![Consider a two compartment model that represents the oxygen level in two adjacent rooms, where the oxygen level is only measurable in the first room. It can be represented by the following state space model: dt 2 -2 0 1. Is the system reachable? [2 marks] 2. Is the system observable? [2 marks] 3. Would an observer of the formABu L( Ca) with observer 5.51 result in a convergent state estimate? [3 marks gain L = 4. Design an observer for the system that has eigenvalues at-2±2 [3 marks]](http://img.homeworklib.com/questions/e3de6e00-805a-11eb-b662-0d1b59765c12.png?x-oss-process=image/resize,w_560)
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Consider a two compartment model that represents the oxygen level in two adjacent rooms, where the...
Problem 8.3 - A New Two-State System Consider a new two-level system with a Hamiltonian given...
Problem 8.3 - A New Two-State System Consider a new two-level system with a Hamiltonian given by i = Ti 1461 – 12) (2) (3) Also consider an observable represented by the operator Ŝ = * 11/21 - *12/11: It should (hopefully) be clear that 1) and 2) are eigenkets of the Hamiltonian. Let $1) be an eigenket of S corresponding to the smaller eigenvalue of S and let S2) be an eigenket of S corresponding to the larger eigenvalue....
Consider a two-tank system, where x, is the level of the first tank, and x2 is the level of the second tank. This dynamic system is described by the -xj-x2. The output to be Q4. following model: dt c...
Consider a two-tank system, where x, is the level of the first tank, and x2 is the level of the second tank. This dynamic system is described by the -xj-x2. The output to be Q4. following model: dt controlled is the level of the second tank. (a)Write down the state-space model in matrix form. Verify the 20% (b)Design a state feedback controller so that the closed-loop poles are 25% controllability of the system located at -3 and -4 (c) The...
Consider the following system: -1-2-21 гг 1 0 1 L Where u is the system input and y is the measur...
control system with observer
Consider the following system: -1-2-21 гг 1 0 1 L Where u is the system input and y is the measured output. 1. Find the transfer function of the system. 2. Design a state feedback controller with a full-state observer such that the step response of the closed loop system is second order dominant with an overshoot Mp settling time ts s 5 sec. Represent the observer-based control system in a compact state space form. 10%...
Problem 2.18 The net potential energy between two adjacent ions, EN, may be represented by Where...
Problem 2.18 The net potential energy between two adjacent ions, EN, may be represented by Where A, B, and n are constants whose values depend on the particular ionic system Calculate the bonding energy Eo in terms of the parameters A, B, and n using the following procedure: (1) Differentiate EN with respect to r, and then set the resulting expression equal to zero, since the curve of Ev versus r is a minimum at Eg. (2) Solve for r...
Question 1: (5 marks) Consider a two-species model for populations Ni and N2 follows as N1 (a -bN1 cN2) dt N2 (d -...
Question 1: (5 marks) Consider a two-species model for populations Ni and N2 follows as N1 (a -bN1 cN2) dt N2 (d - eN2 - Ni) dt (a) What kind of interaction does this system of equations represent? (b) Show that the equations can be simplified to dn1 an n1 (1 d7 dn2 Bn2 (1n2-n1). dT mT into the system of equations and picking by substituting N = kn\, N2 = ln2 and t appropriate constants k, l and m...
I need help with this please, I'm very confused. Given the following relational model database schema:...
I need help with this please, I'm very confused. Given the following relational model database schema: GUEST (email, address, phone_no, name) (phone_no) is a candidate key. Email and address are long strings, phone_no and name are also strings. TYPE (code, description) The type code is a numeric code and the description a length varying string. AMENITY (code, description) The amenity code is a numeric code and the description a length varying string. CITY (city_id, name, state, country) The city identification...
2. Consider the following model: y = XB + u where y is a (nx1) vector...
2. Consider the following model: y = XB + u where y is a (nx1) vector containing observations on the dependent variable, B = Bi , B X is a (n x 3) matrix. The first column of X is a column of ones whilst the second and third columns contain observations on two explanatory variables (x and x2 respectively). u is (n x 1) vector of error terms. The following are obtained: 1234.7181 1682.376 7345.581 192.0 259.6 1153.1) X'X...
3. (Steady state in the Solow model) Consider two economies identical in everything except the production...
3. (Steady state in the Solow model) Consider two economies identical in everything except the production function. Economy 1 has a production function F(K, L)KoL1-a, economy 2 has a production function G(K, L)-aK(1-a)L. For both economies capital grows according to (1). a) Write output per worker as a function of capital per worker for both economies. b) Compute the steady state value of capital per worker for both these economies or, if it does not exist, show graphically that it...
(Steady state in the Solow model) Consider two economies identical in everything except the production function.
3. (Steady state in the Solow model) Consider two economies identical in everything except the production function. Economy 1 has a production function \(F(K, L)=K^{\alpha} L^{1-\alpha}\), economy 2 has a production function \(G(K, L)=\alpha K+(1-\alpha) L\). For both economies capital grows according to (1).a) Write output per worker as a function of capital per worker for both economies.b) Compute the steady state value of capital per worker for both these economies or, if it does not exist, show graphically that...
3. (Steady state in the Solow model) Consider two economies identical in everything except the production...
3. (Steady state in the Solow model) Consider two economies identical in everything except the production function. Economy 1 has a production function F(K, L) KL,economy 2 has a production function G(K, L) aK1 - a)L. For both economies capital grows according to (1). a) Write output per worker as a function of capital per worker for both economies. b) Compute the steady state value of capital per worker for both these economies or, if it does not exist, show...
Problem 8.3 - A New Two-State System Consider a new two-level system with a Hamiltonian given by i = Ti 1461 – 12) (2) (3) Also consider an observable represented by the operator Ŝ = * 11/21 - *12/11: It should (hopefully) be clear that 1) and 2) are eigenkets of the Hamiltonian. Let $1) be an eigenket of S corresponding to the smaller eigenvalue of S and let S2) be an eigenket of S corresponding to the larger eigenvalue....
Consider a two-tank system, where x, is the level of the first tank, and x2 is the level of the second tank. This dynamic system is described by the -xj-x2. The output to be Q4. following model: dt controlled is the level of the second tank. (a)Write down the state-space model in matrix form. Verify the 20% (b)Design a state feedback controller so that the closed-loop poles are 25% controllability of the system located at -3 and -4 (c) The...
control system with observer
Consider the following system: -1-2-21 гг 1 0 1 L Where u is the system input and y is the measured output. 1. Find the transfer function of the system. 2. Design a state feedback controller with a full-state observer such that the step response of the closed loop system is second order dominant with an overshoot Mp settling time ts s 5 sec. Represent the observer-based control system in a compact state space form. 10%...
Problem 2.18 The net potential energy between two adjacent ions, EN, may be represented by Where A, B, and n are constants whose values depend on the particular ionic system Calculate the bonding energy Eo in terms of the parameters A, B, and n using the following procedure: (1) Differentiate EN with respect to r, and then set the resulting expression equal to zero, since the curve of Ev versus r is a minimum at Eg. (2) Solve for r...
Question 1: (5 marks) Consider a two-species model for populations Ni and N2 follows as N1 (a -bN1 cN2) dt N2 (d - eN2 - Ni) dt (a) What kind of interaction does this system of equations represent? (b) Show that the equations can be simplified to dn1 an n1 (1 d7 dn2 Bn2 (1n2-n1). dT mT into the system of equations and picking by substituting N = kn\, N2 = ln2 and t appropriate constants k, l and m...
2. Consider the following model: y = XB + u where y is a (nx1) vector containing observations on the dependent variable, B = Bi , B X is a (n x 3) matrix. The first column of X is a column of ones whilst the second and third columns contain observations on two explanatory variables (x and x2 respectively). u is (n x 1) vector of error terms. The following are obtained: 1234.7181 1682.376 7345.581 192.0 259.6 1153.1) X'X...
3. (Steady state in the Solow model) Consider two economies identical in everything except the production function. Economy 1 has a production function F(K, L)KoL1-a, economy 2 has a production function G(K, L)-aK(1-a)L. For both economies capital grows according to (1). a) Write output per worker as a function of capital per worker for both economies. b) Compute the steady state value of capital per worker for both these economies or, if it does not exist, show graphically that it...
3. (Steady state in the Solow model) Consider two economies identical in everything except the production function. Economy 1 has a production function \(F(K, L)=K^{\alpha} L^{1-\alpha}\), economy 2 has a production function \(G(K, L)=\alpha K+(1-\alpha) L\). For both economies capital grows according to (1).a) Write output per worker as a function of capital per worker for both economies.b) Compute the steady state value of capital per worker for both these economies or, if it does not exist, show graphically that...
3. (Steady state in the Solow model) Consider two economies identical in everything except the production function. Economy 1 has a production function F(K, L) KL,economy 2 has a production function G(K, L) aK1 - a)L. For both economies capital grows according to (1). a) Write output per worker as a function of capital per worker for both economies. b) Compute the steady state value of capital per worker for both these economies or, if it does not exist, show...
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