Ingenieurbüro Rudolf Polzer

A Comparison Between PID Controller and Gradient Controller, both with integrating systems

The PID controller is widely used but has its drawbacks when used with mainly integrating systems: overshoot, limited controlling precision and no possibility of direct influence on the resulting gradient of the system output. A controller fulfilling all these requirements with the controlled system dominated by an integrator is the gradient controller. It was developed by Rudolf Polzer in 2013. A typical application would be a vehicle speed controller.

A comparison between both controllers done with Scilab and Xcos is shown here. The .zcos source file can be downloaded. A simulation with Matlab and Simulink would be similar. The following diagram shows on top the output of the PID controlled system using a black line and below the output of the gradient controlled system using a green line. The green line is obviously closer to the desired rectangular target function. The integrator constant ki of the PID controller is set to a compromise between overshoot and controlling precision. The differentiating constant Kd of the PID controller is set to zero to avoid unnecessary output peaks.

Description of the functional blocks of the gradient controller:
The limiter defines the maximum gradient of the system output. Here it is set to +0.5 and -0.5. The amplification constant ca can be increased to get more controlling speed, but must be limited to avoid oscillations.