Contents Introduction
Mining mechanization is a necessary technical method to ensure safe production, production efficiency and improvement of the operating environment in the coal industry, as well as an effective measure for saving manpower, energy and raw materials. A drum shearer is one of the main pieces of equipment for the current fully mechanized coal mining face. Its main cutting transmission mode is “three-phase asynchronous motor + three stage straight gear deceleration + planetary gear reduction + cutting drum.” In the cutting process, due to uneven coal seam strength, coal caving brittle rock, hard inclusions and rock interlayers, the load on the drum has the characteristics of randomness, large fluctuation and strong impact [1]–[3], and the shearer cutting rocker has a long transmission chain and multi-drive components, making it a weak part in the shearer. Any gear failure will cause the machine to stop working. According to statistics, planetary gear system failure accounts for 30% of all gear transmission failures [4]. At the same time, previous research on reducing the failure rate of the shearer cutting transmission system consists mainly of the evaluation of its healthy running condition, and the reasons for faults are analyzed. Zhao and Sun [5] and Zhao and Ma [6], [7] used virtual prototyping software to analyze and simulate the vibration characteristics and the reliability of the shearer cutting transmission system and improve the stability of the cutting section through optimizing the transmission system. Si et al. [8] employed the vibration of a rocker transmission part and proposed a diagnosis method based on a probabilistic neural network (PNN) and fruit fly optimization algorithm (FOA). Li et al. [9] presented a multi-degree of freedom gear model to describe the dynamic behavior of the coal cutter gear systems. The model can be used as a feasible and reliable tool for gear fault mechanism investigation. However, these methods do not substantially reduce the failure probability of the shearer cutting transmission system, and in the event of failure, maintenance is difficult and the production schedule is affected, which can cause significant economic losses. Therefore, Yang et al. [10] proposed a high-reliability short-range cutting transmission system, which can not only effectively shorten the transmission chain and reduce the failure rate but also achieve buffer damping under load mutation and drum speed control under coal seam changes. The inevitable leakage of the hydraulic system and the pipeline elastic deformation will lead to pressure loss and affect the stability of the end drum speed. Therefore, in order to meet the high power, high efficiency, low failure and other performance requirements of the drum shearer, further exploration needs to be done, including driving components, transmission structure, control strategy and other elements. A semi-direct drive system program with a high-power permanent magnet motor [11] can be proposed for reducing the transmission ratio of the shearer cutting transmission system under the existing shearer cutting transmission system installation conditions. The program reduces the transmission parts between the drive motor and the work unit, especially the uselessness of wearing parts such as planetary gears, which can significantly improve system efficiency and reduce failure rates.
Vector control and direct torque control, as well as the variable frequency speed control strategy, are commonly used for mine PMSM. It is necessary to know the position information of the PMSM rotor to achieve closed-loop control. Mechanical sensors such as Hall position sensors and rotary encoders are used in the traditional method. However, the introduction of mechanical sensors not only increases the rotational inertia of the motor shaft and reduces the mechanical properties but also increases the size and volume of PMSM and increases the external hardware line connection, making the system susceptible to interference and instability. Therefore, the sensorless control technology of the IPMSM is particularly important for shearer cutting transmission systems. At the beginning, the IPMSM sensorless control strategy mainly consists of the open-loop estimation method based on the motor mathematical model, such as the mathematical model based on the direct calculation method [12], [13] and the open-loop flux linkage method based on the voltage equation [14]. These methods have the characteristics of simple principles and faster dynamic response, but they are easily affected by changes in the motor parameters. At present, the sensorless control methods such as the model reference adaptive system (MRAS), the extended Kalman filter (EKF) method and the observer estimation method have attracted much attention due to the superiority of the algorithm. The MRAS takes the mathematical model of the actual observation object as the reference model to establish the same adjustable model [15]. The method also gradually reduces the estimation error through the feedback link. However, it is assumed that the adjustable model and reference model have the same parameters, so it is necessary to combine the motor parameter on-line identification method to further improve its estimation accuracy. The EKF [16], [17] has high observation accuracy and strong robustness. However, the calculation process of this method is too complicated. Especially in the observation of high-speed PMSM, it is very difficult for the algorithm to complete the operation. Compared with the above methods, the SMO, an observer estimation method, is widely used in sensorless control strategy. Based on the theoretical basis of the sliding mode variable structure control, a special sliding mode control method is used to adjust the structure by altering the switching function so that the estimated value quickly approaches the real value [18]–[21]. The SMO has the characteristics of nonlinearity, high observation accuracy and strong robustness. However, the algorithm also has the disadvantage of the sliding mode variable structure being characterized by discontinuous Bang-Bang control, which can produce high-frequency chattering. In response to this problem, Chi [22] proposed a new SMO control strategy in which the saturation function is used. However, the introduction of a low-pass filter and additional position compensation of the rotor usually causes phase delay, and the control requirements of high performance applications cannot be met. Kim et al. [19] proposed a new SMO control strategy to reduce the estimated speed chattering of the motor, in which the switching function is replaced by a sigmoid function. Feng et al. [24] presented a four-level iterative SMO control strategy. A smaller value can be chosen as the sliding mode gain in the motor high-speed range, which can reduce the back-electromotive force (EMF) estimated error. The sliding mode gain is determined step by step on the basis of the selected test data to meet the Lyapunov stability condition. Feng proposed a high-order terminal non-singular SMO control strategy [25] in which the discrete output value of the traditional sliding mode switching function is integrated as the continuous sliding mode control input. It can not only reduce chattering but also eliminate the traditional SMO filter link. Although the low pass filter and phase compensation part are not used, the arc-tangent method is introduced to extract the rotor position according to the estimated orthogonal EMF components in these papers. However, in the process of calculating the rotor position using the arc-tangent method, the existence of noise and harmonics may influence the accuracy of the position estimation. Especially when the EMF crosses zero, obvious estimation error may occur due to the noise signals. In [26], a full-order SMO based on the effective back-EMF is proposed to estimate the rotor position and rotational speed of the PMSM. The observer can filter out the estimated high-frequency slip noise, which is contained in the effective back-EMF. However, the magnitude of the extended EMF is a function of rotor speed and stator current and a derivative of stator current, which means that the load condition will affect the magnitude of the extended EMF. In the shearer working process, the end drum load will cause significant distortions of the waveforms of the extended EMF components of a state transient.
In view of the above problems, this paper presents a shearer PMSRCTS, which consists of a low-speed large torque permanent magnet synchronous motor, three-stage reducer and cutting drum. Because the motor output speed is low and the planetary gear reducer is eliminated, the system can effectively reduce the failure rate. A sensorless control strategy is designed for the system based on a new SMO. The phase-locked loop technique is used instead of the traditional arc-tangent function estimation, and the sigmoid function is introduced to replace the traditional sign function in the new SMO. The stable sliding mode gain is obtained by the Lyapunov stability condition and adjusted through the fuzzy adaptive control algorithm. To verify the validity and accuracy of the scheme, the mathematic model of the IPMSM and end cutting load changing are established. The results show that the proposed new SMO has good dynamic response, high observation accuracy and robustness. Sensorless control for the shearer PMSRCTS has a better control effect.
The Composition of the PMSRCTS and the Design of the Sensorless Control Strategy
Shearer PMSRCTS is shown in Fig. 1. The mine explosion-proof, low-speed, high-torque PMSM is used as a driving source. It can generate large torque at low speeds. The motor output shaft is a hollow shaft with an internal spline, which connects to the gear shaft through an elongated, flexible torque shaft. The PMSM output torque is passed to the end-cutting drum after a three-stage reducer, which can perform cutting work.
The sensorless control strategy for the shearer PMSRCTS is realized through DTC theory based on the new SMO. First, the shearer is started. Second, the traction system is started after the cutting drum speed reaches the command value. The drum is slowly cut into the coal seam. It is known that the coal block rate is related to the cutting thickness and that the cutting thickness is related to the cutting drum and the traction speed. Therefore, the drum speed command value can be calculated according to the required coal block rate and the feedback traction speed. The current value of the cutting motor or traction motor can be used as the feedback value for the traction speed adjustment, and the current can be obtained by the new SMO. Finally, the rotational speed and position information of the IPMSM rotor can be further obtained by observing the current value to realize sensorless control. However, the traction speed, the cutting drum speed and the coal-rock impedance are closely related to the load of the cutting drum, and the observation effect of SMO is directly affected by the load characteristics. Therefore, the influence of the load characteristics must be considered.
Design and Optimization of New SMO for IPMSM
The voltage mathematical model of the IPMSM in the synchronous rotating frame (d-q) is shown as follows:
\begin{align} \left ({ {\begin{array}{l} u_{d} \\[3pt] u_{q} \\[3pt] \end{array}} }\right )=\left ({ {{\begin{array}{*{20}c} {R+pL_{d} } & \quad {-\omega _{e} L_{q} } \\[3pt] {\omega _{e} L_{d} } &\quad {R+pL_{q} } \\[3pt] \end{array} }} }\right )\left ({ {\begin{array}{l} i_{d} \\[3pt] i_{q} \\[3pt] \end{array}} }\right )+\left ({ {\begin{array}{l} 0 \\[3pt] \omega _{e} \psi _{f} \\[3pt] \end{array}} }\right ) \end{align}
where
According to the voltage mathematical model for the IPMSM in the synchronous rotation coordinate system, the dynamic system equation of the stator current is rewritten as follows, \begin{align} \left ({ {{\begin{array}{*{20}c} {{\mathop {i}\limits ^{\bullet }}_{d} } \\[0.3pc] {{\mathop {i}\limits ^{\bullet }}_{q} } \\ \end{array} }} }\right )=&\left ({ {{\begin{array}{*{20}c} {-\dfrac {R}{L_{d} }} &\quad {\dfrac {\omega _{e} L_{q} }{L_{d} }} \\[0.6pc] {-\dfrac {\omega _{e} L_{d} }{L_{q} }} &\quad {\dfrac {-R}{L_{q} }} \\ \end{array} }} }\right )\left ({ {{\begin{array}{*{20}c} {i_{d} } \\ {i_{q} } \\ \end{array} }} }\right )\notag \\&\qquad \qquad \qquad +\left ({ {{\begin{array}{*{20}c} {\dfrac {1}{L_{d} }} &\quad 0 \\ 0 &\quad {\dfrac {1}{L_{q} }} \\ \end{array} }} }\right )\!\left ({ {{\begin{array}{*{20}c} {u_{d} -E_{d} } \\ {u_{q} -E_{q} } \\ \end{array} }} }\right )\qquad \end{align}
where
A. The Design of SMO and Stability Analysis
To obtain the value of the induced EMF in (2), SMO can be designed as [27]\begin{align} \left ({ {{\begin{array}{*{20}c} {\dot {{\hat {i}}}_{d} } \\ {\dot {{\hat {i}}}_{q} } \\ \end{array} }} }\right )=&\left ({ {{\begin{array}{*{20}c} {-\dfrac {R}{L_{d} }} &\quad {\dfrac {\omega _{e} L_{q} }{L_{d} }} \\[0.6pc] {-\dfrac {\omega _{e} L_{d} }{L_{q} }} &\quad {\dfrac {-R}{L_{q} }} \\ \end{array} }} }\right )\left ({ {{\begin{array}{*{20}c} {\hat {i}_{d} } \\ {\hat {i}_{q} } \\ \end{array} }} }\right )\notag \\&\qquad \qquad \qquad +\left ({ {{\begin{array}{*{20}c} {\dfrac {u_{d} -ksgn\left ({ {\hat {i}_{d} -i_{d} } }\right )}{L_{d} }} \\ {\dfrac {u_{q} -ksgn\left ({ {\hat {i}_{q} -i_{q} } }\right )}{L_{q} }} \\ \end{array} }} }\right )\qquad \quad \end{align}
where
The state equation of the current error system can be obtained through the (2) and (3) subtraction as follows:\begin{align} \left ({ {{\begin{array}{*{20}c} {\dot {{\tilde {i}}}_{d} } \\ {\dot {{\tilde {i}}}_{q} } \\ \end{array} }} }\right )=&\left ({ {{\begin{array}{*{20}c} {-\dfrac {R}{L_{d} }} &\quad {\dfrac {\omega _{e} L_{q} }{L_{d} }} \\[0.6pc] {-\dfrac {\omega _{e} L_{d} }{L_{q} }} & \quad {\dfrac {-R}{L_{q} }} \\ \end{array} }} }\right )\left ({ {{\begin{array}{*{20}c} {\tilde {i}_{d} } \\ {\tilde {i}_{q} } \\ \end{array} }} }\right )\notag \\&\qquad \qquad \qquad +\left ({ {{\begin{array}{*{20}c} {\dfrac {E_{d} -ksgn\left ({ {\hat {i}_{d} -i_{d} } }\right )}{L_{d} }} \\ {\dfrac {E_{q} -ksgn\left ({ {\hat {i}_{q} -i_{q} } }\right )}{L_{q} }} \\ \end{array} }} }\right )\qquad \quad \!\! \end{align}
where
The current error observation (4) can be rewritten in vector form as follows, \begin{equation} \dot {\tilde {\boldsymbol {i}}}=\boldsymbol {A}\tilde {{\boldsymbol {i}}}+\boldsymbol {BE}+ksgn\left ({ \tilde {\boldsymbol {i}} }\right ) \end{equation}
where \begin{equation*} \boldsymbol {A}=\left ({ {{\begin{array}{*{20}c} {-\dfrac {R}{L_{d} }} &\quad {\dfrac {L_{q} }{L_{d} }\omega _{e} } \\ {-\dfrac {L_{d} }{L_{q} }\omega _{e} } &\quad {-\dfrac {R}{L_{q} }} \\ \end{array} }} }\right )\!,\quad \boldsymbol {B}=\left ({ {{\begin{array}{*{20}c} {\dfrac {1}{L_{d} }} &\quad 0 \\ 0 & \quad {\dfrac {1}{L_{q} }} \\ \end{array} }} }\right )\!. \end{equation*}
The SMO is used to estimate the current, and its sliding mode plane is defined as, \begin{equation} \boldsymbol {S}=\left [{ {{\begin{array}{*{20}c} {\tilde {i}_{d} } &\quad {\tilde {i}_{q} } \\ \end{array} }} }\right ]^{T}=\mathbf {0} \end{equation}
According to the Lyapunov theorem, when the condition \begin{equation} \boldsymbol {E}_{\boldsymbol {eq}} =\left[{{\begin{array}{*{20}c} {ksgn\left ({ {\hat {i}_{d} -i_{d} } }\right )} &\quad {ksgn\left ({ {\hat {i}_{q} -i_{q} } }\right )} \\ \end{array} }}\right]^{T} \end{equation}
According to (7), the equivalent control amount can be defined as, \begin{equation} \boldsymbol {E}_{\boldsymbol {eq}} =\left ({ {{\begin{array}{*{20}c} {V_{d} } \\ {V_{q} } \\ \end{array} }} }\right )=\left ({ {{\begin{array}{*{20}c} {\left [{ {ksgn\left ({ {\hat {i}_{d} -i_{d} } }\right )} }\right ]_{eq} } \\ {\left [{ {ksgn\left ({ {\hat {i}_{q} -i_{q} } }\right )} }\right ]_{eq} } \\ \end{array} }} }\right )=\left ({ {{\begin{array}{*{20}c} 0 \\ {\omega _{e} \psi _{f} } \\ \end{array} }} }\right ) \end{equation}
The expression of the sliding mode gain \begin{equation} k\ge max\left ({ {\begin{array}{l} \dfrac {E_{d} }{L_{d} }sgn\left ({ {\tilde {i}_{d} } }\right )-\left ({ {\dfrac {R}{L_{d} }+\frac {L_{d} }{L_{q} }\omega _{e} } }\right )\left |{ {\tilde {i}_{d} } }\right |, \\ \dfrac {E_{q} }{L_{q} }sgn\left ({ {\tilde {i}_{q} } }\right )-\left ({ {\dfrac {R}{L_{q} }-\frac {L_{q} }{L_{d} }\omega _{e} } }\right )\left |{ {\tilde {i}_{q} } }\right | \\ \end{array}} }\right ) \end{equation}
B. Rotor Position Estimation Based on PLL
The purpose of SMO is to determine the estimated value of the d-q axis-induced EMF. It can be seen from (2) that the induced EMF of the q axis contains rotor speed information, \begin{equation} \hat {\omega }_{e} =\frac {V_{q} }{\psi _{f} } \end{equation}
Although (10) can be used to obtain the position of the rotor angle, the motor in the process of cutting coal and rock, the permanent magnet flux chain is not a constant value due to the harsh working environment, the temperature and load change. There is some rotor position and speed error between the estimated and the actual value, which can affect the dynamic performance of the entire system.
For better dynamic performance, the PLL technology is used. It is an adaptive closed-loop system with excellent real-time tracking and estimation of the actual rotor position information; even in the voltage phase, angle imbalance, harmonics and other conditions also have better tracking performance. Since the winding of the motor is symmetrical, it is assumed that the motor terminal voltage of the three-phase stator winding [28] is as follows, \begin{equation} \begin{cases} {u}_{a} ={u}\cos \omega _{e} {t} \\ {u}_{b} ={u}\cos \left ({ {\omega _{e} {t}-2\pi /3} }\right ) \\ {u}_{c} =u\cos \left ({ {\omega _{e} {t}+2\pi /3} }\right ) \\ \end{cases} \end{equation}
where
According to the transformation theory of synchronous rotation coordinates, the transformation matrix of the three-phase voltage transform to the d-q coordinate system [28] is \begin{align} T\left ({ {\hat {\theta }_{e} } }\right )=\frac {2}{3}\left ({\!\! {{\begin{array}{*{20}c} {cos\hat {\theta }_{e} } &~{cos\left ({ {\hat {\theta }_{e} -\displaystyle \frac {2}{3}\pi } }\right )} &~{cos\left ({ {\hat {\theta }_{e} +\displaystyle \frac {2}{3}\pi } }\right )} \\ {-sin\hat {\theta }_{e} } &~{-sin\left ({ {\hat {\theta }_{e} -\displaystyle \frac {2}{3}\pi } }\right )} &~{-sin\left ({ {\hat {\theta }_{e} +\displaystyle \frac {2}{3}\pi } }\right )} \\ \end{array} }} \!\!}\right )\!\!\!\!\!\notag \\ {}\end{align}
where
When the neutral point isolation is considered, generally, it does not contain zero sequence components. Substituting the transformation matrix \begin{equation} \left ({ {{\begin{array}{*{20}c} {V_{d} } \\ {V_{q} } \\ \end{array} }} }\right )=\left ({ {{\begin{array}{*{20}c} {usin\left ({ {\hat {\theta }_{e} -\theta _{e} } }\right )} \\ {ucos\left ({ {\hat {\theta }_{e} -\theta _{e} } }\right )} \\ \end{array} }} }\right ) \end{equation}
When the estimated value tracks the actual position of the rotor, the error is zero. According to the definition of the synchronous rotation d-q coordinate system, it can be defined as
Therefore, a closed-loop PI regulator can be established according to (13). The rotor position information can be obtained. The specific block diagram is shown in Fig. 2.
According to (16), a closed-loop control block diagram can be obtained based on the PI regulator, as shown in Fig. 3.
The closed-loop transfer function of the system can be obtained from Fig. 3\begin{equation} G\left ({ s }\right )=\frac {\hat {\theta }_{e} \left ({ s }\right )}{\theta _{e} \left ({ s }\right )}=\frac {V_{q} P\left ({ s }\right )}{s+V_{q} P\left ({ s }\right )} \end{equation}
In addition, the form of the PI regulator’s transfer function is as follows, \begin{equation} P\left ({ {s} }\right )=\gamma _{p} +\frac {\gamma _{i} }{s} \end{equation}
Upon substituting (15) into (14), the closed-loop transfer function becomes \begin{equation} G\left ({ s }\right )=\frac {V_{q} \left ({ {\gamma _{p} +\frac {\gamma _{i} }{s}} }\right )}{s+V_{q} \left ({ {\gamma _{p} +\frac {\gamma _{i} }{s}} }\right )}=\frac {\sqrt {2} \omega _{n} s+\omega _{n}^{2} }{s^{2}+\sqrt {2} \omega _{n} s+\omega _{n}^{2} } \end{equation}
According to the desired bandwidth of the closed-loop system, the PI regulator’s parameters can be obtained \begin{equation} \gamma _{p} =\frac {\sqrt {2} \omega _{n} }{V_{q} },\quad \gamma _{i} =\frac {\omega _{n}^{2} }{V_{q} } \end{equation}
C. Optimization of Fuzzy Sliding Mode Observer Based on New Switching Function
Because the ideal switching function is used in the above SMO, the discontinuous open-loop characteristic can result in a large chattering for the observer’s value during the switching process. At the same time, in order to increase the anti-interference ability of the observer and ensure the generation of sliding mode, the sliding mode switching gain is usually chosen to be too large, but this will further increase the chattering noise in the state estimate. Therefore, it is possible to reduce the chattering noise in the system by improving the ideal switching function and introducing the intelligent control method to effectively estimate the switching gain according to the sliding mode arrival condition.
First, the ideal switching function is improved in the designed SMO. Then, the fuzzy rule is designed according to the fuzzy control theory for optimizing the switching gain. Finally, the switchover gain is effectively estimated according to the sliding mode arrival condition. The new sigmoid function is as follows, \begin{equation} sigmoid\left ({ s }\right )=\frac {\mathit {2}}{\mathit {1}+e^{-as}}-\mathit {1} \end{equation}
where \begin{align} \left ({ {{\begin{array}{*{20}c} {\dot {{\hat {i}}}_{d} } \\ {\dot {{\hat {i}}}_{q} } \\ \end{array} }} }\right )=&\left ({ {{\begin{array}{*{20}c} {-\dfrac {R}{L_{d} }} &\quad {\dfrac {\omega _{e} L_{q} }{L_{d} }} \\[0.6pc] {-\dfrac {\omega _{e} L_{d} }{L_{q} }} &\quad {\dfrac {-R}{L_{q} }} \\ \end{array} }} }\right )\left ({ {{\begin{array}{*{20}c} {\hat {i}_{d} } \\ {\hat {i}_{q} } \\ \end{array} }} }\right )\notag \\&\qquad \qquad +\left ({ {{\begin{array}{*{20}c} {\dfrac {u_{d} -ksigmoid\left ({ {\hat {i}_{d} -i_{d} } }\right )}{L_{d} }} \\ {\dfrac {u_{q} -ksigmoid\left ({ {\hat {i}_{q} -i_{q} } }\right )}{L_{q} }} \\ \end{array} }} }\right )\qquad \quad \end{align}
When the system is in sliding mode motion, if the absolute value of the error
Through the above analysis, the input field of the fuzzy controller is defined as seven fuzzy subsets. Four fuzzy subsets are defined on the output domain. The trigonometric function is used to design the membership function of the input and output, and the degrees of membership for the input and output are shown as Figs. 4 and 5.
Based on the Mamdani type fuzzy logic reasoning, the rules are as follows,
Rule 1:
If the input error
S Rule 2:
If the input error
S Rule 3:
If the input error
S Rule 4:
If the input error
S Rule 5:
If the input error
S Rule 6:
If the input error
S Rule 7:
If the input error
S
Finally, the fuzzy outputs need to be converted to precise variables through centroid defuzzification method. The switching gain can be adjusted through the output proportional factor of the sliding mode switch. The chattering reduced structure of the observer is shown as Fig. 6,
The Mathematical Model of Shearer Cutting Drum Load
The change of the shearer cutting load characteristics has a great influence on the sensorless control strategy of the IPMSM. The change in load directly affects the observation effect of the new SMO, so it is necessary to establish the mathematical model of the shearer cutting load. In the continuous cutting process, the spiral drum not only rotates around the drum axis but also continues at a certain traction speed. During the rotation of the drum for one circle, each pick is only half the time in the cutting coal and rock. The shearer cutting process is shown in Fig. 7.
The cutting thickness is related to the traction speed, the cutting drum speed and the pick configuration. The maximum cutting thickness [29] is, \begin{equation} h_{max} =\frac {100V_{q} }{mn} \end{equation}
The average cutting thickness is, \begin{equation} \bar {h}=\frac {2}{\pi }h_{max} \end{equation}
where
To study the cutting transmission system and traction system of the shearer, the cutting resistance and traction resistance model of the cutting drum are established. The drum load is closely related to the coal and rock parameters, props shape, pick arrangement, and machine movement. Generally, the drum load is calculated by the former Soviet Union method [29], [30]. The average cutting force \begin{equation} Z_{d} =Z_{0} +{f}'\left ({ {Y_{d} -Y_{0} } }\right ) \end{equation}
where
The average cutting force on a single sharp pick is, \begin{equation} Z_{0} =\frac {10A_{P} \left ({ {0.35b_{p} +0.3} }\right )\bar {h}l_{i} K_{Z} K_{Y} K_{\varphi } K_{C} K_{ot} }{\left ({ {b_{p} +K_{\psi } \bar {h}^{0.5}} }\right )cos\beta } \end{equation}
where \begin{align} M_{Z} =0.5D\sum \!{\left ({\! {\begin{array}{l} \dfrac {10A_{P} \left ({ {0.35b_{p} +0.3} }\right )\bar {h}l_{i} K_{Z} K_{Y} K_{\varphi } K_{C} K_{ot} }{\left ({ {b_{p} +K_{\psi } \bar {h}^{0.5}} }\right )cos\beta } \\ \quad +100{f}'\delta _{cm} S_{a} K_{\delta } \\ \end{array}}\! }\right )}\!\!\!\!\notag \\ {}\end{align}
where
It can be seen from the (22) that the mathematical model of the cutting drum load is a binary function whose independent variable is the shearer drum speed and the traction speed. The relationship is shown in Fig. 8.
The relationship among cutting load torque, traction speed and drum cutting speed.
Numerical Simulations and Analysis
To verify the observed effect, the robustness of the new SMO and the validity of the sensorless control strategy, the discrete model is used to build the simulation model, which must be discretized for the continuous time system. The inverse differential transformation method is used to discretize the current observation equation.\begin{align} \begin{cases} {\hat {i}_{d} ( {k+1} )=A_{d} \hat {i}_{d} ( k )+B_{d} \left [{ {u_{d} ( k )-V_{d} ( k )+\omega _{e} L_{q} \hat {i}_{q} ( k )} }\right ]} \\[0.4pc] {\hat {i}_{q} ( {k+1} )=A_{q} \hat {i}_{q} ( k )+B_{q} \left [{ {u_{q} ( k )-V_{q} ( k )+\omega _{e} L_{d} \hat {i}_{d} ( k )} }\right ]} \\ \end{cases}\!\!\!\!\!\!\notag \\ {}\end{align}
The system shown in Fig. 9 has been implemented in the Matlab/Simulink programming environment, and the IPMSM parameters are listed in Table 1. As seen from the fourth part, the shearer cutting load is directly related to the drum speed and traction speed. To study the control effect of the sensorless control strategy, the traction speed is set to the rated value,
In the control of speed and current references, PI control is used to effectively reduce the accumulative errors and using the estimated position and speed of the rotor, the closed sensorless control of the motor is implemented. The PI parameters of the speed loop are the proportional gain
Fig. 10 shows the speed and position of the IPMSM rotor using a sign function. Fig. 11 shows the speed and position of the IPMSM rotor using a sigmoid function and fuzzy logic. In the simulation, the reference speed is changed from 0 to 350 r/min. It can be seen from Figs. 10 and 11 that the IPMSM rotor speed and position can be estimated from the proposed SMO and chattering phenomenon is reduced when the sign function is replaced by a sigmoid function with the fuzzy logic introduction. The robustness of the new SMO is studied by changing the internal parameters of the motor. Fig. 12 shows the estimated speed results when the IPMSM parameters used in the SMO have been changed. Fig. 12 (a) displays the result when the stator resistance
Simulation results obtained by the proposed SMO using sign function: (a) The speed of the IPMSM rotor. (b) Estimated motor speed error. (c) The position of the IPMSM rotor. (d) Estimated motor position error.
Simulation results obtained by the proposed SMO using sigmoid function and fuzzy logic: (a) The speed of the IPMSM rotor. (b) Estimated motor speed error. (c) The position of the IPMSM rotor. (d) Estimated motor position error.
Estimated speed curves obtained by the proposed SMO using sigmoid function and fuzzy logic when motor parameters changed: (a) Only stator resistance
Fig. 13 (a) gives the result when the reference speed changed from 100 r/min to 350 r/min at 0.5 s. Fig. 13 (b) shows the end load torque and IPMSM output torque when reference speed changed from 100 r/min to 350 r/min at 0.5 s. Fig. 13 (c) displays the result when the end load torque increased 10000 N suddenly at 0.5 s. Fig. 13 (d) shows the end load torque and IPMSM output torque when Fig. 13 (c) displays the result when the end load torque increased 10000 N suddenly at 0.5 s. It can be seen from Fig. 13 that when the motor speed and end load change, the estimated speed can converge to the actual value quickly, which verifies the dynamic response capability of the proposed approach.
The speed and torque: (a) The speed of the IPMSM when the reference speed changed. (b) The output torque of the IPMSM and the end load torque when the reference speed changed. (c) The speed of the IPMSM when the end load torque changed. (d) The output torque of the IPMSM and the end load torque when the end load torque changed.
Conclusions
This paper presents a PMSRCTS with low-speed and high-torque IPMSM as the driving source and sensorless control strategy for the PMSRCTS based on a new SMO. Because the motor output speed is low and the planetary gear reducer is eliminated, the system can effectively reduce the failure rate. In the new SMO, the phase locked loop technique is used instead of the traditional arc-tangent function estimation, and the sigmoid function is introduced to replace the traditional sign function. The stable sliding mode gain is obtained by the Lyapunov stability condition and adjusted through the fuzzy adaptive control algorithm. The dynamic response capability of the SMO is tested through speed changing and end load mutation. The robustness of the SMO is discovered by changing the internal parameters of the IPMSM. The results show that the proposed new SMO has good dynamic response capability, high observation accuracy and robustness.