Define terms;
1. Linear means arranged in or extending along a straight or nearly straight line.
Non linear means not arranged in a straight line or not sequential or straightforward.
2. In control engineering, a state-space representation is a mathematical model of a physical system as a set of input, output and state variables related by first-order differential equations or difference equations. State variables are variables whose values evolve through time in a way that depends on the values they have at any given time and also depends on the externally imposed values of input variables. Output variables’ values depend on the values of the state variables.
3. Robustness means the quality or condition of being strong and in good condition.
4. In silico is an expression meaning "performed on computer or via computer simulation" in reference to biological experiments.
5. High-throughput screening (HTS) or experiment is a method for scientific experimentation especially used in drug discovery and relevant to the fields of biology and chemistry. The results of these experiments provide starting points for drug design and for understanding the noninteraction or role of a particular location.
6.System identification is a methodology for building mathematical models of dynamic systems using measurements of the system's input and output signals. The process of system identification requires measuring the input and output signals from system in time or frequency domain.
Define terms; 1) linear/nonlinear 2) state space equation 3) robustness 4) in silicoexperiment 5) high-throughput experiment...
Classify each equation as linear or nonlinear dy/dx = y^3 - 9 linear y" = 3y' - 6 nonlinear > 3y y' = 6-4 linear > 4x^2 y" - 3x y' + 4y = 2x - 4 linear
3. a) Find a state space representation for a linear system represented by the following differential equation, where v(t) denotes the input and y(1) is the output: b) Consider a linear system represented by the following differential equation, where x() denotes the input and y(t) is the output: )+4()+4y()x(t) i) Write down its transfer function and frequency response function i) What is the form of the steady state response of the above system due to a periodic input that has...
Determine whether the differential equation is linear or nonlinear Problems For Problems 1-6, determine whether the differential equa- tion is linear or nonlinear. d3 y day +4 2. dy + sin x dx = xy2 + + tan x dx3 dx2 COS X. 1 6. Vxy" + '++. In x = 3x3.
A) For the schematic above find the state-space equations that define this system. B) Using the controllability rank test determine if this system is controllable. C) Using the observability rank test determine if this system is observable. 1. Controllability and Observability L = 100 m R1 = 10 Ohms Mm R2 = 100 Ohms R4 = 100 Ohms ( = 100 microfarads ult) 1V R3 = 100 Ohms R5 = 100 Ohms Xı = i(t) y = valt) vi(t) =...
If the sample space of a random experiment is S={0, 1, 2, 3, 4, 5, 6} and events A={2, 4}, B={1, 3, 5}, C={2, 3, 4, 5}, and D={1, 6}, which of the following is not correct? a. b. {0, 2, 3, 4, 6} c. {1, 2, 3 ,4 ,5} d. {0, 1, 2, 3, 4, 5, 6}
1. (12 points) Classify the following equations as lincar or nonlinear, and state their order. Linear or nonlincar? Order Equation + tdk + t'y = cost they + t dope + t'y = cosy. dy 2y-2
3. Consider the ODE: 22+3 +5x2 = sin nt A) Is this ODE linear or nonlinear? Use the superposition property to support your conclusion. If nonlinear, state term(s) that make it nonlinear. B) Is this ODE time varying or time-invariant? If time varying, state term(s) that make it time varying. 4. Consider the ODE: 23+3xx +5t2x = 5t A) Is this ODE linear or nonlinear? Use the superposition property to support your conclusion. If nonlinear, state term(s) that make it...
4 A Markov chain with state space {0, 1, 2, 3, 4, 5} has the following transition matrix: P= 1/2 1/2 0 0 0 0 1/4 3/4 0 0 0 0 0 0 1/3 2/3 0 0 0 0 1/2 1/2 0 0 1/16 1/16 1/4 1/4 1/4 1/8 1/6 1/6 1/6 1/12 1/12 1/3 1/6) (1) Starting from state 4, find the mean time spent in state 5 before absorption. (5 marks) (ii) Starting from state 4, find the...
1-5 I. Define precisely the heat of formation of a compound. 2. In this experiment, if a student had measure an incorrectly high ?? for the Mg + HCl reaction, would the ??/ of MgO() be too exothermic, not exothermic enough, or unaffected? Explain your answer 3. In this experiment, if a student had measure an incorrectly high AT for the MgO +HCl reaction, would the answer AHf of MgOs) be too exothermic, not exothermic enough, or unaffected? Explain your...
Simple Linear Regression Problem QUESTION 6 The state office of Australia Post believed that mail throughput at suburban post offices increases with the number of employees. From a random sample of twelve major suburban post offices, the following regression equation was estimated: Y =-2.59 + 78.15 X Standard error of the estimate: 238.54 Sum of squares of X: 112.5 where Y is the average number of mail packages processed per hour and X is the number of effective full-time employees...