Continuous and Discrete-Time PID Control of DC Motor Position - Assignment Example

Control and Instrumentation Name: Course: Instructor: Institution: Date of Submission: Continuous and Discrete Time PID Control of DC Motor Position Part 1 1a. Digital control applications are highly applied and used in modern applications, which is mainly related to the easy control the individual has on the applications and performance attainable. For instance, industries today have many digitized applications mainly the usage of computers, whose power and size varies in different ways. The digital application is been used in modern applications highly because it improves and increases measurement sensitivity, which is reflected on the efficiency of workloads in a company. That is; digital power in modern applications has increased the load of work that can be done in a day while relying on the digital power for success (Ming, 2011). Digital power in modern applications helps significantly in controlling tasks to ensure they perform the results desired. For instance, when used in closed loop systems, they improve the performance of the system. Digital systems provide hybrid systems, ensuring the output tasks among others are controlled through continuous and discrete time parts. Thus, the digital control is used in modern applications to provide satisfactory emulation designs. The systems are more beneficial since they ease the operations of business while reducing the expenses of labour. At the same time, they increase the reliability through the improved performance of the digitized control systems. 1b. The linear control based PID control strengths include the ease of implementation. That is; the PID controllers can undertake a dominant role in ensuring the industrial applications that often demand transparent and simple procedures. They can be tuned easily in using a small form of information. The robustness, simplicity of the system are key benefits including the controller gains of the system related to the parameters used (Krakow, 2006). Limitations include mainly the poor stability of the controllers. That is; if the parameters are chosen incorrectly, the output is also unstable. The PID controller also has a poor limited performance. The, performance is influenced by factors such as the noise, disturbances of the system and other problems. It operates on an error signal basis. The performance is variable mainly because the systems are linear. Noise changes the output quantity received, thus affects the performance of the system. 1c. The wood-chip level control system can use the PI controller successfully. The system does not apply a constant speed level, the PI control in the system is used to ensure the chip level of the tank is equal to the measured and actual level of the system. The PI controller changes the input to the proportional plus the integral error signal. Proportional integral PI controls systems use the PI to control the simple analytical tuning of the fluid system (Ming, 2011). The analytical tuning determines the PI coefficient through the physical properties of the motion and fluid system. It is based on observations since it uses numerous coefficients obtained through trial and error tuning (Krakow, 2006). The PI controller increases the system order, where the Ki maintains the system stability. The input is reduced as the transient part is steadily controlled. However, the precision actuator using the PI controller does not attain the systems stabilization. The air conditioner machines use the PID controllers through the automatic control of the temperature of the room. The system presents an open loop system control where the feedback gain loop. Thus, the output and input relationship in a linear time invariant system to allow the perfect transfer function of the system. Thus, the system provides a proportional compensation through the gain attained that is proportional to the possible error that occurs through the input and output systems. The derivative compensation through the system will be a unitary feedback system that introduces the error signal through the gain. The integral compensation also introduces the integral error signal. The PID while using the MATLAB software ensures the error or trial processes remain unnecessary. The Matlab balances the performance through the bandwidth and response, as well as the robustness through the margins of stability. Thus, the air conditioner system uses the PID controller machine through the signals of the output been amplified from the sensors so they feed back the function to the PID controllers. Thus, when the error and trial process is perceived or demarcated as the set point value  and also the φ they get measured and are the controllable variables (Samson, 2010). The PID controller generates the control inputs attained from the actuators that supply air as the air conditioner system is operational thus reducing error, related to the proportional gain. The data on the operations of the air conditioner machine presents that the control signal occurs as a summation of three factors. Firstly, it considers the proportional term through demonstrating how the systems error is proportional. Secondly, the integral term gain is presented as the gain that is relative to the integral system error. On the other hand, the derivative term presents the derivative gain or error of the system (Yamazaki, et al., 2011). The PID controller factors are therefore related to the proportional gain represented as kp, integral gain demonstrated as ki and the derivative gain kd. The proportional gain represents the value of error in the system while the systems past errors are given through the integral gain and the future errors that can be predicted are given through the derivative that improves the linear extrapolation (Johan, 2002). 1d. The Matlab software is related to motor position control, where it shows its relevance in complex systems such as robotic manipulators since it is a software that manipulates array-based data (Archana, et al., 2014). That is; when using such complex systems it will lead to the quick and easy coding of the language in the systems while efficiently using the rich data types of robotic manipulators. More importantly, it will lead to the attainment of high quality visualization and graphics; and are portable in a wide range of platforms. The Matlab software provides a better and clear structure of complex data, thus better for the control application. The Matlab software has numerous functions that benefit robotic manipulation. For instance, the Matlab toolbox process allows the process of solving dynamics, kinematics, and inversing the functions. It allows better simulation processes. The Matlab software for robotic manipulators is relevant since it represents the dynamics and kinematics of the serial-link of the robotic manipulators. The Matlab software in robotic manipulators helps define and compute the dynamics and kinematics of the systems for effective simulations. Thus, it improves the performance of the controller through efficient robotic manipulator simulations (Chamanirad, 2009). 1e. The dead-beat control is the most widely used alternative to PID controllers for the control of electromechanical systems. The dead-beat control is mainly used in discrete time systems where it locate the needed input signal that should be applied to the system to convey the anticipated output signal at a stable state. This must be completed when applying the least possible steps. The dead-beat control systems have occasionally been used in the process control part as they improve the dynamic properties. The PID controllers, on the other hand, controls feedback loop mechanism that are applied in industrial systems. It is effective in continuous time systems as it constantly demonstrates the error value of the system unlike the dead-beat on discrete times. It presents the set point difference between the measured variable process that applies a proportional, derivative and integral part. The dead-beat system has a minimum rise and settling time with a zero state of stable error. The system introduces a high signal control output. On the other hand, the PID controller parameters do not show a steady state since if the parameters are incorrect, the input to be controlled is unstable. Also, its behavior is dependent on the application at the set point change. Part 2 The shaft point of a DC motor is measured by changing the input voltage, which is given through the presentation of u in the circuit. It also considers the current I flows over the resistor R, and the inductor represented as L and the motor of the system. 2a). Write the electrical and mechanical equations of the systems u = voltage input i = current flows of the circuit R = resistor L = motor inductor System Parameters J = 0.1 (The inertia moment of the system) b = 0.01 (viscous co-efficient friction of the motor) Ke = 0.01 (e.m.f constant) Kt = 0.01 (torque constant) The Voltage and current of the circuit relationship while using Ohm’s law is as follows ΔV = I • R Power = ΔE/t P= ΔV * Q/t Q/t = Current flow (I) S(Js + b)Ɵ(s) = Ki(s) (Ls + R)I(s) = V(s) – KsƟ(s) P(s) = Ɵ(s) / V(s) = K/ (Js +b)(Ls + R) + K2 [rad/sec/ V] Thus, the electrical PID, DC motor controller transfer equation is as follows C(s) = Kp + Ki/s + Kds =(Kds2 + Kps + Ki)/s 2a.1. Mechanical Equation: Using the 2nd Law of Newton 2nd Law of Newton = F =Mass * acceleration F(s) = Ms2x + Kx = X [Ms2 + k] X(s) = F/Ms2 + k = F(1/m) / s2 + k/M Transfer function of the mechanical equation is therefore G(s) =x(s) / F(s) = 1/M/ s2 + K/M 2a.2. Transfer Function The systems transfer function is presented as H (s) =W1(s)/tm (s). When one applies the Laplace transform modelling, the transfer function can be written as provided. G(s) = Y(s)/ U(s) = Kt / s[(Js + b)(Ls + R) + Kt Ke] The equation shows the electrical circuit consists of the L, R, and C. V0 is assumed to be the output and the ei the output. Thus, it proves the transfer function is appropriate as it presents that G(s) = output / input given that both are functions of s. That is; the open loop transfer action occurs since it has eliminated the I(s) of the equations, as it consider the rotational speed where the output and input voltages are given. The transfer function of the motor is given through the voltage input and mass displacement output. The given equation expresses the transfer function G(s) readily (Sinha, 2008). References Archana, J., Suganthini, P. & Malathi, C., 2014. DC Motor Speed Control Using Matlab. International Journal of Scientific Research Engineering & Technology, 2(12), pp. 832-834. Chamanirad, M., 2009. Design and Implementation of Controller for Robotic Manipulators using Artificial Neural Networks. Malardalens Hogskola, pp. 1-32. Johan, K., 2002. PID Control. Control System Design, pp. 1-36. Krakow, I. K., 2006. System-Specific PI Control Theory for Fluid and Motion Systems. New York: Universal Publishers. Ming, M., 2011. Communication Systems and Information Technology: Selected Papers from the 2011 International Conference on Electric and Electronics. New York: Springer Science & Business Media. Samson, A., 2010. Controllers and Controlled Systems. Technical Information, pp. 1-60. Sinha, K. N., 2008. Control Systems. New York: New Age International. Yamazaki, T., Yamakawa, Y., Kamimura, K. & Kurosu, S., 2011. World's Largest Science, Technology & Medicine Open Access Book Publisher. Advances in PID Control. National Institute for Environmental Studies, pp. 1-22. Read More