Simulation of Position Control System - Assignment Example

Simulation of Position Control System Part Action Part 2: Investigating the systems transient response under Proportional Control: Characteristic Equation: Js2+Cs+K = (1)s2+(12)s+K =s2+12s+K Action # 2: Verification from Simulink a) Fast Response (K=36) b) Sluggish Exponential Response (K36, in this case K=70) Part 3: Investigating the systems Steady State Response under Proportional Control: a) Transient Response to Step Input (Input disturbance=0) b) Transient Response to Ramp Input (Input disturbance=0) c) System’s Response to Step Input (Input disturbance=unit step at 12 sec) Action # 3: Steady State Errors for Ramp Input and step disturbance Part 4: Tuning the systems steady state response under PID control. Step response with unit step disturbance using Proportional Controller (Kp=70) Step response with unit step disturbance using PD Controller (Kp=70,Kd=5) By introducing PD controller the rise time has increased a little but there are no overshoots in the system. The transient performance has improved. Step response with unit step disturbance using PID Controller (Kp=70,Kd=5,Ki=2) By introducing a PID controller the steady state error is removed. The integral part of the PID controller increases the type of the system and hence the steady state error due to unit step disturbance is removed. Discussion a) Discuss how PD influences the transient response of the closed loop system. PD improves the transient response of the system by taking the derivative of the error and adding it in the control signal. By introducing the derivate of the error the overall bandwidth of the system is increased which results in a smaller rise time The phase margin of the system is also improved which results in lesser overshoots. One of the disadvantages of the PD controller is that it accentuates the noise which appears in the plant output and causes difficulty for the controller. PD does not have any impact on the steady state error of the system and it is mostly used to improve the transient performance such as reducing the overshoots and reducing the rise time of the controlled system. b) Discuss how PI influences the steady state response of the closed loop system. PI controller increases the system type i.e. adding a pole at the origin, hence removes the steady state error. PI controller decreases the bandwidth of the overall system which results in a slower rise time. The control signal generated by the PI controller accumulates over time due to the integral action. Because of the integral action the control signal remains at a constant value even when the control error becomes zero. c) Discuss your strategy for the manual tuning of the PID controller. We start from a proportional controller with a gain equal to ‘Kp=70’. The system has overshoots and because of the step disturbance introduced at 12 seconds there is a constant steady state error. First of all a derivate part is introduced hence converting the Proportional Controller into a Proportional-Derivative Controller (PD). The ‘Kd’ gain of the PD controller is chosen to be 5. This value was chosen so that the overshoots are completely removed while maintaining the same rise time as was the case in P controller. (Rise time was 0.5 seconds in P as well as PD controller). Since the system has a constant steady state error hence integral portion of the PID controller is introduced with a gain of ‘1.0’. It can be observed from the figure that the steady state error due to the step disturbance is completely removed. d) Briefly discuss other techniques for tuning the controller such as Ziegler Nichols. Ziegler Nichols can be applied in cases where the plant transfer function is not known. A step response of the plant is obtained and calculations are performed on the step response to determine the parameters of the PI, PD or PID controller. Ziegler-Nichols is widely used in process industry where the plants are exceptionally non-linear and modeling them is not an option. Ziegler Nichols provides an initial guess of the Kp, Kd and Ki (parameters of the controllers). e) The investigation into the systems transient response under Proportional Control. When a Proportional controller is introduced in the feedback loop it improves the transient response of the system as well as makes the system more robust. The rise time as well as the peak time to overshoot becomes smaller and the system responds more quickly. When the gain of the proportional controller is increased the system might overshoot or in some cases becomes unstable. The root locus of the motor control problem is given below: It can be observed that the system never becomes unstable no matter what is the gain of the proportional controller (since the poles remains in the left hand plane). Respnse of the control system with three different values of Kp is shown below. It can be observed that with increasing value of Kp the rise time becomes smaller. The system has overshoots at Kp=70. f) The investigation into the systems steady state response under Proportional Control. The Proportional Controller cannot completely eliminate the steady state error because it does not increase the system type. However Proportional controller can reduce the steady state error. As the proportional gain (Kp) is increased the steady state error keeps on reducing but it cannot be completely eliminated. In physical systems there is s certain limit on the proportional gain after which the system saturates and hence steady state error cannot be further reduced. g) The role of simulation methods in Dynamics and Control. Simulations plays a very crucial part in the understanding of the dynamics and control of a real system. Controllers cannot be tested on real systems therefore a plant model is developed in the simulation and the performance of the controller is verified in the simulations. If the controller has satisfactory performance then the controller can be implemented on the real system. The simulation helps us in understanding the behavior of the controller as well as it is safe to try and test the controller on simulation so that we know a priori what is the maximum performance a control system can deliver. h) Report Presentation Individual Flair Report has been presented in a reasonable manner with simulation results from Matlab/SIMULINK Software. All the claims in the report are substantiated by simulation results from SIMULINK. Read More