A Multi-mode Electronic Load Sensing Control Scheme with Power Limitation and Pressure Cut-off for Mobile Machinery

In the Flow Control (FC) mode, the purpose is to fulfill the flow requirements of hydraulic actuators. The flow feedforward control concept is introduced by directly calculating the flow rates across the valve based on the input signals. In contrast to existing HMLS systems, it has been proven that the flow feedforward method has the advantages of high energy efficiency and fast response [26, 27]. Neglecting the pump leakage, the control signal can be written aswhere \(C_{{\text{d}}}\) is the discharge coefficient, \(u_{{{\text{v}}i}}\) is the valve signal, \(\Delta p_{{\text{n}}}\) is the nominal pressure drop, \(\rho\) is the oil density, \(n_{{\text{p}}}\) is the pump rotational speed, and \(k_{{{\text{pp}}}}\) is the displacement gain. Note that there exists a signal difference when switching from another mode to the FC mode, so a first-order inertial part is added to avoid signal jump, which is expressed aswhere \(\tau_{{\text{p}}}\) is the time constant, \(s\) is the Laplace operator.

Although the flow controller has the aforementioned advantage, there is a remarkable disadvantage of pressure impact and energy consumption under flow excess [25]. Thus, a load sensing mode is designed to solve this issue. Like the HMLS system, the LS controller aims to maintain the pressure margin as a preset value. To avoid signal jump when switching from other modes, an incremental Proportional-Integral-Derivative (PID) controller is thereby designed to control the pressure margin, which can be expressed aswhere \(t_{{\text{q}}}\) is the initial moment of switching to LS mode, \(u_{{{\text{pl}}}} \left( {t_{{\text{q}}} } \right)\) is the output of the MELS controller when switching into the LS mode, \(k_{{{\text{lp}}}}\), \(k_{{{\text{li}}}}\), and \(k_{{{\text{ld}}}}\) are the PID parameters in the LS mode. \(e_{{{\text{pr}}}}\) is the pressure margin error, which can be expressed aswhere \(p_{{{\text{dm}}}}\) is the preset pressure margin, \(p_{{{\text{pm}}}}\) is the actual pressure margin, \(p_{{\text{p}}}\) is the system pressure. \(p_{{{\text{lm}}}}\) is the highest load pressure, which can be expressed aswhere \(p_{{{\text{l}}i}}\) is the load pressure.

The purpose of the power controller is to limit the system output power to avoid engine stall. Under a limited value \(P_{{\text{n}}}\), the derived pump flow rate can be expressed as \(q_{{\text{p}}} = {{P_{{\text{n}}} } \mathord{\left/ {\vphantom {{P_{{\text{n}}} } {p_{{\text{p}}} }}} \right. \kern-0pt} {p_{{\text{p}}} }}\) [4]. The power controller is designed aswhere \(u_{{{\text{vlc}}}}\) is the compensator based on dynamic pressure feedback to achieve active damping control [28], \(\hat{G}_{{\text{p}}}\) is the identified pump model. The Laplace form of \(u_{{{\text{vlc}}}}\) is given bywhere \(k_{{{\text{cp}}}}\) and \(\omega_{{{\text{cp}}}}\) are the control gain and the cut-off frequency of the compensator, respectively. The pump dynamic is modeled as a first-order term [4], which is given bywhere \(\tau_{{\text{c}}}\) is the time constant, \(V_{{\text{p}}}\) is the pump displacement.

When the resistive load of the system is too large, the pressure controller is triggered to limit the system pressure and prevent affecting the hydraulic system adversely. Therefore, the pressure controller aims to maintain the outlet pressure of the pump at a certain value. Referring to the pressure cut-off circuit in current machinery, an electronic pressure controller is designed using incremental PID control to avoid signal jump when switching into the PC mode. The PC mode can be activated when the cylinder reaches the end stop, also it can work under the condition that the external load is too high. Moreover, to avoid faulty activation caused by pressure impact in the FC or LS mode, incremental control is defined to be active when the supplied flow is not excessive (\(p_{{{\text{lm}}}} \left( t \right) \le p_{{{\text{dm}}}}\)). Thus, the incremental PID controller is designed bywhere \(k_{{{\text{rp}}}}\), \(k_{{{\text{ri}}}}\), and \(k_{{{\text{rd}}}}\) are the PID parameters in the PC mode, and the function \(\phi \left( t \right)\) is defined by

The pressure error is defined aswhere \(p_{{{\text{dc}}}}\) is the desired pressure, it is also the upper bound in PC mode (in Section 3.5 below). The initial value of the pressure controller is defined as the output of the MELS controller when switching into the PC mode. Since the pressure controller does not require high dynamic in actual applications, a smaller control gain can be selected to reduce pressure overshoot and oscillation. To avoid that the power exceeds the limited value in the PC mode, an upper bound \(u_{{{\text{pr}}}} = {{P_{{\text{p}}} } \mathord{\left/ {\vphantom {{P_{{\text{p}}} } {n_{{\text{p}}} k_{{{\text{pp}}}} p_{{{\text{dc}}}} }}} \right. \kern-0pt} {n_{{\text{p}}} k_{{{\text{pp}}}} p_{{{\text{dc}}}} }}\) is set for the pressure controller.

The control structure with four modes is simple and can be easily implemented in current control hardware. In addition, another concern is the switching rule to ensure the overall system stability. Based on Refs. [4, 25], a multi-mode switching rule is designed to avoid potential stability caused by continuous switching between different modes, as shown in Figure 2.

To simplify the switching rules and ensure the system stability, the bilateral switching rules are defined as “FC ⟷ PC”, “FC ⟷ LS” and “FC ⟷ PL”, considering the open-loop structure of flow control, in which the symbol “⟷” means the switching is bilateral. Moreover, some unilateral switching rules are defined. For instance, the switching between LS and PC is unilateral, and switching from LS to PC is not allowed. For this reason, the LS controller has a small stability margin, so potential instability due to continuous switching in local conditions is avoided. A similar unilateral switching rule is established between LS and PC. Since an upper bound has been configured in the PC mode, so a unilateral switching rule is also designed between PL and PC. The switching rules are summarized in Table 1, in which the modes in the first row mean those before switching, and the modes in the first column mean those after switching.

To ensure stability when switching between PC and FC, a hysteresis switching rule with dwell-time is designed. As given in Figure 3, the rule is defined aswhere \(p_{{{\text{db}}}}\) and \(p_{{{\text{dc}}}}\) are the lower bound and the upper bound for pressure control, respectively (\(p_{{{\text{db}}}} < p_{{{\text{dc}}}}\)). \(t_{0}\) is the initial moment of mode switching. The dwell time is chosen at \(\Delta T{ = }{{0.5} \mathord{\left/ {\vphantom {{0.5} {f_{\min } }}} \right. \kern-0pt} {f_{\min } }}\), where \(f_{\min }\) is the lowest natural frequency of the overall system, which is measured when the load of excavator bucket is heaviest, and its calculation method can be referred to the Ref. [29].

The switching rule No. 7 is defined as \(p_{{\text{p}}} \left( t \right) < p_{{{\text{dc}}}}\) and \(u_{{{\text{pl}}}} \left( t \right) \ge u_{{{\text{pp}}}} \left( t \right)\). The unidirectional switching rules No. 8 and No. 9 are defined as \(p_{{\text{p}}} \left( t \right) \ge p_{{{\text{dc}}}}\). From the switching rules, it is predicted that there are some load conditions under which several rules are satisfied simultaneously. To determine the control mode in this case, the control priority is defined in Table 2. From Table 2, it is seen that the PC mode has the highest priority compared with other modes. That is, once the system pressure \(p_{{\text{p}}}\) is equal to or larger than \(p_{{{\text{dc}}}}\), the controller will switch into the PC mode. Moreover, the PL mode has the second priority: when the control signal in the LS or FC mode is greater than the power limitation value, it switches into the PL mode so that the system power is controlled within the setting range.

One concern is whether stability can be guaranteed when switching dynamically between different modes. Rules 1 and 2 between LS and FC are designed in the previous work based on multiple Lyapunov functions [24]. Rules 3 and 4 are to select the smaller value in the LS and FC modes, and the stability can be also ensured based on the analysis result using the describing function tool [4]. Thus, after designing the stable hysteresis switching rule between FC and PC, the remaining work is to analyze the stability under pressure control, which is carried out based on the linearization mathematical model in the Laplace form as below. The pump flow is expressed bywhere \(k_{{{\text{lp}}}}\) is the pump leakage coefficient. Based on the flow continuity equation, the expressions are obtained aswhere \(\beta_{{\text{e}}}\) is the effective bulk modulus, \(V_{{{\text{p}}i}}\) is the chamber volume between the pump and valve, \(V_{1}\) is the volume between the valve and cylinder, \(q_{1}\) is the flow rate out of the control valve, \(p_{1}\) is the pressure in the cap-side chamber, \(A_{1}\) is the effective area of cap-side chamber, \(v_{1}\) is the cylinder velocity. The flow equation of the valve is expressed bywhere \(k_{{\text{q}}}\) is the flow coefficient, \(k_{{\text{v}}}\) is the gain of the valve displacement, \(k_{{{\text{pq}}}}\) is the flow-pressure coefficient. Since the external load is relatively large in the PC mode, the pressure in the rod-side chamber is neglected, so the force balance equation of the cylinder is simplified aswhere \(m_{1}\) is the load mass, \(b_{1}\) is the viscous damping, \(F_{{\text{e}}}\) is the external force. As mentioned before, the PC mode can be active in two cases: ① the cylinder reaches the end stop; ② the external load is too large but the cylinder still moves forward. Actually, Case 1 can be considered as a special condition of Case 2. For the system pressure, the stability condition in Case 1 is more rigorous, since the moving cylinder provides equivalent damping to the system from Eq. (16). To obtain a conservative stability condition, the pump leakage is neglected, and the transfer function from the valve signal to the cylinder pressure in Case 1 is drawn from Eqs. (9)–(10) and (14)–(18) aswhere

\(N_{0} = V_{1} V_{{{\text{p}}i}} \tau_{{\text{c}}}\),

\(N_{1} = V_{1} V_{{{\text{p}}i}} + k_{{{\text{pq}}}} V_{{{\text{p}}i}} \beta_{{\text{e}}} \tau_{{\text{c}}} + k_{{{\text{pq}}}} V_{1} \beta_{{\text{e}}} \tau_{{\text{c}}} + k_{{{\text{pp}}}} k_{{{\text{rd}}}} n_{{\text{p}}} V_{1} \beta_{{\text{e}}}\),

\(N_{2} = k_{{{\text{pq}}}} V_{{{\text{p}}i}} \beta_{{\text{e}}} + k_{{{\text{pq}}}} V_{1} \beta_{{\text{e}}} + k_{{{\text{pp}}}} k_{{{\text{pq}}}} k_{{{\text{rd}}}} n_{{\text{p}}} \beta_{{\text{e}}}^{2} + k_{{{\text{pp}}}} k_{{{\text{rp}}}} n_{{\text{p}}} V_{1} \beta_{{\text{e}}}\),

\(N_{3} = k_{{{\text{pp}}}} k_{{{\text{pq}}}} k_{{{\text{rp}}}} n_{{\text{p}}} \beta_{{\text{e}}}^{2} + k_{{{\text{pp}}}} k_{{{\text{ri}}}} n_{{\text{p}}} V_{1} \beta_{{\text{e}}}\),

\(N_{4} = k_{{{\text{pp}}}} k_{{{\text{pq}}}} k_{{{\text{ri}}}} n_{{\text{p}}} \beta_{{\text{e}}}^{2}\).

Since the flow-pressure coefficient \(k_{{{\text{pq}}}}\) provide a positive effect on the stability, the extreme condition \(k_{{{\text{pq}}}} = 0\) is considered, and then Eq. (19) is simplified aswhere \(N^{\prime}_{1} = V_{1} V_{{{\text{p}}i}} + k_{{{\text{pp}}}} k_{{{\text{rd}}}} n_{{\text{p}}} V_{1} \beta_{{\text{e}}}\), \(N^{\prime}_{2} = k_{{{\text{pp}}}} k_{{{\text{rp}}}} n_{{\text{p}}} V_{1} \beta_{{\text{e}}}\) and \(N^{\prime}_{3} = k_{{{\text{pp}}}} k_{{{\text{ri}}}} n_{{\text{p}}} V_{1} \beta_{{\text{e}}}\). Eq. (20) is a third-order system actually. Based on the Routh stability criterion, its stability condition can be expressed as

Then, the stability condition in the PC mode can be drawn from Eqs. (21)–(22) as

Based on Eq. (23), the PID parameters can be properly selected to ensure the system stability.

A comparative experimental study is performed on a test rig with a 2-ton hydraulic excavator to validate the MELS controller, as shown in Figure 4. The hydraulic excavator is equipped with an electronically controlled pump (SYDFEE from Bosch Rexroth, Inc.) and a multi-way control valve (PVG 32 from Danfoss, Inc.). Further information about the test rig can be found in Ref. [30]. Motion control tests were then carried out and the main parameters are listed in Tables 3 and 4.

To validate the effectiveness of the proposed MELS controller, the pure flow control method (Section 3.1) for the system is taken as a comparison.

Firstly, valve control signals are given to complete the typical reciprocating movement of the boom. The movement process of the boom cylinder is: low-speed extending, high-speed extending, holding and retracting, as shown in Figure 5. The control signals of the valve and pump are also shown in Figure 6, and the test result is shown in Figures 7 and 8. The pump displacement and actuator velocity are shown in Figure 7, and the system pressure and power consumption are shown in Figure 8.

Similarly, the typical reciprocating movement of the arm cylinder is tested. The movement process of the arm cylinder is: high-speed retracting, low-speed retracting, holding and extending, as shown in Figure 9. The control signals of the valve and pump are shown in Figure 10, and the results are shown in Figures 11 and 12.

The boom/bucket compound motion test is also carried out to validate the proposed controller. The schematic diagram of the boom/bucket compound movement is shown in Figure 13, which contains two movement phases. The control signals are given in Figure 14. The test results are shown in Figures 15 and 16. In the compound motion test, the power limitation point is set at 3.4 kW.

A comparison simulation under variable external load is also carried out to validate the proposed MELS controller, and the other controller used for comparison is the existing ELS control with pressure control. To ensure the consistency of the external load when using different controllers, a simulation model is conducted by using grey box modeling [31] in the AMESim Software, as shown in Figure 17. The actual parameters of the pump and valve in the test rig above are identified and utilized to establish the simulation model, including static/dynamic characteristics of the pump and valves (given in Ref. [25]), dimensions of the cylinder, and the mechanical arm (further information can be found in Ref. [30]). As shown in Figure 18, it can be seen that the results of valve flow mapping, pump dynamic response, and boom velocity response in the simulation are consistent with those in the actual test with satisfying accuracy.

Then, this model is used to take a comparative study under the variable external load. The boom cylinder carried out the sequential movement of extending, holding, and retracting, as shown in Figure 19. In addition, a variable external load force is applied at the endpoint of the bucket at t = 15.5–23 s when the boom cylinder is retracted, and its variation trend is also shown in Figure 19. The simulation results (the system pressure and the cylinder velocity) are shown in Figure 20, respectively.