Consider the following mass-spring-damper system Q The differential equation describing the motion of the mass is...

 

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Consider the following mass-spring-damper system Q The differential equation describing the motion of the mass is d²z m (1) Rise Time <3 (3) (5) k ww Settling Time ≤ 10. Maximum Force ≤ 0.5 m C dr (1)+c(t) + kr(t) - x(t) F(t) Assume the parameter values m- 1, c-0.1, k-0.1 and zero initial conditions (0) (0)-0. Design a PID controller for F(t) that can make r(t) converge to the target position target t→∞o and satisfies the following requirements: F(t) (2) Overshoot < 0.1 (4) Steady-State Error 0 1 as Report your designed K₂, K₁, and Ka values, use MATLAB ode45(-) to solve the closed-loop differential equation and plot the time history of r(t), and report the rise time, overshoot, settling time, steady- state crror, and maximum force of your design. Consider the following mass-spring-damper system Q The differential equation describing the motion of the mass is d²z m (1) Rise Time <3 (3) (5) k ww Settling Time ≤ 10. Maximum Force ≤ 0.5 m C dr (1)+c(t) + kr(t) - x(t) F(t) Assume the parameter values m- 1, c-0.1, k-0.1 and zero initial conditions (0) (0)-0. Design a PID controller for F(t) that can make r(t) converge to the target position target t→∞o and satisfies the following requirements: F(t) (2) Overshoot < 0.1 (4) Steady-State Error 0 1 as Report your designed K₂, K₁, and Ka values, use MATLAB ode45(-) to solve the closed-loop differential equation and plot the time history of r(t), and report the rise time, overshoot, settling time, steady- state crror, and maximum force of your design.