Problem A certain dynamic process is governed by the following differential equations x2 = x1-3T2 +...
Problem 1 A certain dynamic process is governed by the following differential equations where co const. is an exogenous variable. Assuming To is a measured quantity, a control law 1T1- is required, which 8+j5, and . Places the closed loop poles at s . Forces r2 to zero in the steady state.
Problem 1 A certain dynamic process is governed by the following differential equations where co const. is an exogenous variable. Assuming To is a measured quantity, a control...
Problem 1 A certain dynamic process is governed by the following differential equations: 121 +22+ u where xo = const is an exogenous variable. Assuming ro is a measured quantity, a control law is required, which 5, and . Places the closed loop poles at s =-8 . Forces T2 to zero in the steady state. Problem 3 Suppose that the exogenous i is of c2, i.e, nput zo is white noise with spectral density v, and that the only...
Problem 1 An inverted pendulum driven by a d-c motor is governed by the following differential and algcbraic equa tions: (a) Determine the transfer function of the process. (b) It is proposed to control the process using "proportional control": where yr is a constant reference value. Determine the value Kmir for which the gain K must exceed in order that the closed-loop system be stable. (c) Determine the value of K for which the magnitude of the error is less...
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...
Problem 7.2 The differential equations for a second-order thermal system are y=x2 where u is the control input. (a) Show that the plant is type zero. As a consequence, the steady-state error using proportional control is non-zero. Find the steady-state error as a function of G (b) To achieve zero steady-state error, integral control will be used, by adding the state variable zo with which is appended to the original equations, making the system third-order. For the resulting third-order system,...
Problem 4 (25%) Consider the attitude control system of a rigid satellite shown in Figure 1.1. Fig. 1.1 Satellite tracking control system In this problem we will only consider the control of the angle e (angle of elevation). The dynamic model of the rigid satellite, rotating about an axis perpendicular to the page, can be approximately written as: JÖ = tm - ty - bė where ) is the satellite's moment of inertia, b is the damping coefficient, tm is...