In brushless DC motor servo control systems, sensorless position detection is crucial. Sensorless systems offer advantages such as small size, high accuracy, high reliability, and ease of maintenance, leading to their widespread application in servo systems. Common rotor position detection methods include back electromotive force (EMF) detection, flux linkage estimation, and Kalman filtering, with back EMF detection being the most mature and widely used. It measures the three-phase terminal voltage and detects the zero-crossing point of the back EMF to obtain the rotor phase signal for commutation. However, at low speeds, due to noise interference, the amplitude of the back EMF is relatively small compared to the noise signal, making it difficult to detect and causing the motor to lose synchronization. Adaptive noise cancellation addresses noise interference by utilizing the uncorrelated nature of the noise signal and the original measured signal. It adaptively adjusts the filter's transmission characteristics to suppress or significantly attenuate noise interference, improving the signal-to-noise ratio during transmission. Furthermore, the adaptive LMS filtering algorithm is computationally simple and easy to process in real-time, making it widely used. This paper proposes a back electromotive force (EMF) detection method based on adaptive noise cancellation technology. The center point is used as the interference signal, and the terminal voltage is used as the signal source with the interference signal. Utilizing the uncorrelated characteristics of the signal source and noise interference, the back EMF is extracted to obtain the zero-crossing point for position detection. 1 Design Principle 1.1 Basic Principle of Adaptive Noise Cancellation The signal source is transmitted to the signal sensor, which adds uncorrelated noise n(k). The combined signal is y(k) = s(k) + n(k), which enters the canceller. The output x(k) of the noise sensor is fed into the canceller's output signal z(k) after passing through a parameter-adjustable digital filter. Based on the correlation between the two noise signals and the independence of the signal and noise, an adaptive algorithm is used to adjust the parameters of the digital filter so that the output signal z(k) approximates the noise n(k) superimposed on the signal source. Thus, the canceller's output signal e(k) approximates the measured signal s(k). (See Figure 1). 1.2 Adaptive Filtering Algorithm The optimal criteria used in adaptive filtering include: minimum mean square error criterion, least squares criterion, maximum signal-to-noise ratio criterion, maximum likelihood criterion, statistical detection criterion, and some improved optimal criteria. The minimum mean square error criterion is adopted here. The LMS algorithm is a method that replaces the mean square error gradient vector with the instantaneous power gradient, that is: The iterative algorithm steps are as follows: (1) Initialization, select the initial weight w(k); (2) Calculate the output of the filter at time k as z(k) = wT(k)x(k); (3) Canceler error output e(k) = y(k) - z(k); (4) Update the weight vector at the next time step as w(k+1) = w(k) + 2μe(k)x(k); (5) Jump to step (2) when k = k+1, repeat the iteration until the algorithm converges. The stability of the algorithm depends on two factors, the adaptive step size parameter μ and the autocorrelation matrix R. The convergence condition of the algorithm is 0 < μ < 1/λmax, where λmax is the largest eigenvalue of the correlation matrix R, and the weight vector approaches the optimal Wiener solution. The value of μ is inversely proportional to the order of the filter. Different step sizes can be used according to the order of the filter to ensure better processing results. Another parameter, Ψ, measures the steady-state offset and is defined as the ratio of the mean square error of the average overshoot to the mean square error of the minimum overshoot. The offset is approximately expressed as: Ψ is proportional to μ. When the filter order is constant, the magnitude of μ controls the convergence speed of the algorithm and the magnitude of the offset at which steady state is reached. Convergence speed and offset are contradictory. Choosing a larger μ results in a faster convergence speed, but because a large μ value corresponds to a lower signal-to-noise ratio, it leads to a larger offset, causing oscillations during the transient process and preventing convergence. If the μ value is too small, the signal-to-noise ratio is high, but the convergence speed will be very slow, so a compromise must be made. 1.3 Brushless DC Motor Without Position Detection As shown in Figure 2, Vx is the voltage at a certain phase to ground, the three-phase windings are connected in a star configuration, Vn is the voltage at the center point to ground, Ex is the back electromotive force, and R, L, and Ix are the phase resistance, phase inductance, and phase current, respectively. The equivalent circuit equation of the winding is as follows: For a star-connected two-phase conduction, the sum of the three-phase currents is equal to 0. The back electromotive forces (EMFs) of the two conducting phases are equal in magnitude and opposite in direction. At the instant the back EMF crosses zero, adding the three equations together yields: From the above equation, the zero-crossing point of the back EMF can be easily detected. A 30° phase shift is sufficient to obtain the commutation point. At low speeds, the back EMF is submerged in noise signals and difficult to detect. Using noise cancellation technology, the center point Vn is used as the noise source, and the terminal voltage VK is used as the signal source. After processing by an adaptive filter, the noise output approximates Vn in amplitude and phase, and the back EMF is output by subtracting it from VK. 2. Computer Simulation and Performance Analysis The adaptive filter is simulated using Matlab, and the waveform can be easily observed. Therefore, the author developed a corresponding program to obtain the input signal source waveform curve, the weight vector iteration curve, and the output error waveform curve, as shown in Figure 3. Here, the signal source uses a sine wave mixed with Gaussian white noise. The sine wave signal s = sin*(0.05*n), and the interference noise randn(1, 2-10) follows a (0, 1) normal distribution. The horizontal axis iterates through 1024 data points, the step size parameter μ is 0.001, and the FIR order is 10, which can completely simulate the terminal voltage and center point voltage signals of the brushless DC power supply. As shown in Figure 3, in the original signal represented by the first simulation curve, the sine wave is completely masked by the noise signal, making it difficult to extract using general filtering methods. After applying the LMS adaptive FIR filtering method, the useful sine wave waveform after noise cancellation can be obtained in the second curve. The output e(n) gradually decreases in amplitude over a period of time, approaching the desired sine wave signal. In the third weight vector change graph, as e(n) converges, W gradually approaches the optimal filtering coefficient W0. 3. DSP Implementation of Adaptive Filter The TMS230LF240X series chip is a 24X series fixed-point DSP product manufactured by TI. It has advantages such as good processing performance, high peripheral integration, large program storage capacity, fast A/D conversion speed, and abundant I/O port resources. It has superior performance, low power consumption, and low cost, and can perform efficient and practical digital control of motors. Here, a part of the DSP module is used to complete the adaptive LMS noise cancellation function. Its block diagram is shown in Figure 4. 3.1 Overall Block Diagram The chip's ADC sampling channel can have up to 16 conversion channels, thus it can sample four analog quantities: three-phase terminal voltage and center point voltage. As shown in Figure 4, the reference input has two main channels, connected to the motor's non-conducting terminal voltage signal terminal and the center point signal terminal, respectively. After preliminary low-pass filtering, the signal is sent to the DSP's A/D module, discretized into digital input quantities for signal processing. After conversion, the signal is smoothed by a low-pass filter and then stored in the corresponding register of the channel. 3.2 Algorithm Implementation To achieve coefficient iteration, a circular addressing method can be used, which can be implemented using the RPT instruction. First, initialize module B, the ARk register, and the accumulator. Block B1 stores the weighting coefficients wi(n), and the sampled signal x(n-N+1) is placed in B0. The block length N is the filter order. AR0 points to the address of wi(n), AR1 points to the address of x(n-N+1), and AR2 points to the desired signal y(n). The product of the two data parts is added to the accumulator using MPYA. The store instruction is executed N-1 times repeatedly using RPT, the program register pointer points to the next sampled signal value, and the accumulator value is updated. The program flowchart is shown in Figure 5. 4 Conclusion The adaptive noise cancellation system is an extension based on the adaptive filtering principle. In digital speech signal processing, it can effectively extract applicable speech signals, effectively reduce noise, and improve signal processing quality. This paper applies this idea to the noise processing of motors, combining it with the terminal voltage detection method to extract the back electromotive force. Simulation results show that the adaptive noise cancellation method can effectively reduce noise, enabling normal detection even during motor startup and low-speed operation. The scheme is simple and feasible. Since the LMS algorithm has convergence characteristics and the offset is affected by the step size, the optimal step size is not easy to determine. Therefore, improved LMS algorithms such as NLMS and RLS can be used, which have more ideal results.