Systems Modelling Lab Report Example | Topics and Well Written Essays - 1000 words

Systems Modelling - Lab Report Example MATLAB inbuilt function ss() is then called and given the matrices as input arguments so as to generate the state space model. The ss() function takes state matrices as inputs and generates the state space model. The program begins with the definition of variables to be used i.e. mass, spring constant and the damping coefficient. Next, the transfer function is defined and it poles computed. The function pole() returns a pair of poles that have real and complex parts. To establish stability, the sign of the real parts are checked. Negative real part means the pole is in the LHS of the S-Plane thus implying that the system is stable. Otherwise the system will be unstable if poles have positive real parts. The program then illustrates the response of the system to initial conditions. Step input could also be used to demonstrate response of the system. From Figure 1.2 the conjugate pair has negative real parts. According to our criterion, the system is stable. The 2 poles are on the left hand side of the S-Plane indicating that the system is stable. Figure 1.3 demonstrates how the MSD system responds to initial condition of x0 = [1, 0]. From the graph it can be seen that the system undergoes a transient state and attains steady state as time increases. The code above has been modified in order to allow stability of the system to be determined for different values of gain. Gain is usually multiplied by the numerator of the transfer function, therefore the program will prompt the user to enter a value for the gain then the program computes the stability. First the constants are defined. The user is then prompted to enter the gain for the system which forms the numerator of the transfer function. The denominator is defined as a vector containing mass, spring and dumping constants. The transfer function is then determined and its poles computed. The sign of the poles is checked and stability determined. When run with 8 as the gain, the system shows it is stable.

Math project Essay Example | Topics and Well Written Essays - 500 words

Math project - Essay Example I considered various factors, including my family expenditure in every month. Finally I came to a conclusion that I could afford to purchase a Honda CR-V within a period of sixteen months. I borrowed a loan from one of the banks in our country. I made this decision with considerations to the costs and interest payments. I also considered down payments, trade in allowances and other debts. This was not the only payment I had to make, thus I allocated an affordable amount to this budget. I had some rent, insurance and taxes that needed to be paid within every month. I therefore had to limit my debt payments to less than 45% of my monthly gross income. My entire household earns $5,000 in terms of gross wages every month. 24% of this amount was spent on rent. This is approximately $1,200. After paying this, only $ 2,550 remains. I still needed money for insurance, groceries, fuel and other household expenses. I decided to budget 20% of my total earnings to the purchase of the car. This meant that I had to set aside $ 1,000 for purchase of the car. The car is one that I can finance for not more than $2,000 per month. I could not spend more than this amount on the car since I needed to cater for all the other needs. I have a family to provide for alongside all other requirements in life. The amount that was hereby allocated to car payments included insurance and registration fees. The car selected is a front wheel drive and costs approximately $31,600. I chose this car since it was affordable for me then. The car also favored my taste and preference. A front wheel drive car is cheaper than a four wheel drive. I had to borrow $32,000 from the bank. This was the lowest amount possible depending on the situation at hand. In making this decision, I had considered all factors, including the total payment, loan term and interest rate. I tried to make the initial