Step Response Data Research Articles

A state space formulation for model predictive control

AbstractModel predictive control (MPC) schemes such as MOCCA, DMC, MAC, MPHC, and IMC use discrete step (or impulse) response data rather than a parametric model. They predict the future output trajectory of the process {ŷ(k + i), i = 1, …, P}, then the controller calculates the required control action {Δu(k + i), i = 0, 1, …, M − 1} so that the difference between the predicted trajectory and user‐specified (setpoint) trajectory is minimized. This paper shows how the step (impulse) response model can be put into state space form thus reducing computation time and permitting the use of state space theorems and techniques with any of the above‐mentioned MPC schemes. A series of experimental runs on a simple pilot plant shows that a Kalman filter based on the proposed state space model gives better performance that direct use of the step response data for prediction.

Computer Aid Design of Approximate Model Design Technique

AMDTCAD, an interactive computer package, has been developed for computer aided design of multivariable process control system by using approximate model design technique. Besides having effective human/computer Interface and graphic capability, the package can provide not only aid design for multivariable process control systems whose models are unknown or highly complex in the frequency domain based on open-loop step-response data alone, but also analysis of robust stability for designed system. By combined with our Frequency Multivariable System CAD software Package, AMDTCAD has created an environment attractive to both industrial users and academics.

A frequency and time domain study of the horizontal and vertical vestibuloocular reflex in the pigeon.

1. The horizontal and vertical vestibuloocular reflex (HVOR and VVOR, respectively) was studied in four chronically instrumented pigeons. Eye movements were measured using the magnetic search-coil technique and were produced by rotation in the dark. During the rotation paradigms, the pigeons were either pharmacologically aroused (using amphetamine) or drug free (normal). The pigeon HVOR and VVOR were tested using step and sinusoidal rotational stimulation. The range of frequencies (0.03-6.0 Hz) and the magnitude of the sinusoidal stimuli were chosen to match those used in a previous study of the responses of semicircular canal primary afferents (SCPAs) in unanesthetized (i.e., normal) pigeons. 2. The gain of the HVOR and VVOR in both normal and aroused pigeons was independent of stimulus magnitude (6-30 degrees/s) over the frequency range tested. In aroused pigeons, the frequency independent gain (G) of the HVOR (G = 0.6) and VVOR (G = 0.9) was roughly twice that for normal pigeons. Pigeon VOR phase under all combinations of orientation and arousal level was independent of stimulus magnitude except at the lowest frequency tested (0.03 Hz). At this frequency, phase lead decreased as stimulus magnitude increased for the HVOR and VVOR in both normal and aroused pigeons. 3. The step and sinusoidal gains were greater for the VVOR than for the HVOR under the same level of arousal. Neither the gain nor the dominant time constant of the VOR (tau vor) differed for rotation direction (clockwise or counterclockwise) for the HVOR or VVOR in normal or aroused pigeons. 4. The mean value of tau vor was 4.0 +/- 0.5 (SE) s as estimated from frequency response data and 4.3 +/- 0.4 s as estimated from step response data for the HVOR and VVOR in both normal and aroused pigeons. In comparison, the mean value of the dominant or cupular time constant (tau c) of normal pigeon SCPAs was approximately 10 s as estimated from frequency response data. These results indicate that tau vor is shorter than tau c in the pigeon. 5. At higher frequencies, the pigeon HVOR and VVOR exhibit an increasing phase lag unaccompanied by a gain change--characteristics produced by a pure time delay. The value of this time delay was about 7 ms for both the HVOR and VVOR in both normal and aroused pigeons. The HVOR and VVOR in normal and aroused pigeons lacked the higher frequency lead characteristics present in the frequency responses of most pigeon SCPAs.

Case Studies and Modelling Advances in Producing Conductivity- Depth Sections

Since the development of a technique called Depth Image Processing (DIP) for direct transformation of multifold, step-response EM data into an imaged conductivity-depth section, a number of test and production surveys have been carried out. The results demonstrate the effectiveness and accuracy of the technique when the geological section is quasi-layered. Two recent case studies show very good correlation with available drill-hole results. Scale and computer model data have been generated for a number of conductive/resistive inhomogeneities in a layered earth, and this data base is being studied with a view to improving the ability of the DIP process to better image these non-layered features. The results from this will be reported at the conference.

A model-free method for mass spectrometer response correction.

A new method for correction of mass spectrometer output signals is described. Response-time distortion is reduced independently of any model of mass spectrometer behavior. The delay of the system is found first from the cross-correlation function of a step change and its response. A two-sided time-domain digital correction filter (deconvolution filter) is generated next from the same step response data using a regression procedure. Other data are corrected using the filter and delay. The mean squared error between a step response and a step is reduced considerably more after the use of a deconvolution filter than after the application of a second-order model correction. O2 consumption and CO2 production values calculated from data corrupted by a simulated dynamic process return to near the uncorrupted values after correction. Although a clean step response or the ensemble average of several responses contaminated with noise is needed for the generation of the filter, random noise of magnitude less than or equal to 0.5% added to the response to be corrected does not impair the correction severely.

EXPERIMENTAL INVESTIGATIONS USING FEEDBACK-INDUCED BIFURCATION: CARBONMONOXIDE OXIDATION OVER SUPPORTED SILVER

The use of feedback-induced bifurcation experiments for discriminating between rival models for the CO-02 reaction over supported silver is investigated. Model parameters are estimated or bounded by fitting the postulated kinetic mechanisms to steady-state and transient step-response data. Experimental steady-state bifurcation data is accurately reproduced by the models but each model fails to simulate adequately the Hopf bifurcation results. The dynamic bifurcation results are found to be sensitive to small time-scale dynamics that could not be resolved from the step-response experiments. Long transients in the catalyst activity are observed that cannot be reproduced by the kinetic models.

Accurate frequency response determinations from discrete step response data

An approach is presented for quickly obtaining the complex frequency response of a system from sampled step-response data. Digital signal processing techniques are used extensively. An analysis of errors resulting from sampling, quantization, first differencing and record length is included.

System identification via generalized block pulse operational matrices

Owing to the elegant properties of generalized block pulse operational matrices, a SID (system identification) matrix can be derived to identify transfer function coefficients of a linear time-invariant system from the unit step response data. The identification algorithm performs in a least-squares sense and can be recursive according to previous work. This approach not only yields satisfactory results but also provides a more precise and efficient method for the system identification problem.

A Concept of Industrial Adaptive Control Based on Robust Design Principle and Multi-Model Approach

The discussed concept of industrial control strategy for single loop temperature control in plastics extrusion contributes to problem solutions according to computer aided or automatic proper tuning of a standard PID-Type controller. The adaptive feature is realized by a controller parameter scheduling. The scheduling depends on actual plant characteristics identified during start-up phase or after significant set-point changes. The available controller parameter sets {KP, TI, TD} are gained by a systematic search of the best compromise of a multiple performance description of simulated closed loop step response. Robustness of each controller parameter set is met using a family of plant models representing a nominal, an upper, and a lower boundary of plant step response data. The multi model plant description results from least square identification. No changes of the standard PID controller structure is necessary; a tuning loop only superimposes the well known digital control loop leading to a more easy to use PID control device which behaves robust and adaptive.

Identification of UA in Thermal Storage Devices-Two Methods

Two methods are described for identifying the key overall fluid to storage material heat transfer product, UA, and the degree of stratification, NT, for use in the analysis of storage test data The first method, called the generalised model approach, permits a wide range of non-linearities as well as arbitrary test initial and boundary conditions to be accommodated The second method, called the simplified graphical method, demands high quality step response data but is very easy to use Three examples taken from recent work in the SSTG programme are examined and these include a fully mixed response, a fully stratified response and a partially stratified response. The graphical method is shown to give a good estimate of the UA value for each case, even for the difficult case of partial stratification.

Controller design for unknown multivariable systems using monotone modelling errors

The problem of controller design for an unknown discrete or continuous multivariable system in the frequency domain based on open-loop step-response data alone is considered. The approach is based on the use of simple approximate plant models possessing the property that the resulting error in modelling the plant open-loop step response is both monotonic and sign-definite as a function of time. In such circumstances, the frequency-domain properties of the approximating feedback system and the error involved in predicting steady-state characteristics are sufficient data to predict the stability of the real feedback system. If integral controller elements are included, the results also provide sufficient conditions for exact tracking of step demands. Under certain circumstances, the technique has strong connections with the well known inverse Nyquist array design method and can be regarded in part as a modification and generalisation of that techniqiue to cope with unknown interaction dynamics.

MODEL COMPARISONS FOR DYNAMIC k L a MEASUREMENTS WITH INCOMPLETELY MIXED PHASES

Oxygen transfer coefficients for gas-liquid systems can be determined by dynamic response experiments. Calculation of the unknown k L a parameter involves analysing the step response data with a model which suitably describes the gas and liquid phase mixing phenomena as well as the electrode dynamics. Various combinations of plug-flow, disperion-flow and well-mixed models are proposed to describe particular gas-liquid systems. Through Laplace transformation, the first moments are calculated in terms of the model parameters. From experimental step response data, the first moment is obtained as the area above the response curve. Using the tabulated relations, dynamic k L a response data can be analysed for many particular gas-liquid oxygen transfer situations. Comparisons between the moment relationships serve for the calculation of the errors in k L a which would be incurred when using an incorrect two-phase model. In general, approximate models may lead to large errors.

Time to Frequency Domain Conversion of Step Response Data

Time to Frequency Domain Conversion of Step Response Data

A technique for fitting system response data using a priori information.

System response data are frequently analysed by fitting with a trigonometric Fourier series. However, the trigonometric series is not necessarily the best choice since the number of terms required to give a desired integral-square error (i.s.e.) fit may be excessive and may not provide the intuitive feeling for the system-response poles. A general method is given wherebya priori orposteriori information about the system poles may be used to fit the data with a small number of terms and satisfy i.s.e. criteria. An application example shows a three-term series that fitted biological stretch-receptor step-response data with two terms other than d.c. and yielded an i.s.e. of only 0·5 to 1·2% for the non-d.c. data.

Treatment of data in step-response dielectric relaxation measurements

We report a satisfactory method for the direct conversion of step-response (transient) data (such as is obtained from the rate of discharge of a capacitor) into the frequency dependence of the complex relative permittivity. This computer-based method has no a-priori restriction on the shape of the loss peak or functional dependence of the decay response. In this it differs from a number of approaches described in the literature.1–4 The method herein described is compared to such other techniques for converting step-response data, and assessed in relation to the predicted behaviour for single and unresolved double Debye relaxations. The dielectric relaxation behaviour of a sample of poly(vinyl acetate) is also investigated using the described method of data analysis.

The Measured Time and Frequency Response of a Miniature Superconducting Coaxial Line

A miniature superconducting 52 ohm coaxial transmission line 278 meters long, having a lead outer conductor (0.129 cm id), a teflon dielectric, and a niobium center conductor (0.038 cm), has been measured in both the time and frequency domains. The observed system step response (10% - 90%) times were 1.5 ?s at room temperature, 375 ns at 77K, and 255 ps at 4. 2K. The system step response data for 4.2K was processed by a numerical system identification routine to determine the step response of the miniature superconducting line; the processed data gave a 220 ps risetime. Although the observed step responses at 4.2K were smooth transitions, the observed swept frequency (0.1 GHz - 12 GHz) attenuation at 4. 2K was a quasi-periodic function of frequency, which indicated that the nonuniformity of the superconducting line was significant. For example, near 5 GHz and at 4.2K, the attenuation minimum was 1.1 dB while about 0.5 MHz away the attenuation was 5 dB. By making normal conductivity measurements of the Nb conductor and incorporating the results into the two fluid model, the uniform line attenuation for 5 and 10 GHz was calculated with the classical and anomalous limits. The lowest observed attenuation values in the vicinity of 5 and 10 GHz fell between the computed classical and anomalous limit attenuation values.

A nonlinear analysis of the mechanics of accommodation

Continuous measurements of the motion of the cat lens in response to ciliary ganglion stimulation have been made for step and sinusoidal changes in stimulation rate. The lens responses of five cats are averaged to arrive at representative, continuous recordings relating lens motion and stimulation rate. A mathematical model is constructed using the step response data as a basis and various dynamic and static system nonlinearities are thereby identified. The sinusoidal data is used as a further check on the general validity of the model. Comparison of the model with experimental results reported by others would indicate the accommodative system in cats is highly damped; exhibits both ciliary muscle and lens dynamics and uses both lens deformation and rigid body translation to change the refractive state of the eye.