Regulation Control

The objective of the regulation control is to execute the commanded speed from the supervisory control. Under different types of engine, automatic transmission in the gear box and brake system in each vehicle, a normal driver can still operate the throttle and brake systems easily to reach the suitable speed. In view of this, the design concept to the regulation brings from the human-driving behavior. By importing the human-driving experience into fuzzy rule, not only avoid the difficulty for control designing based on such complicated mathematical model, but we also make the system satisfy the humanlike driving behavior.

In constructing the fuzzy inference rules, we usually make different inference rules for every input variable. By choosing two fuzzy inputs as the speed error (VC −Vf ) and the error-change, if we set 5 membership functions for each input variable, then there will be 25 fuzzy rules in the whole fuzzy rule table. There will be a drawback that building many fuzzy rules will increase the computation load for implementation loop. Conventionally, we usually use a look-up-table to approximate a fuzzy rule table in programming. However, the method not only needs more storage space on the memory of device, but also causes discontinuous outputs which will worsen the controlling performance of original FLC. Therefore, a PD-based single-input fuzzy logic control (SFLC) is employed in the regulation control design.

Fig. 4-7. Derivation of the signed distance.

For conventional FLC’s, the fuzzy rule base is constructed in a two-dimension (2-D) space for using the error and error change phase-plane, i.e. ( ,e e ). It can be inspected that most 2-D fuzzy rule bases have the so-called skew-symmetric property as shown in Fig. 4-7; thus, the

switching line which represents the main hyperplane of 2-D fuzzy rule table can be defined as:

: 0

S e+αe= (4-53) where α is the slope of the switching line.

The original fuzzy inputs of the error and error change can be replaced by one signed distance, which is defined as the perpendicular distance from an operating point Q( ,e e ) to the projection point on the switching line S. As illustrated in Fig. 4-7, a new fuzzy input of the signed distance can be calculated as

sgn( ) where the sign function is

1 for 0

Now the fuzzy input Ds is a combination of speed error and error change with a proportional gain and a derivative gain, respectively,

s p d

D =k e k e+  (4-55) with k_p =α 1+α² and k_d =1 1+α² .

The associated fuzzy rule form is

Rk : If Ds is LDk , then u is LUk . (4-56) where LDk and LUk are the linguistic term sets for the fuzzy input and output in the kth rule, respectively.

The fuzzy rule table of SFLC is established as in Table 4-3. The membership functions of SFLC are shown in Fig. 4-8. The total numbers of the fuzzy rules on throttle and brake control of the regulation control are only 5, which are much fewer than 25 fuzzy rules of 2-D fuzzy control such that the generation and tuning of rules are much easier. Especially, control effect of the PD-based SFLC is equivalent to that of 2-D fuzzy control (details can be referred to [49]). In the defuzzication operation, the center of mass (COM) method is applied to calculate the control output

where µk represents the weighting value of each rule k, and uk is the crisp value of each rule consequence.

TABLE 4-3. Rule table of the SFLC.

Ds NB NS ZO PS PB

u NBu NSu ZOu PSu PBu

(a)

(b)

Fig. 4-8. Membership functions of (a) the fuzzy input and (b) the fuzzy output.

Fig. 4-9. Overall structure of the proposed regulation control structure.

Figure 4-9 shows the overall structure of the regulation control. To test the performance of our PD-based FLC, we consider the constant velocity-tracking case. We find that there always

exists a steady-state error (around 2.5 km/h) for the desired velocity-tracking (80 km/h), as shown in Fig. 4-10(a). This is possibly due to the grad of uphill-road and the friction between vehicle’s rubber-tires and asphalt roads. Therefore, we add an integral controller with limited saturation [1, -1] to compensate this error. Figure 4-10(b) shows the improved performance of the proposed PID-based FLC.

(a) (b) Fig. 4-10. Constant velocity-tracking performance for the proposed PD-based FLC (a) and

PID-based FLC (b).

Fig. 4-11. Control surface of the single-input fuzzy control.

Further, the SFLC of the regulation control can be simplified into 5 linear equations from mapping between Ds and u. We can exploit the control-surface concept of SFLC, as shown in

5 fuzzy inference rules and other process of fuzzy logic control such as fuzzifier and defuzzifier are substituted, the performance equals that of original SFLC. In this way, we can decrease a considerable quantity in the programming complexity of fuzzy inference. Note that the offset db (corresponding to the negative membership of ZO of Fig. 4-8(a)) presents the reachable deceleration for the vehicle due to the rolling resistance and the engine inertia, and can be obtained experimentally by

b p s ave d ave

d k T V k V

t

= ⋅ ⋅ ∆ + ∆

∆ (4-58) where ∆Vave < 0 is the average speed variation during a interval ∆t with throttle and brake being off.

Remark: The term of integral control is neglected in (4-58) due to the small values which are limited within [1, -1].

As to the switching strategy to implement the integrated control between throttle and brakes, it should be noted that the normalized universe of discourse of the driving voltage is limited to the range [0, 1] and negative voltages can not provide inverse torques from the throttle motor.

Therefore, the negative voltage can be output into the brake driver for deceleration control. In other words, the SFLC is designed to provide a positive voltage (phase I and III in Fig. 4-11) with regard to acceleration for the throttle driver while provide a negative voltage (phase II and IV in Fig. 4-11) with regard to deceleration for the brake motor. By using an inverse operation, the negative voltage can be inverted to the brake motor. Due to this nature of input voltage to motor drivers, the switch between the throttle and the brake control can be directly constructed. As shown in Fig. 4-11, the switching strategy is summarized as follows:

－Throttle control region. For the case of Ds > 0, the summation of speed error and error change is positive and it implies that the throttle should be acted to achieve the desired speed.

－Switching control region. For the case of 0 < Ds < db, the summation of speed error and error change is slightly negative. Only by engine brake, the speed can be decreased to the desired speed. In this region, neither throttle nor brake should be acted.

－Brake control region. For the case of Ds < db, the summation of speed error and error change is more negative and thus the brake should be acted to decrease the speed to achieve the lower desired speed.

As a result, only the throttle will be acted if the requested speed is greater than the current speed; otherwise, only the brake will be acted whenever the vehicle is required to be

decelerated (Ds < db). The situation of both throttle and brake being active can be prevented by the switch control region. Besides, the error change in Ds can improve the controlling response for instant variance in vehicle speed. A normal driver operates the brake pedal more rapidly than the throttle pedal, and thus in the design of SFLC the brake control surface (in phase II) is more sloping than that of throttle control surface (in phase I). In addition, the foot action for pressing the throttle/brake pedal initially is quick and then smooth in deeper position, and therefore the slopes in phase III and IV are smaller than that in phase I and II.