**4. Force sensorless damping control system design**

412 Smart Actuation and Sensing Systems – Recent Advances and Future Challenges

Valve Control Signal 4.0

0 2 4 6 810

 Real Force Estimated Force

Time [s]

(b) Case 02 (Working load: 3kg; Vibrating control signal: (3V, 1.5Hz); Damper applied current: 1.0A)

0 2 4 6 810

 Real Force Estimated Force

Time [s]

(c) Case 03 (Working load: 3kg; Vibrating control signal: (3V, 2.0Hz); Damper applied current: 2.0A) **Figure 20.** Comparisons between the real and estimated damping forces of the TR02 system using the

4.5

16.5

Piston Displacement

17.0

Piston Displacement [(x10-3)m]

17.5

18.0

Piston Displacement

5.0

Piston Displacement [(x10-3)m]

5.5

2


0


self-sensing method based on the optimized BBM.


Damping Force [N]

0

500

1000

Valve Control Signal

2

4

Valve Control Signal [V]

6

8


Damping Force [N]

0

500

1000

4

Valve Control Signal [V]

6

8

In this section, the force sensorless control technique, combined from the BBM and IBBM models, is developed to be applied to systems using this damper for damping control with force self-sensing behavior. The BBM model, which uses a self-tuning fuzzy system optimized by neural network technique, was designed to overcome the disadvantages of conventional models. The BBM built in the form of the simple fuzzy mapping laws is considered to estimate directly the damping force output with respect to the characteristics and inputs of the MR damper. In order to improve the accuracy of the suggested model, the back-propagation learning rule based on the gradient descent method has been used to train the fuzzy parameters to minimize a defined modeling error function. Next, the IBBM model is derived from the optimized BBM and suggested to use as an effective force controller. In addition, the IBBM structure is online adjusted with respect to the control error to improve the system performance.

Finally, the proposed controller based on the BBM and IBBM is built for the force sensorless damping system as shown in Fig. 21. Here, the BBM model works as a virtual force sensor while the IBBM takes part in direct damping control without using other control techniques.

**Figure 21.** Structure of the proposed force sensorless damping control system.
