There are many tuning methods such as **manual tuning**, **Ziegler–Nichols**, **Tyreus Luyben**, **Cohen–Coon**, **Åström-Hägglund** and **software tools** such as Simulink in Matlab or Excel PID Simulator(enclosed). I’ve used 2 tuning methods like manual tuning, Ziegler-Nichols method and software tools such as Matlab, Simulink, and Excel. (According to Wikipedia: PID Controller)

**Manual Tuning(****Trial and error****)**

__How do the PID parameters affect system dynamics?__

We are most interested in four major characteristics of the closed-loop step response. They are

**– Rise Time:** the time it takes for the plant output y to rise

**– Overshoot:** how much the peak level is higher than the steady state, normalized against the steady – state.

**– Settling Time:** the time it takes for the system to converge to its steady state.

**– Steady-state Error:** the difference between the steady-state output and the desired output.

(**NT**: No definite trend. Minor change.)

__How do we use the table?__

Typical steps for designing a PID controller are Determine what characteristics of the system needs to be improved.

– Use **K***P* to decrease __the rise time__.

– Use **K***D* to reduce __the overshoot and settling time__.

– Use **K***I* to eliminate __the steady-state error__.

– This works in many cases, but what would be a good starting point? What if the first parameters we choose are totally crappy? Can we find a good set of initial parameters easily and quickly?

– Ziegler and Nichols conducted numerous experiments and proposed rules for determining values of **K***P*, **K***I*, and **K***D* based on the transient step response of a plant.

– They proposed more than one methods, but we will limit ourselves to what’s known as the first method of Ziegler-Nichols in this tutorial. It applies to plants with neither integrators nor dominant complex-conjugate poles, whose unit-step response resemble an S-shaped curve with no overshoot. This S-shaped curve is called the reaction curve. This S-shaped curve is called the reaction curve.

– The S-shaped reaction curve can be characterized by two constants, delay time **L** and time constant **T**, which are determined by drawing a tangent line at the inflection point of the curve and finding the intersections of the tangent line with the time axis and the steady-state level line.

– __The Ziegler-Nichols Tuning Rule Table__

Using the parameters **L** and **T**, we can set the values of **K***P*, **K***I*, and **K***D*according to the formula shown in the table above.

These parameters will typically give you a response with an overshoot about 25% and good settling time. We may then start fine-tuning the controller using the basic rules that relate each parameter to the response characteristics. **K***P*, **K***I*, and **K***D* based on the transient step response of a plant.

– Matlab: PID Controller Tuning

– Simulink: PID Controller Tuning

– Excel PID simulator

– Etc

**PID control VS On/Off control**

– **On/Off control**: An on-off controller is the simplest form of temperature control device. The output from the device is either on or off, with no middle state. An on-off controller will switch the output only when the temperature crosses the setpoint. For heating control, the output is on when the temperature is below the setpoint, and off above setpoint. Since the temperature crosses the setpoint to change the output state, the process temperature will be cycling continually, going from below setpoint to above, and back below. In cases where this cycling occurs rapidly, and to prevent damage to contactors and valves, an on-off differential, or “hysteresis,” is added to the controller operations. This differential requires that the temperature exceeds setpoint by a certain amount before the output will turn off or on again. On-off differential prevents the output from “chattering” or making fast, continual switches if the cycling above and below the setpoint occurs very rapidly. On-off control is usually used where a precise control is not necessary, in systems which cannot handle having the energy turned on and off frequently, where the mass of the system is so great that temperatures change extremely slowly, or for a temperature alarm. One special type of on-off control used for alarm is a limit controller. This controller uses a latching relay, which must be manually reset, and is used to shut down a process when a certain temperature is reached.

– **PID control**: This controller provides proportional with integral and derivative control, or PID. This controller combines proportional control with two additional adjustments, which helps the unit automatically compensate for changes in the system. These adjustments, integral and derivative, are expressed in time-based units; they are also referred to by their reciprocals, RESET, and RATE, respectively. The proportional, integral and derivative terms must be individually adjusted or “tuned” to a particular system using trial and error. It provides the most accurate and stable control of the three controller types, and is best used in systems which have a relatively small mass, those which react quickly to changes in the energy added to the process. It is recommended in systems where the load changes often and the controller is expected to compensate automatically due to frequent changes in setpoint, the amount of energy available, or the mass to be controlled.