controller IAE p IAE a IACF IADCF

μ σ μ σ μ σ μ σ

Proposed controller 3.99 0.45 0.52 0.27 29.40 2.60 64.33 3.10

Double PID 9.10 3.28 1.99 0.35 38.50 3.11 96.12 3.15

shown in Fig. 4 and Fig. 5, proposed BELBIC has good performance and robustness
in tracking and disturbance rejection. Below, four performance measures are defined
for comparison and evaluation [11]:

• IAE a : Integral Absolute Error for cart position

• IAE p : Integral Absolute Error for pendulum angle

• IACF : Integral of Absolute values of Control Force

•

IADCF : Integral of Absolute values of derivation of Control Force
Tables 1, 2, and 3 present above measures for both of proposed BELBIC con-
troller and basic controller. In Table 1 results of evaluation measures without ap-
plying disturbance are presented. For disturbance tests the experiments carried out
10 times and the mean and the standard deviation of four measures are calculated.
Tables 2 and 3 show results of first and second disturbance tests respectively.
We can see the fast learning ability of BELBIC and less oscillation than basic
controller in Table 1. Due to control force which is penalized by stress signal, it is
lower than control force in other controllers and has less oscillation [11]. As it can
be seen in Tables 2 and 3, in presence of disturbance, proposed BELBIC is more
robust and shows better disturbance rejection.

7 Conclusion and Future Works

When a learning controller such as BELBIC is used to control unstable systems
or system with unstable equilibrium, without any background knowledge of sys-
tem dynamics, they might cause low performance in initial steps of learning pro-
cess because of producing false control commands. In this paper we proposed a
novel approach in optimization of brain emotional learning based intelligent con-
troller to control systems with unstable equilibriums. The proposed approach takes
place in three phases, in the first phase BELBIC learns to produce a proper control
signal in an imitation process from a basic controller. In the next two phases, an
optimization improves the stress which is produced by emotional cue generator. In
the second phase, particle swarm optimization finds a new solution having much
better performance rather than basic controller considering position and angle er-
ror, and eventually, in the third phase, the optimization process continues between
candidate solutions to reduce errors. To have an efficient performance evaluation
three experiments have been performed. Proposed controller shows better perfor-
mance than basic controller in all experiments, especially in disturbance tests. Be-
cause of learning capability, good disturbance rejection and robustness of BELBIC,