A design scheme that integrates fault reconfiguration and fault-tolerant position control is proposed for a nonlinear servo system with friction. Analysis of the non-linear friction torque and fault in the system is used to guide design of a sliding mode position controller. A sliding mode observer is designed to achieve fault reconfiguration based on the equivalence principle. Thus, active fault-tolerant position control of the system can be realized. A real-time simulation experiment is performed on a hardware-in-loop simulation platform. The results show that the system reconfigures well for both incipient and abrupt faults. Under the fault-tolerant control mechanism, the output signal for the system position can rapidly track given values without being influenced by faults.
Modern wars require rapid troop mobility over a large combat field. This means that ground operation platforms have to accurately determine the current position and must also possess ground navigation ability [
In the servo control unit, both the azimuth and pitch motors are DC servo motors. The inverting problem is complicated from a theoretical viewpoint and is constrained by operating conditions in actual applications. Multiple faults such as electrical brush faults, open circuits in component, interturn short circuits, and coil resistance caused by temperature increases may occur during operation, which leads to difficulties in system maintenance of DC motors. Friction is almost ubiquitous in servo systems. Nonlinear friction torque impacts greatly the dynamic and static performance of a system. As a consequence, the output response will have a large static error or produce steady-state limit-cycle oscillations. The influence on dynamic performance is manifest as the creep phenomenon at low speed [
In this paper, a servo control unit is investigated for electromechanical tracking and a steady servo platform. The effect of faults and nonlinear friction torque in the DC servo motor control system is first analyzed. Then an SMC is used for control of the DC azimuth and pitch servo motors, taking advantage of its nonlinear processing capacity. On this basis, a fault reconfiguration algorithm and an algorithm for rectifying the control parameters using the output of an observer are developed, both of which contribute to achieving active fault-tolerant control (FTC) of the system.
The remainder of the paper is organized as follows: Section
Under normal conditions, DC servo motors used for azimuth and pitch control can be simplified into linear second-order elements. However, under low-speed conditions, the system shows severe nonlinearity because of strong friction. The system can be described by [
When
When
Assume that
Then (
Actuator faults involve sticking, constant-gain variations or constant errors, and time-varying errors for execution of order in the control circuit. Then the input signal becomes
To ensure that the azimuth and pitch axis stabilization and tracking platform can operate reliably during combat missions, the tracking precision of the antenna should be guaranteed under all circumstances. Therefore, the most important purpose of fault diagnosis is to ensure that the system can maintain accurate tracking of the azimuth and pitch motors for a given angle, even under a fault condition, that is, to implement FTC for the system.
FTC is divided into passive and active fault tolerance for the control mechanism. Passive FTC only takes controller robustness into consideration and can assure system performance to a certain extent. However, its self-adaptive ability related to fault timing and amplitude is poor, so passive FTC has a limited fault tolerance capacity. On the contrary, active FTC readjusts the controller parameters after a fault has taken place and can even change the structure of a controller if necessary. Thus, it can greatly increase the system performance [
Structural diagram of FTC of a servo motor.
In Figure
For the driving module and nonlinear system for the servo motor shown in Figure
The advantage of SMC is that when a sliding mode occurs on a surface, the system has better invariance and robustness with regard to uncertainties such as modeling errors, parameter variations, and disturbances [
We define the control error as
When no fault has occurred (i.e.,
It is evident from (
Considering that the state variable
First, the sliding mode observer for the system in (
If the errors of the observer and the fault reconfiguration are defined as
If
Next,
By considering the previous steps, the time derivative of
Assuming that
Similarly, according to the equivalent principle for the sliding mode variable structure, it follows that a sliding motion takes place in finite time and during the sliding motion
To reduce chattering in the sliding mode variable structure and eliminate high-frequency interference, a continuous function can be used to replace the sign function in (
The FTC algorithm is
The procedures of the system control algorithm are summarized as follows.
Construct the sliding state observer using (
Calculate the estimated value of
Calculate the reconfigured value of the generalized fault using (
Calculate the FTC output using (
For a real-time control program it is more difficult to rectify online parameters and monitor the system in real time. Debugging is time consuming and expensive. Hardware-in-loop (HIL) simulation and debugging are used to test and verify the effectiveness of the proposed control algorithm. In HIL simulation, the part that needs to be inspected represents the actual object and the other part is simulated digitally. Compared with pure digital simulation, this method is closer to real conditions. Simulink/xPC is used to carry out HIL simulation of our position servo system. xPCTarget is a product based on the framework provided by RTW (Real-Time Workshop) in MATLAB and this tool kit can provide a real-time simulation environment in which the host and target machines are independent from each other using standard PCs. In this environment, a model is built on the host machine using Simulink. The model is compiled as an executable file through RTW and a C compiler. The executable file is sent from the host to the target machine via serial port communication for operation. Thus, xPCTarget provides a precise approach for accomplishing simulation between two machines.
In the environment MATLAB/xPCTarget, the real-time simulation system is constructed with the host machine and the target machine based on two microcomputers. The configuration is shown in Figure
Configuration for the hardware-in-loop simulation.
The host machine is a PC that controls the algorithm online and achieves real-time interaction during simulation. The PC is responsible for operating Matlab/Simulink/RTW to generate the code in real time, and performing interaction control and curve display functions during operation. The target machine is also a PC equipped with a GT-400-SV controller with an I/O interface board. The core of the controller is an ADSP2181 digital signal processor and FPGA, which implements high-performance control and computation. The target machine is responsible for executing the code downloaded by the host machine and performing data exchange with the external object via the I/O channel. The external object comprises the DC servo motor, the drive circuit consisting of the isolated driver circuit and the power switch tube, and the incremental photoelectric encoder. This type of HIL simulation is also known as rapid control prototyping.
Under a Simulink environment, the control algorithm determined by (
During system operation, serial communication between the host machine and the target machine enables the host to receive a real-time feedback signal from the motor. The response curve is displayed in real time during system operation. The control parameters are also rectified in the Simulink environment according to the control state reflected by the curve until satisfactory system performance is achieved. Finally, an executable code is directly transferred from the host to the target machine, which is the core of the system control, and thus rapid prototyping of the control system is accomplished.
Since the system shows strong nonlinearity only under low-speed conditions, a low-amplitude and low-frequency sinusoidal signal are used as the given position signal, chosen as
The fault configuration ability and fault-tolerant performance of the system are tested by the following two types of faults.
An incipient actuator fault is given as
The experimental results obtained using xPC Target for Scope are shown in Figures
The given position and output position.
The speed and its estimation.
The incipient fault and its reconstruction.
Figure
Figure
An abrupt actuator fault is given by a step waveform.
When
The abrupt fault and its reconstruction.
This paper presents a design for fault reconfiguration and FTC integrated in a built-in test system for electromechanical tracking of a servo platform. In comparison with fault detection by evaluation of residuals, the proposed fault reconfiguration approach better overcomes false or missing diagnoses for incipient faults. More importantly, the fault reconfiguration not only detects fault occurrences but also estimates the waveform and amplitude of the fault development, so that more precise fault diagnosis can be implemented. Furthermore, a simplified hardware configuration can be achieved by specific design of the state observer in which the observation of other state variables can be carried out as long as the value of one of them is known. Specific to this case, one angular displacement transducer is sufficient for data collection for the application example considered. The experimental results indicate that, in addition to efficient reconfiguration of actuator faults, the present algorithm allows the position output of the servo system to rapidly track the signal of a given position, even under fault conditions, which means that effective FTC is accomplished.
This work is supported by the Natural Science Foundation of China (nos. 61273157 and 61104024), Hunan Provincial Natural Science Foundation of China (no. 13JJ8020), and Hunan Province Education Department (no. 12A040).