Fault-Tolerant Control
6.2 Normal Controller (NC)
As mentioned in Chaps. 3, 4, and 5, under the fault-free condition, there is a three-level control system using the IMV, represented in Fig. 6.2. The IMV can be composed of four 2-way poppet or two 3-way spool valves. To distinguish themselves, these valves are remarked as “V1, V2, V3, and V4". To further investigate the fault-tolerant control, the studied system is equipped with an electronically controlled pump that supplies the required flow. Therefore, the three control input variables consist of the control signals of inlet /outlet valves and the pump. Hence, three control input variables (u1, u2, up) consist of the control signals of inlet /outlet valves and the pump.
In addition, the system is equipped with velocity and pressure sensors, in which the velocity sensors are only used for monitoring and do not used for the actual control.
Fig. 6.2 Normal control system under the fault-free condition for four 2-way poppet valves, or two three-way PDVs
6.2 Normal Controller (NC) 105
6.2.1 MIMO System in the IMCS
At least there are three control inputs (u1, u2, up) and three control output (v, pa or pb, ps) in the normal control system, which infers that it is a typical MIMO system in Fig. 6.3. The actual number of control variables is three since the input pressure is coupled with the backpressure via velocity. The cylinder velocity (v), backpressure (pb), and supply pressure (ps) are generally selected as the output control variables.
Therefore, it can balance precise motion-tracking and energy-saving performance with this selection.
Because of the cross-coupling of the MIMO system, there is not only one arrange- ment method for control inputs and outputs. However, the choice of the appropriate control line depends not only on the specific system parameters, but also on the basic transmission characteristics of the controlled system. According to Chap. 4, in order to weaken the cross-coupling characteristics between one main control line to another, it is recommended to use the valve corresponding to the high-pressure side for velocity control and the valve corresponding to the low-pressure side for pressure control [10]. Certainly, the flow or the supply pressure is controlled by the pump.
Consequently, the control variable pairs of the MIMO system are exhibited by the solid line in Fig. 6.4, while the transmission behavior where one control line affected another main control line is exhibited by the dotted line. According to Chap. 3, there are a group of operating modes, only three typical operating modes in Table 6.1 are investigated in this chapter: first is the actuator extension with a positive load (Power extension, PE); second is the actuator retraction with a negative load (low-pressure retraction regeneration, LSRR), also marked as “LPR” in Chap. 5; third is High Side Regeneration Extension (HSRE) for light actuator, also marked as “HPR” in Chap. 5.
The other operating modes in the IMCS are similar to them. Under the LSRR mode, the actuator is lowered down by the negative load in the differential hydraulic circuit without the pump control, so the control output variables only contain the velocity and pressure of actuator.
Fig. 6.3 MIMO of the independent metering control system
F F
F pa
uv1
pb
v
uv2
ps
up
G(s)
l
(a) Extension with a positive load (b) Retraction with negative load uv2(<0)
uv1(>0)
up(>0)
pb
v
ps
pb
v
up ps
uv2(<0) uv1(<0)
Fig. 6.4 Main control line under fault-free conditions
Table 6.1 List of two typical operating modes
MODE PE LSRR HSRE
LOAD CONDITION
HYDRAULIC CIRCUIT
Fl
v
Fl
v
Fl
v
6.2.2 Normal Control Design
Referring to Chaps. 4 and 5, control strategies under normal (fault-free) conditions are designed according to the control variable pairs. Under the PE mode, the Inlet and outlet valves independently control the flow and pressure of the hydraulic actuator.
The velocity control is employed to distribute the supply flow among multiple actu- ators. In addition, the pressure control is employed to make the outlet valve can open as large as possible to reduce the backpressure, such that the outlet throttling losses can be reduce. In the ELS controllers in Chap. 5, the pump control uses a closed-loop control to adjust the pump swash-plate angle to maintain a pressure margin between the supply pressure and the maximum load pressure.
As shown in Fig. 6.5, the strategies of detailed control strategies are designed only by the pressure sensors. Under the PE mode, Open-loop velocity control is established by offline calibrated inverse valve flow mapping, as depicted in Eq. (6.1). In addition, a closed-loop pressure control based on a PI regulator is used to make the outlet valve open as large as possible, such that the backpressure can be reduced. Then, to prevent cavitation, the target backpressure is set at 0.2 MPa rather than zero.
uv1 = qv−1(vref Aa, ps − pa) (6.1)
uv2 = Kp pbe(t) + Ki tn
∫
t0
pbe(t)dt (6.2)
6.2 Normal Controller (NC) 107 where pbe is the subtraction between pref and pb.
A cascade dead zone compensator (DZC) is designed to handle the dead zone of the spool, such that a higher response of the close-loop controller can be obtained.
The relationship between the control input and the spool opening signal is optimized by using the nonlinear DZC in Eq. (6.3), as represented in Fig. 6.6.
uv =
⎧ ⎪
⎨
⎪⎩
A1uv + A2 i f uv > ur xv,ad
xv,r · uv i f −ur ≤ uv ≤ ur A1uv − A2 i f uv <−ur
(6.3)
(a) PE mode
(b) LSRR mode Fig. 6.5 Normal control system under the fault-free condition
xv,ad
xv,m
xv
uv
xv,r
uvr
xv,m xv
uv
uv after DZC
uv into DZC DZC in
equation (9)
Valve after DZC
Fig. 6.6 Design of dead zone compensator for the valve spool
where A1 = xxv,mv,m−−xxv,ad v,r , A2 = uvmx(vx,mv,ad−−xvx,r v,r ) , ur = uvm xv,xm v,r ,
where xv,ad, xv,r show the estimated and preserved dead zones of the spool inde- pendently, which are 13% and 1% percent of the maximum displacement of spool xv,m.
The ELS pump controller contains both feedforward and feedback loops. Firstly, acccording to Eq. (6.4), the feedforward loop evaluates the swash-plate angle approx- imately by the pump flow mapping [11]. Nonlinear leakage flow in terms of pump displacement, pressure and velocity is captured by calibration of the pump flow mapping. Meanwhile, to maintain an appropriate preset pressure margin between the supply pressure and the highest load, a closed-loop control loop containing a PI regulator is introduced to compensate for the flow deviation on the feedforward loop.
up(t)=
[(
Kp pse+Ki
∫tn t0
psedt )
+(∑qi,ref+ps·Cp)
] Vpnm
(6.4)
pse =ps − pa − pm (6.5)