User manual MATLAB SIMULINK CONTROL DESIGN 3

[. . . ] Simulink® Control DesignTM 3 User's Guide How to Contact The MathWorks Web Newsgroup www. mathworks. com/contact_TS. html Technical Support www. mathworks. com comp. soft-sys. matlab suggest@mathworks. com bugs@mathworks. com doc@mathworks. com service@mathworks. com info@mathworks. com Product enhancement suggestions Bug reports Documentation error reports Order status, license renewals, passcodes Sales, pricing, and general information 508-647-7000 (Phone) 508-647-7001 (Fax) The MathWorks, Inc. 3 Apple Hill Drive Natick, MA 01760-2098 For contact information about worldwide offices, see the MathWorks Web site. Simulink® Control DesignTM User's Guide © COPYRIGHT 2004­2010 by The MathWorks, Inc. The software described in this document is furnished under a license agreement. The software may be used or copied only under the terms of the license agreement. [. . . ] The operating point is the initial output of the block with a loop opening. 6-5 6 Frequency Response Estimation of Simulink® Models The estimated frequency response is related to the input and output signals as: G(s) fast Fourier transform of yest (t) fast Fourier transform uest (t) r where uest(t) is the injected input signal and yest(t) is the corresponding simulated output signal. For more information about estimating frequency response models, see "Estimating Frequency Response" on page 6-18. 6-6 Creating Input Signals for Estimation Creating Input Signals for Estimation In this section. . . "Supported Input Signals" on page 6-7 "Creating Sinestream Input Signals" on page 6-7 "Creating Chirp Input Signals" on page 6-14 "Modifying Input Signals" on page 6-16 Supported Input Signals Frequency response estimation uses sinestream or chirp input signals. Sinusoidal Signal Sinestream When to Use Recommended for most situations. Especially useful when: · Your system contains strong nonlinearities. · You do not require highly accurate frequency response models. See "Creating Chirp Input Signals" on page 6-14. Creating Sinestream Input Signals · "What Is a Sinestream Signal?" on page 6-8 · "How to Create Sinestream Signals" on page 6-8 6-7 6 Frequency Response Estimation of Simulink® Models · "How Frequency Response Estimation Treats Sinestream Inputs" on page 6-10 What Is a Sinestream Signal? A sinestream signal consists of several adjacent sine waves of varying frequencies. Each frequency excites the system for a period of time. f1 f2 f3 Amplitude Time How to Create Sinestream Signals You can create a sinestream signal from both continuous-time and discrete-time signals in Simulink models. Signal at Input Linearization Point Continuous Discrete Command frest. Sinestream frest. createFixedTsSinestream 6-8 Creating Input Signals for Estimation Create a sinestream signal in the most efficient way using a linear model that accurately represents your system dynamics: input = frest. Sinestream(sys) sys is the linear model you obtained using exact linearization techniques (see Chapter 4, "Exact Linearization Using the GUI"). You can also define a linear system based on your insight about the system using the tf, zpk, and ss commands. frest. Sinestream uses the linear system to determine these signal characteristics: · Frequencies at which the linear system has interesting dynamics (Frequency option) · Number of periods for the system to reach steady state at each frequency (SettlingPeriods option) · Total number of periods for each frequency (NumPeriods option) SettlingPeriods NumPeriods 6-9 6 Frequency Response Estimation of Simulink® Models For example, create a sinestream signal from a linearized model: magball io(1) = linio('magball/Desired Height', 1); io(2) = linio('magball/Magnetic Ball Plant', . . . 1, 'out'); sys = linearize('magball', io); input = frest. Sinestream(sys) The resulting input signal stores the frequency values as Frequency. frest. Sinestream automatically specifies NumPeriods and SettlingPeriods for each frequency: Frequency : [0. 05786;0. 092031;0. 14638 . . . ] (rad/s) Amplitude : 1e-005 SamplesPerPeriod : 40 NumPeriods : [4;4;4;4 . . . ] RampPeriods :0 FreqUnits (rad/s, Hz): rad/s SettlingPeriods : [1;1;1;1 . . . ] ApplyFilteringInFRESTIMATE (on/off) : on SimulationOrder (Sequential/OneAtATime): Sequential For more information about sinestream options, see the frest. Sinestream reference page. Estimate a frequency response model to evaluate the quality of your input signal. How Frequency Response Estimation Treats Sinestream Inputs Frequency response estimation using frestimate performs the following operations on a sinestream input signal: 1 Injects the sinestream input signal you design, uest(t), at the linearization input point. 6-10 Creating Input Signals for Estimation 2 Simulates the output at the linearization output point. frestimate adds the signal you design to existing Simulink signals at the linearization input point. u est (t) u(t) y(t) 6-11 6 Frequency Response Estimation of Simulink® Models 3 Discards the SettlingPeriods portion of the output (and the corresponding input) at each frequency. The simulated output at each frequency has a transient portion and steady state portion. SettlingPeriods corresponds to the transient components of the output and input signals. The periods following SettlingPeriods are considered to be at steady state. SettlingPeriods Input Output 4 Filters the remaining portion of the output and the corresponding input signals at each input frequency using a bandpass filter. When a model is not at steady state, the response contains low-frequency transient behavior. Filtering typically improves the accuracy of your model by removing the effects of frequencies other than the input frequencies. 6-12 Creating Input Signals for Estimation These frequencies are problematic when your sampled data has finite length. These effects are called spectral leakage. frestimate uses a finite impulse response (FIR) filter. The software sets the filter order to match the number of samples in a period such that any transients associated with filtering appear only in the first period of the filtered steady-state output. After filtering, frestimate discards the first period of the input and output signals. SettlingPeriods Filtered portion Input Output Used for estimation You can specify to disable filtering during estimation using the signal ApplyFilteringInFRESTIMATE property. 6-13 6 Frequency Response Estimation of Simulink® Models 5 Estimates the frequency response of the processed signal by computing the ratio of the fast Fourier transform of the filtered steady-state portion of the output signal yest(t) and the fast Fourier transform of the filtered input signal uest(t): G(s) fast Fourier transform of yest (t) fast Fourier transform uest (t) r To compute the response at each frequency, frestimate uses only the simulation output at that frequency. Creating Chirp Input Signals · "What Is a Chirp Signal?" on page 6-14 · "How to Create Chirp Signals" on page 6-15 What Is a Chirp Signal? The swept-frequency cosine (chirp) input signal excites your system at a range of frequencies, such that the input frequency changes instantaneously. Alternatively, you can use the sinestream signal, which excites the system at each frequency for several periods. See "Supported Input Signals" on page 6-7 for more information about choosing your signal. 6-14 Creating Input Signals for Estimation How to Create Chirp Signals Create a chirp signal in the most efficient way using a linear model that accurately represents your system dynamics: input = frest. Chirp(sys) sys can be the linear model you obtained using exact linearization techniques (see Chapter 4, "Exact Linearization Using the GUI"). [. . . ] Notice a small arrow pointing away from a small circle just above the signal line. Select Linearization Points > Output Point from the menu to place another output point on this signal line. The model diagram should now look similar to that in the following figure: 9-108 setlinio Create an I/O object with the getlinio function: io=getlinio('magball') Make changes to io by editing the object or by using the set function. For example: io(1). Type='in'; io(2). OpenLoop='on'; Assign the new settings in io to the model diagram: oldio=setlinio('magball', io) 9-109 setlinio This assignment returns the old I/O settings (that have been replaced by the settings in io). Linearization IOs: -------------------------Block magball/Controller, Port 1 is marked with the following properties: - An Output Measurement - No Loop Opening - No signal name. [. . . ]