Properties of Non-Linear Systems

More documents

Recommendations

Info

Describing Function Method Procedure for analyzing Non-Linear Control problems based on quasi-linearization Replacement of the non-linear system by a system that is linear except for a dependence on the amplitude of the input waveform An example might be the family of sine-wave inputs; in this case the system would be characterized by an SIDF or sine input describing function H (A, ω) giving the system response to an input consisting of a sine wave of amplitude A and frequency ω. (This SIDF is a generalization of the transfer function H (ω) used to characterize linear systems) Other types of describing functions that have been used are DF's for level inputs and for Gaussian Noise inputs. The DF's often suffice to answer specific questions about control and stability. Example piecewise linear function: Slope F s1 ( y) Slope s2 CAS-DSP, Sigtuna 2007-Control Theory-S.Simrock Slope s3 y 4
Phase Plane Method Refers to graphically determining the existence of limit cycles The Phase Plane, applicable for second order systems only, is a plot with axes being the values of the two state variables, vs x x 2 1 [ ( ) ( ) ] Vectors representing the derivatives f2 x1,x2 , f1 x1,x2 at representative points are drawn ( With enough of these arrows in place the system behaviour over the entire plane can be visualized and limit cycles can be easily identified ) -0.5 x2 -0.5 0.5 0.5 stable CAS-DSP, Sigtuna 2007-Control Theory-S.Simrock unstable x1 5
Page 1 and 2: Properties of Non-Linear Systems So
Page 3: Control Design of Non-Linear System
Page 7 and 8: The Lur'e problem Control systems
Page 9 and 10: Example for Popov Criteria The non
Page 11 and 12: Gain Scheduling It is an approach
Page 13 and 14: Feedback Linearization Common appr
Page 15 and 16: Sliding Mode Control In Control th
Page 17 and 18: Consider a linear system The contro
Page 19 and 20: Caused by delays (no ideal sliding
Page 21 and 22: Identification Steps Experiment de
Page 23 and 24: Experiments and Data Collection Oft
Page 25 and 26: Design Experiment for Model Estimat
Page 27 and 28: Remove: Data Pre-Filtering Transie
Page 29 and 30: Model structures based on input-out
Page 31 and 32: AR Model Process model where outpu
Page 33 and 34: ARX Model (Cnt‘d) Set the model
Page 35 and 36: Box Jenkins Model Provides a compl
Page 37 and 38: State Space Model All previous met
Page 39 and 40: Determine Parameters Determining t
Page 41 and 42: Variety of model structures availab

Properties of Non-Linear Systems

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?