Rafal T. Grygiel

Are anti-aliasing filters really necessary for sampled-data control?

In the paper the role of anti-aliasing filters is revised based on control quality assessment of various setups of analog filters used prior to sampling, or their lack. Numerical results show that contrary to common belief possible benefits gained from anti-aliasing filters are very restricted.

Averaging sampling: Models and properties

In the paper we study the properties of a sampling method for stochastic signals corrupted by a wide-band stochastic noise where samples are taken as average values of the signal over the sampling interval to diminish the influence of noise. We also study possible improvement attained by discrete-time Kalman filtering applied to the sampled signal. We compare the results with two competitive methods: classical point-wise sampling followed by discrete-time filtering, and continuous- time Kalman filtering prior to sampling possibly followed by digital filtering. The study is performed for a wide range of sampling periods and noise-to-signal ratios and leads to important practical conclusions.

Sampling of noisy signals: spectral vs anti-aliasing filters

Abstract In the paper we study the properties of sampling stochastic signals corrupted by a wideband stochastic noise where samples are taken either directly from resulting signal, or as the output from a continuous-time filter. We consider two types of filters: anti-aliasing filters whose characteristics depend solely on sampling period, and Kalman filters, whose characteristics depend on spectra of signals of interest. We also study possible improvement attained by discrete-time Kalman filtering applied to the sampled signal. We compare the results of two competitive methods: classical point-wise sampling followed by discrete-time filtering, and continuous-time filtering prior to sampling possibly followed by digital filtering. The study is performed for a wide range of sampling periods and noise-to-signal ratios and leads to important practical conclusions.

Attitude and heading reference system based on 3D complementary filter

The paper presents the idea, design and performance evaluation of a low-cost Attitude and Heading Reference System (AHRS). It is based on an Inertial Measurement Unit (IMU), being a single sensor pack that provides all the raw data required to feed the designed filter. An extension of a complementary filter in form of feedback control system with PI controller, called 3D complementary filter provides attitude estimates in Euler angles representation. A developed algorithm of filtering and data fusion poses small computational requirements for the designed low-power embedded hardware. Test were performed based on the sensor model and next using a real IMU. Experimental results obtained by means of rapid prototyping of designed filtering algorithm in different operating states are presented and discussed.

On significance of second-order dynamics for coupled tanks systems

Coupled tanks systems play an important role in teaching of control theory. Although due to the existence of two independent storages, making them a second order system, it has been shown that one time constant is at least 6 time greater than the other. In normal operation conditions this ratio is about 10-20. Therefore, special attention is necessary to explain their properties.

Naive Kalman filtering for estimation of spatial object orientation

In the paper an efficient and accurate method for estimating object orientation in three-dimensional (3D) space is proposed. Classical approaches based on Kalman filtering requires mathematical formulation of plant model, which in most cases is based on the nonlinear equations of rotational kinematics of rigid bodies. It follows that linearization operations are necessary. This approach is correct but in many cases leads to difficulties in computations and implementations. To simplify this problem, using the assumption of Bayesian classification systems, in the paper the angular velocity vector is treated as three separate events. Therefore, tree independent Kalman filters are used to estimate Euler angles for each Roll-Pitch-Yaw coordinate system. This new approach is called Naive Kalman Filter. Data fusion for real IMU sensor which integrates data from triaxial gyroscope, accelerometer and magnetometer is presented in order to illustrate accuracy and computational efficiency of proposed filter.

On the effect of anti-aliasing filters on sampled-data PID control

In the paper the role of anti-aliasing filters is revised based on control quality assessment of PID controllers when using a Butterworth antialiasing filter prior to sampling versus sampling without any analog filter. Numerical results show that contrary to common belief possible benefits gained from anti-aliasing devices are very restricted.

Sampled-data program control via model-reference LQG

A sampled-data controller which simultaneously tracks a pre-programmed set-point profile and minimizes the influence of stochastic disturbance for a linear continuous-time process is synthesized based on the model-reference concept and linear quadratic Gaussian (LQG) problem formulation.

High performance single tank level control as an example for control teaching

A detailed analysis of a PI tank level control is performed with respect to both load disturbance attenuation and set-point change. Certain performance indices are given providing guidelines for achievable accuracy and controller settings. Exact formulas for extrema of time responses are derived, which use a novel parametrization of system poles. For transfer between equilibria under control signal limitations, set-point generators with a feed-forward from the reference signal are proposed. The effect of an anti-windup controller augmentation is examined. A method based on solution of the non-linear differential equation describing the tank draining is proposed for a tank model identification. Moreover, invariance of the control system properties with respect to the actual equilibrium is highlighted.

Impact of anti-aliasing filters on optimal sampled-data PID control

In the paper the role of anti-aliasing filters is investigated based on control quality assessment of optimal PID controllers when using a Butterworth antialiasing filter prior to sampling versus sampling without any analog filter. Numerical results show that contrary to common belief possible benefits gained from anti-aliasing devices are very restricted.