2. Consider a non-linear dynamic model Which of the following statements are true? (A) The linearized model at the equilibrium point x1 =x2 = 0 has poles at -0.5 ± j3.12 (B) The linearized model at the equilibrium point x1 =x2 = 0 has poles at 0.5± j3.12 (C) The linearized model at the equilibrium point x1 = π, x2 = 0 has poles at -3.7 and 2.7 (D) The lin arized m odel at the equilibrium point x1 = π, x2 = 0 has poles at 3.7 and -2.7 (E) The linearized model at the equilibrium point x1 = π, x2 = 0 has poles at 0.5 ± j3.12

複選題10. Read the following paragraph that introduces the concept of model predictive control(MPC): Model predic- tive control (MPC) is an advanced method of process control that is used to control a process while satisfying a set of constraints. It has been in use in the process industries in chemical plants and oil refneries since the 1980s. In recent years it has also been used in power system balancing models and in power electronics. Model predictive controllers rely on dynanic models of the process, most often linear empirical models ob- tained by system identifcation. The main aduantage of MPC is the fact that it allous the current timeslot to be optimized, while keeping future timeslots in account. This is achieued by optimizing a finite time-horizon, but only implementing the current timeslot and then optimizing again, repeatedly, thus differing from Linear- Quadratic Regulator (LQR). Aiso MPC has the ability to anticipate future events and can take control actions accordingly. PID controllers do not have this predictive ability. MPC is nearly universally implemented as a digitaI control, although there is research into achieving jaster response times with specially designed analog circuitry. (test acquired from Wilipedia) According to the above paragraph, which of the following statements are true? (A) MPC applies an optimization solver to acquire the optimal control action with the consideration of the predicted responses and system constraints. (B) PID controllers do not have the predictive ability because they can be tuned without knowing the dy- namic model. (C) The performance of MPC may be deteriorated if the dynamic model is inaccurate. (D) LQR control cannot optimize the control action over a finite time-horizon. (E) Although it is possible to implement MPC on analog circuitry, MPC is usually implemented on computers or microprocessors.

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