1. Introduction

Nowadays, modern control-based technical devices such as robotics, assistive machines and home appliances are popularly used to improve the level of human being's life. In these devices,

© 2018 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited.

control algorithm is one of the most important components which brings comfortable requirements to the consumer. The development of control algorithms in recent years is abundantly being undertaken from the aspect of classical control to salient characteristics of intelligent control. The classical control methods are frequently combined with modern control technique to resolve parameter uncertainties and disturbances those are existed in most of control devices. A controller which is formulated using more than two different control schemes is called "a hybrid controller" or "composite controller" [1, 2]. Among many candidates of the hybrid controller, the type of hybrid adaptive controller is the most popular since its structure is relatively simple and its control performance is very robust against the uncertainties or/and external disturbances. A hybrid adaptive control with fuzzy model and wavelet neural networks was presented in [1, 3] in which the sliding mode control was used to connect the parameters of the fuzzy model and the neural networks. This method is the typical model to develop the adaptive control in the last few years. Besides of uncertain nonlinear system, the problem of unknown input nonlinearity such as dead-zone or backlash-like hysteresis was also studied through the hybrid adaptive control [4]. It has been also shown that the neural works can be designed for a good performance of the hybrid adaptive control to deal with the uncertain system [5]. A hybrid adaptive controller possessing the robustness against input and parameter uncertainties was studied using the sliding mode controller associated with the fuzzy model [6, 7]. When a hybrid adaptive controller is formulated, in general the adaptation laws are simultaneously calculated. Furthermore, the back-stepping method was integrated with the fuzzy mode to achieve high performance of the hybrid adaptive controller [8].

fuzzy neural networks model and prescribed performance of the sliding surface associated with adaptation laws to guarantee robust stability (HAC-PP in short). The second hybrid adaptive controller is formulated by combining inversely fuzzified value with H-infinity control to minimize computational cost algorithm (HAC-IFV in short).The stability of both adaptive controllers are rigorously proved based on the Lyapunov stability and appropriate control gains are determined to evaluate vibration control performance. It is shown that both proposed adaptive controllers are very effective and robust for controlling unwanted vibrations or excitations from the road profiles. These are validated by presenting control results showing significant reduction of both the displacement and acceleration at the seat position subjected to

As mentioned in Introduction, the online interval type 2 fuzzy neural networks (OIT2FNN in short) model is used to formulate two adaptive controllers. The rule base of OIT2FNN can be

ð Þ i ¼ 1;…; n; j ¼ 1;…; m are fuzzy sets, m is the number of rules, and a

<sup>2</sup> <sup>¼</sup> <sup>θ</sup><sup>T</sup>

<sup>r</sup> <sup>¼</sup> wr

T

symbolize the relation of the rule layer and type-reduction, and the weighted firing strength

, ξf

As a problem formulation, consider a single-input and single-output (SISO) nonlinear system

where f(x)∈ Rn and g(x)∈ Rn are two unknown non-linear function vectors, u(t)∈ R<sup>1</sup> is control function, d(t) ∈R<sup>n</sup> is an external disturbance vector, |d(t)| ≤ δd where δd∈R<sup>n</sup> is upper bound

<sup>r</sup> <sup>¼</sup> <sup>f</sup> <sup>1</sup> Pn i¼1 f i

f 2 Pn i¼1 f i

x\_ ¼ f xð Þþ g xð Þu tð Þþ d tð Þ (3)

l ξ f <sup>l</sup> <sup>þ</sup> <sup>θ</sup><sup>T</sup> r ξf r

<sup>1</sup> w<sup>r</sup> <sup>2</sup> w<sup>r</sup> 3…w<sup>r</sup> n

sets. The calculation process of OIT2FNN is clearly explained in [22]. The defuzzified output is

<sup>f</sup> <sup>n</sup> Thengis a

j <sup>0</sup> <sup>þ</sup>X<sup>n</sup> i¼1 a j i

Robust Adaptive Controls of a Vehicle Seat Suspension System

http://dx.doi.org/10.5772/intechopen.71422

5

hi (1)

j

<sup>2</sup> (2)

… <sup>f</sup> <sup>n</sup> Pn i¼1 f i

T

� � are the weighting vectors, which

f 3 Pn i¼1 f i <sup>i</sup> are interval

<sup>f</sup> <sup>1</sup> and…andhn isH<sup>j</sup>

gf <sup>¼</sup> gl <sup>þ</sup> gr

external excitations.

2. Formulation of HAC-PP

Rj

<sup>l</sup> <sup>¼</sup> <sup>w</sup><sup>l</sup>

governed by the following equation:

ξ f <sup>l</sup> <sup>¼</sup> <sup>f</sup> 1 Pn i¼1 f i

<sup>1</sup> wl <sup>2</sup> w<sup>l</sup> 3…w<sup>l</sup> n � � and θ<sup>T</sup>

> f 2 Pn i¼1 f i

f 3 Pn i¼1 f i … f n Pn i¼1 f i

<sup>f</sup> : If <sup>h</sup><sup>1</sup> isHj

expressed as follows [22].

where, H<sup>j</sup>

fi

then determined by

In the above, θ<sup>T</sup>

vectors given by

As mentioned earlier, both the fuzzy model and the neural networks model are frequently used for the formulation of high performance of a hybrid adaptive controller [9]. Recently, a modified type of the fuzzy model called interval type 2 was combined with the back-stepping method to design of a hybrid adaptive control [10, 11]. It is remarked that the fixed fuzzy model always provides a safe choice in design of a hybrid adaptive control. However, this choice may cause a large error in finding the final values. To resolve this problem, an adaptive interval type 2 fuzzy neural network was developed on the basis of the online technique which can strengthen the flexibility of design parameters against the uncertainties [12]. Besides the above, there are many approaches to formulate new hybrid adaptive controllers such as output feedback control approach to take account for unknown hysteresis [13]. From the aspect of experimental implementation of hybrid adaptive controllers, several dynamic systems featuring magneto-rheological (MR) mount and MR damper are adopted for vibration control [2, 14–18]. Most of hybrid adaptive controllers used in these experimental realizations have been formulated by combining the models of interval type 2 fuzzy and interval type 2 fuzzy neural networks, and the control techniques of H-infinity control and sliding mode control. The advantage of using the interval type 2 fuzzy model is its flexibility in which optimized fuzzy values can be achieved unlike the classical fuzzy rule with the fixed value [19]. In order to improve the fuzzy model, clustering method [20] and data-driven for fuzzy rules [21] were also introduced.

As a subsequent work to develop a new hybrid adaptive controller, in this work two different new hybrid adaptive controllers are developed and their control performances are evaluated by investigation on vibration control of a semi-active seat suspension system installed with MR damper. The first hybrid adaptive controller is designed by combing online interval type 2 fuzzy neural networks model and prescribed performance of the sliding surface associated with adaptation laws to guarantee robust stability (HAC-PP in short). The second hybrid adaptive controller is formulated by combining inversely fuzzified value with H-infinity control to minimize computational cost algorithm (HAC-IFV in short).The stability of both adaptive controllers are rigorously proved based on the Lyapunov stability and appropriate control gains are determined to evaluate vibration control performance. It is shown that both proposed adaptive controllers are very effective and robust for controlling unwanted vibrations or excitations from the road profiles. These are validated by presenting control results showing significant reduction of both the displacement and acceleration at the seat position subjected to external excitations.
