Holooly Plus Logo
Holooly Plus Logo

Question 20.5: For Exercise 20.1, suppose that a constraint is placed on th...

For Exercise 20.1, suppose that a constraint is placed on the manipulated variable, u_{k+j} \leq 0.2 for j=1,2, \ldots, M-1. Let \Delta t=2 and N=40. Select values of M, P, and R so that these constraints are not violated after a unit step disturbance occurs.

The Blue Check Mark means that this solution has been answered and checked by an expert. This guarantees that the final answer is accurate.
Learn more on how we answer questions.

There are many sets of values of M, P and R that satisfy the given constraint for a unit load change. One such set is M=3, P=10, R=0.01 as shown in Exercise 20.4(iii). Another set is M=3, P=10, R=0.1 as shown in Exercise 20.4(iv). A third set of values is M=1, P=5, R=0 as shown in Exercise 20.4(i).

Related Answered Questions

Repeat Exercise 20.12 for Q = diagonal [0.1 0.1] and (i) M = 1 and (ii) M = 5.

Verified Answer:
We repeat problem 20.12, but this time we look at ...

Repeat Exercise 20.11 for R = diagonal [0.1, 0.1] and: (i) M = 1 and (ii) M = 4.

Verified Answer:
Note: These results were generated using the PCM D...

Consider the PCM distillation column module of Appendix E with the following variables: CVs: Overhead Composition (xD) and Bottom Composition (xB) MVs: Reflux Ratio (R) and Vapor Flow Rate (V) DV: Column Feed Flow Rate (F) Do the following, using the transfer function models given below: (a) Design

Verified Answer:
We repeat 20.10 for R \left[\begin{array}{l...

In Section 20.6.1, MPC was applied to theWood–Berry distillation column model. A MATLAB program for this example and constrained MPC is shown in Table E20.8. The design parameters have the base case values (Case B in Fig. 20.14) except for P = 10 and M = 5. The input constraints are the saturation

Verified Answer:
(Use MATLAB Model Predictive Control Toolbox) a) [...

Consider the PCM furnace module of Appendix E with the following variables (HC denotes hydrocarbon): CVs: HC exit temperature THC and oxygen exit concentration cO2 MVs: fuel gas flow rate FFG and air flow rate FA DV: HC flow rate FHC Do the following, using the transfer function models given below:

Verified Answer:
Note: These results were generated using the PCM F...

Design a model predictive controller for the process Gp(s) = e^−6s/10s + 1 Gv = Gm = 1 Select a value of N based on 95% completion of the step response and Δt = 2. Simulate the closed-loop response for a set-point change using the following design parameters: (a) M = 1 P = 7 R = 0 (b) M = 1 P = 5

Verified Answer:
The open-loop unit step response of G_{p}(s...

Consider the unconstrained, SISO version of MPC in Eq. 20-65. Suppose that the controller is designed so that the control horizon is M = 1 and the weighting matrices are Q = I and R = 1. The prediction horizon P can be chosen arbitrarily. Demonstrate that the resulting MPC controller has a simple

Verified Answer:
The unconstrained MPC control law has the controll...

For Exercise 20.1, consider two sets of design parameters and simulate unit step changes in both the disturbance and the set point. Assume that the disturbance model is identical to the process model. The design parameters are (a) M = 7 P = 10 R = 0 (b) M = 3 P = 10 R = 0 Which controller provides

Verified Answer:
(Use MATLAB Model Predictive Control Toolbox) As s...

Consider the transfer function model of Exercise 20.1. For each of the four sets of design parameters shown below, design a model predictive controller. Then do the following: (a) Compare the controllers for a unit step change in set point. Consider both the y and u responses. (b) Repeat the

Verified Answer:
The step response is obtained from the analytical ...

Control calculations for a control horizon of M = 1 can be performed either analytically or numerically. For the process model in Exercise 20.1, derive Kc1 for Δt = 1, N = 50, and P = 5, Q = I and R = 0, using Eq. 20-65. Compare your answer with the analytical result reported by Maurath et al.

Verified Answer:
From the definition of matrix S, gi...