Questions and Answers of Systems Analysis And Design Using MATLAB

Consider a static system with two inputs, x1 and x2, and two outputs, y1 and y2, where y1¼f1(x1, x2) and y2¼f2(x1, x2). The LUT representing these two functions is given in Table 6.3 and Figure
Consider a system with three inputs, x, y, and z, and one output,f. The LUT representing the function is given in Table 6.4. Use trilinear interpolation to find the value of the function at points
Consider the 1-D function y¼p(x) defined byWe first nonuniformly sample this function at N¼10 points and create the LUT given in Table 6.7.(a) Use the Shepard interpolation to estimate the value of
6.1 Consider the 1-D functionCreate a 1-DLUT of size 102 by uniformly sampling the function from 0 to 1.(a) Use linear interpolation to estimate the values of the function at x1¼0.234 and x2¼0.568.
6.3 Consider the 2-D function given by(a) Create a 2-D LUT of size 1010 by uniformly sampling the function from 0 to 1 in both directions. The total number of grid points is 100.(b) Use bilinear
6.4 Consider the 3-D function(a) Create a 3-D LUT of size 121212 by uniformly sampling the function from 0 to 1 in all directions. The total number of grid points is 1728.(b) Use trilinear
6.5 Consider a CMY printer characterized through the 3-D LUT given in Table 6.19.(a) Use trilinear interpolation to find the L*a*b* values corresponding to the following CMY patches:(b) Is this
6.7 Show that the Shepard interpolation algorithm given bywill result in a differentiable function if parameter m>1. 1=1 if d # 0 for all i if d; =0 for some j
6.8 Assume that we have a CMY ! L*a*b* printer characterization function with Jacobian J at the nominal value CMY¼[120 67 145] given byFind the range of parameter m that guarantees convergence of
6.9 Consider a scanner characterization color space transformation from a calibrated scanner RGB to a device-independent color space L*a*b* given by the 4-level (64 grid points) LUT shown in Table
6.10 (a) Using the RGB to L*a*b* LUT of Problem 6.9, estimate the Jacobian of the transformation at the nominal value RGB¼[120 67 145] using numerical differentiation and trilinear interpolation.
Use K-means (Linde–Buzo–Gray [LBG]) algorithm [12] to divide the 104 input–output printer modeling data into 10 clusters. Describe the critical steps in the algorithm.
Using RLS algorithm and training samples from Example 7.1, (a) obtain a piecewise linear affine model and (b) piecewise linear quadratic and cubic model for different clusters. Show the model
In aCMYK printing system, inputCMYK values are sampled uniformly between 0 and 255 to create 104 input–output characterization data set. The spectral data for each patch is measured at 31
Use Example 7.3 input–output characterization data and apply log-PCA model to show the improvements to modeling accuracy.
A clustered PCA-based model is to be constructed for a 104 spectral characterization data. Use the K-means algorithm to cluster the color data in spectral space.Obtain spectral PCA vectors for each
For a four-color CMYK printer, develop a spectral Neugebauer model (Equation 7.51) with Demichel weights for 16 Neugebauer primaries. Estimate the weights using training samples with least-squares
A four-color CMYK printer has 16 usage basis colors for combinations of two states(0% and 100% area coverages) whose measured spectral curves are shown in Table 7.6 at 10 nm interval between 400 and
Generate a GCR constrained ICC destination profile with a 3-to-3 control-based inversion using the GCR function of Figure 7.25 for a test printer. Evaluate the quantitative round trip accuracy and
Construct a K-restricted GCR for a uniformly sampled printer input–output data using the analytic functions of Equations 7.90 and 7.91 and a 4-to-3 control-based inversion approach. Show the
7.1 Using the RLS algorithm, obtain a global linear model for a CMY gray color[C¼127¼M¼Y, K¼0]. The solution should include some details of the experimental procedure.
7.2 Using the RLS algorithm, obtain a local linear model for a CMY gray color[C¼127¼ M¼Y, K¼0]. The solution should include some details of the experimental procedure.
7.3 Using the RLS algorithm, obtain a quadratic and cubic model for the printer.Calculate the modeling errors with respect to the virtual printer model shown in Chapter 10. Is a quadratic and cubic
7.4 In a printing system CMYK values are sampled between 0 and 255 in a uniform grid to obtain up to 104 input–output characterization data. Patches are printed and measured by the
7.5 Use bootstrapping techniques to gain confidence in the PCA-based modeling.
7.6 A clustered PCA-based model is to be constructed for a 104 spectral characterization data. Use the K-means algorithm to cluster the color data in spectral space. Obtain PCA vectors for each
7.7 Simulate a node color convergence near the gamut boundary using a poleplacement algorithm. Show DE*ab convergence errors with and without the best actuator algorithm. Use the Neugebauer model to
7.8 Simulate a node color convergence using a pole placement algorithm and a 4 to 3 control-based inversion. Use the Neugebauer model to represent the printer.Choose any suitable GCR as nominal CMYK
7.9 Extend Problem 7.8 for additional in-gamut nodes (say, seven gray targets with L* of 25–90, in steps of 10 with a*¼b*¼0) along the neutral axis. If the nodes are not in-gamut change the L*
7.10 Run a 4 to 3 control loop for the nodes in Problem 7.9. Is the convergence error near zero at steady state? Plot actual K separation values along the neutral axis from 4 to 3 control loop and
7.11 Produce a ray-based control model for mapping an out-of-gamut spot color described with, xc¼[Lc¼80, ac ¼50, bc ¼30], and the gamut centroid, x0¼[L0¼50, a0¼0, b0¼0]. Repeat this for
7.12 Black point compensation algorithm is used to retain shadow details in images since many images contain colors that are darker than the darkest color a printer can make. Using the algorithm
7.13 Repeat the profiling example shown in Section 7.8 to build a 173 destination ICC profile using MATLAB. Obtain Gamut corner plots and round trip accuracy (overall and to corner points). Simulate
Assume that N¼11 Cyan patches with digital counts of 0, 25, 50, 75, 100, 125, 150, 175, 200, 225, and 255 are printed on a color digital printer. The measured L*a*b* values of these 11 patches and
Assume that a 999 CMY to L*a*b* characterization LUT is measured for a digital color printer. This LUT is used to compute the CMY values corresponding to the gray values of ai* ¼ bi* ¼ 0, Li* ¼ 15
8.1 Ten yellow patches with digital input of Y¼25.5i, i¼0, 1, 2, . . . , 10 and C¼M¼0 are printed on a digital printer. The DEa*b difference between the output patches and paper are tabulated in
8.2 (a) Write a general MATLAB code to find the inverse of function f(x) graphically from data given by a LUT.(b) Write a general MATLAB code to find the inverse of function f(x) numerically from
8.3 Ten gray patches are printed on a digital printer and their L*a*b* values are measured. The resulting data is shown in Table 8.12.(a) Find the cyan, magenta, and yellow gray-balanced TRCs for
8.4 Design a control loop for 1-D DEa*b from paper linearization using state feedback where the plant is modeled as combination of printer and DEa*b sensor. Linearize the overall system and check the
8.5 Use Neugebauer model, drive a closed-form expression for the sensitivity matrix B at a nominal CMY value. TABLE 8.11 AEb Difference between the Output Patches and Paper Y 0 25.5 51 76.5 102 127.5
8.6 Use the sensitivity matrix B obtained in Problem 8.5 to simulate the in-gamut spot-color convergence when the spot color is inside the CMY gamut class. Use the pole-placement algorithm and three
8.7 Perturb the sensitivity matrix with reasonable DB and show the robustness of spot-color recipe obtained in Problem 8.6 for CMY gamut class.
8.8 Repeat Problems 8.6 and 8.7 for CYK, MYK, and CMK gamut classes by choosing in-gamut colors in the respective gamut classes.
Test the following electrostatic control system for controllability. The system is at the nominal operating point {Vgo ¼ 600V, Xlo ¼ 8 ergs=cm2}. 10 [0.9798 x(k+1)= + 01 03315 11.1026](K) 1 0 y(k)
Using the gain matrix of Example 9.2 and the electrostatic model described in Chapter 10, simulate the transient performance of the closed-loop linearelectrostatic control system when the desired
Test the following developability control system for complete controllability. The system is given at the nominal operating point {Uho¼600 V, Ulo¼100 V, Ubo¼300 V}. [1 00 0.0282 0.5024 -0.2633"
The cost of the electrostatic sensing system can be reduced by removing the charge sensor (ESV) and associated level 1 control loop. It is now required to design a three-input three-output
State equations for a closed-loop TC control system are given below. Design the gain matrix for placing the poles at (a) l1¼0.2, l2¼0.25 and (b) l1¼0.6, l2¼0.65. Assume TC target in percent.
Consider the design of a TC feedback system with a transport delay using a state feedback estimator and controller. Design the observer gain matrix and the controller gain matrix using pole-placement
9.1 Let the state-space equations for the level 1 electrostatic system beUse the control law shown in Equation 9.26 with the feedback gain matrix givena. Show the evolution of the states for xd¼[550
9.5 The cost of an electrostatic sensing system can be reduced by removing the charge sensor (ESV) and associated level 1 control loop. It is now required to design a three-input three-output
9.7 Let the vector U0 contain the input patch gray levels (or area coverages) for controlling DEa*b from paper for magenta separation shown in Table 9.4. They are shown in the second column. In the
10.1 Let the parameters of a charging system be(a) Plot VP(L) as a function of grid voltage Vg. Assume VP(0)¼0.(b) Find sensitivity of the photoconductor surface voltage with respect to the grid
10.2 Consider a charging system given by differential equationwhere the grid voltage Vg¼800 V, S ¼ 0:9 106 A V-m, and C ¼ 9:486 107 C V-m2.(a) Find photoconductor surface voltage Vp(t) if
10.3 Consider the Springett–Melnyk exposure model given by(a) Solve the above equation numerically and plot V(X) as a function of eh0 C X.Assume the following parameters for the model: Vi¼500 V,
10.5 For a two-component conductive magnetic-brush development system, assume that the toner charge per unit area completely neutralizes the photoconductor charge per unit area. Show that with this
Assuming a D50 light source, compute the XYZ values of a color patch with a reflectance spectra of R(A)=-6.25 x 106x2 + 0.0063A-1.225 380 < < 730
Assuming a D50 light source, compute the L*a*b* values of a color patch with a reflectance spectra of R(X)=-6.25 x 10-2 +0.0063A-1.225 380 < < 730
Convert the following L*a*b* values to ROMMRGB: L*a*b=[60_0_0] and L*a*b= [40 -16 50]
Find the L*a*b* with respect to paper of a color patch with absolute L*a*b*¼[53 -16 15] . Assume that the paper L*a*b* ¼ [90 0 0].
Assuming a D50 light source, compute the tristimulus values of perfect white.
10.7, obtain the printer gamut for five different paper types. Use measured paper reflectance spectra for each type.
Find DEa*b and DE2000 color difference between the following two color patches L*a*b*2 ¼ [65 120 70] and L*a*b*1 ¼ [68 117 68]. These color patches are shown in Figure A.10
10.6 For a four-color printing system, using the techniques described in Section
10.4 A square sheet 2m on a side situated in the x–y plane and centered on the origin has a charge of 1 nC uniformly distributed over its surface.(a) Find the electric potential V at a distance of
9.14 For a four-input three-output controller with TC target as one of the actuator, design the LQR to emphasize the TC target. Show the equation for the steadystate value and plot it as a function
9.13 Describe the relationship between TC control and a typical inventory management system. Compare the controllers.
9.12 Simulate the TC performance for a system with the state feedback controller and estimator in Example 9.10 when the TC system has a fixed transport lag of 3 and 10 cycles. Apply the Smith
9.11 For TC system with PI controller ~umin¼0 and ~umax¼a reasonable limit, simulate the situation with integrator windup. Design a antiwindup compensator with high gain L and simulate the
9.10 Design the gain matrix for the PI controller of Example 9.10 using the LQR method. Compare your TC performance with the pole-placement technique.Comment on the results.
9.9 Consider a scenario where the level 1 loop of Example 9.1 is closed for every print and the level 2 loop of Example 9.6 is closed for every 5 prints.Let level 1 loop be designed for a dead beat
9.8 Obtain an inversion using control-based inversion for Problem 9.7. Use identity as the reference TRC. Process magenta separated image through the inverted TRC and printer model.
9.6 For a level 2 controller (Figure 9.8), design the antiwindup compensator gain matrix and show the performance with and without the compensator.
9.4 Consider the development control system of Example 9.5. The development system is characterized by the Jacobian matrix B, at the nominal operating point.Find the expression for the steady-state
9.3 Consider the electrostatic control system of Figure 9.4. The charging system is characterized by the Jacobian matrix B, at the nominal operating point.a. Write the open- and closed-loop transfer
9.2 Determine the controllability and observability matrices and then ranks for Problem 9.1. What are the eigenvalues of the open-loop system with and without the integrator in the loop? Is the
As an example, we find the optimal gray levels by solving Equation 9.134 for spatial TRC data. The quality of TRCs derived from equispaced levels is compared with the quality derived from levels
Use Equation 9.63 as the TC system and the PI controller with closed-loop poles l1¼0.6, l2¼0.65 and Smith predictor Equations 9.93 through 9.96 to simulate the performance of TC system with a
Let the vector, U0, contain the input patch gray levels (or area coverages) for controlling DMA on the photoconductor for cyan separation shown in Table 9.1.The vector x contains the normalized
Let the vector U0 contain the input patch gray levels (or area coverages) for controlling DMA on the photoconductor for the magenta separation shown in Table 9.1 below. The vector x contains the
Let the desired closed-loop poles for level 2 controller be located at p1, p2, p3.(i) Using Equation 9.45 for the Jacobian matrix of Example 9.5 find the gain matrix that will provide equal poles
Let the charge on the photoconductor at the exposure station be decayed by 30 V(i.e., Vh at the exposure station is equal to 550þ30 V). Simulate the transient performance of the controller shown in
For the open-loop electrostatic system shown in Example 9.1, find the gain matrix K to place the closed-loop poles within the unit circle on the real axis at 0.2 and 0.3.
6.6 Repeat Problem 6.3 using(a) Tetrahedral interpolation(b) Shepard interpolation(c) Moving matrix
6.2 Consider the 1-D LUT shown in Table 6.18.(a) Use linear interpolation to estimate the value of the function at x¼3.8.(b) Repeat part a using(i) The Shepard technique (use L1 norm and m¼1)(ii)
Consider the 1-D function y¼P(x) given by the LUT shown in Table 6.9.Use the moving-matrix approach, interpolate, and compute the corresponding value of P(x) at x¼0.5. Use m¼2 and e¼104.
Consider aCMY printer with the 333 forward printermap LUT(CMY!L* a* b*)given in Table 6.8. Use the Shepard interpolation algorithm to find(a) The CMY corresponding to L*¼50, a*¼30, and b*¼40.
Consider the transformation from device-dependent CMY to device-independent L*a*b* given by the LUT shown in Table 6.6.Using tetrahedral interpolation, find the L*a*b* values corresponding to the
Consider the 1-D LUT given in Table 6.2. Use linear interpolation to interpolate the value of the function at x¼5.4.
=+How software developers use design patterns to avoid duplicating effort by applying
=+the knowledge and experience of other developers to a particular problem. A pattern
=+describes a particular way of doing something that has proved effective in real world projects.
=+• How patterns are used to record knowledge, to document solutions and to aid reuse.
=+• when the client can call the function
=+• what parameters should be passed
=+• what the function does
=+• what kind of result is returned (type and value)
=+• what effect the function has on global data
=+• what action the function takes if there is a problem
=+1. What is a ‘class invariant’? Choose only one option.

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